Neutrosophic Knowledge-Based Frameworks for Intelligent Decision Support Under Deep Uncertainty: Applications in Smart Agriculture

Neutrosophic Knowledge-Based Frameworks for Intelligent Decision Support Under Deep Uncertainty: Applications in Smart Agriculture | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Systematic Review Neutrosophic Knowledge-Based Frameworks for Intelligent Decision Support Under Deep Uncertainty: Applications in Smart Agriculture Deva dharshini, Kalpana Muthuswamy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9385567/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Neutrosophic statistics and logic are generalized Fuzzy logic models of uncertainty via an explicit account of terms of truth, indeterminacy and falsity, as extensions of classical probability, fuzzy sets and intuitionistic fuzzy sets. Over recent years, many neutrosophic extensions and hybrid models have been suggested in response to complex decision-making problems involving incomplete, imprecise, and conflicting information. This paper provides a summary of neutrosophic statistical and logical methods, focus on high-level structures, including single-valued, hypersoft, topological, cubic and spherical neutrosophic sets. Mathematical foundations, aggregation operators, and multi-criteria decision-making (MCDM) mechanisms within these frameworks are critically analysed and comparatively discussed. Rapidly evolving formulations in applications, such as multi-criteria and hybrid neutrosophic-learning models are overviewed to demonstrate the ability of neutrosophic models to model hierarchical, multi-attribute, and indeterminate information systems. Smart agriculture has been taken as a representative area of application to illustrate real-world modelling situations without limiting the generality of the offered frameworks. This study proposes a unified conceptual framework integrating neutrosophic theory and multi-criteria decision-making for intelligent decision support under deep uncertainty. The review also presents the major implementation and methodological issues such as parameterization based on experts, absence of standard benchmarks, insufficient software chains, and complexity. Future research directions are provided, including scalable neuro-neutrosophic models, explainable artificial intelligence (XAI) integration, and large-scale decision-support systems. Applied Statistics Neutrosophic sets Multi-criteria Decision Making (MCDM) Uncertainty modelling Computational intelligence Decision support systems (DSS) Smart agriculture Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The global population is projected to reach 9.7 billion by 2050, which means that food production efficiency and security will have to be increased by 60% above their existing levels primarily to fulfil the demand. As a result, the agricultural sector has seen a significant shift, and the idea of smart agriculture and Agriculture 4.0 have emerged [ 1 ]. Smart agriculture is an interdisciplinary subfield of agricultural science, technology, data science, and environmental science, aimed at increasing the efficiency of farming and solving problems like land shortage, climate change, and resource depletion. This transformation shifts farm management toward data-driven decisions that optimize labour, water and fertilizer use while at the same time lowering environmental damage [ 2 , 3 ]. This transformation creates a cyber-physical farm management system, which unites the network infrastructure, powerful hardware, and advanced analytics [ 4 ]. IoT, artificial intelligence, robotics, big data analytics, and remote sensing are some of the key enabling technologies in smart agriculture. [ 4 – 8 ]. Core technologies Primarily among these technologies is the Internet of Things (IoT), which enables real-time data acquisition and connectivity in real-time. Sensors commonly employed in smart farming include those used for monitoring soil moisture, plant disease detection, pH, temperature. These technologies make possible AI-powered decision tools that leverage the combination of IoT, sensor networks, climate analytics, and machine learning for the provision of climate-informed guidance on crop management. Wireless communication like LoRa, NB-IoT are extensively used in precision agriculture to transfer data to processing systems, thereby improving crop quality and agricultural production [ 9 ]. Machine learning and deep learning models are used to analyse the acquired data for time-series forecasting [ 10 ], yield prediction [ 11 ], disease detection [ 12 ], and resource optimization using spatial data [ 13 ]. Data uncertainties While these are promising technologies with vast benefits, there is often a limitation to their performance because of the uncertainties inherently existing in the data [ 14 ]. Research indicates global crop models, has shown that models trained using historical data could be susceptible to biased responses in extreme climatic conditions, highlighting the systematic difficulty regarding uncertainty in crop growth data due to drought conditions, warming, rainfall, and seasonality [ 15 ]. Field sensors often suffer from calibration drift, communication loss, and physical damage, leading to biased and missing readings in IoT networks [ 16 ]. Power connectivity problems and lack of historical records make its datasets incomplete and diverse [ 17 ], and issues in integrating diverse agricultural datasets such as weather data, soil, and market data into multiple scales and resolutions also increase heterogeneity in datasets [ 18 ]. Qualitative insights provided through linguistic terms, such as qualitative classifications and rankings, can be heavily influenced by uncertainty and incomplete information [ 19 ]. Furthermore, classical probability struggles to capture the nuanced thresholds and risk levels that agronomists and policy experts often face. Classical statistics usually assumes that observations are realized around a single true value, and uncertainty is mainly due to sampling variability [ 20 ]. However, alternative uncertainty frameworks are motivated by the chance that these representations fail to adequately capture epistemic and internal uncertainty [ 21 , 22 ]. To better understand these limitations, distinguishing between aleatory and epistemic types of uncertainty in agricultural data is essential [ 23 ]. Aleatory uncertainty is caused by inherent randomness in the world, while epistemic uncertainty is due to a lack of knowledge [ 24 ]. Both types affect predictions and forecasting in agriculture datasets, but they are conceptually different, one is irreducible randomness, and the other is ignorance. Indeterminacy caused by incomplete and vague data specifically challenges Bayesian statistics, classical statistics, probability and fuzzy or intuitionistic fuzzy sets (IFS) [ 25 ]. Even Bayesian methods tend to give only one predictive distribution, which restricts the explicit modelling of indeterminacy (p (Y | data)). Classical sets and probability only consider aleatory uncertainty, mainly as random variation around true value and treat data as precise value. Zadeh et al. [ 26 ] implemented fuzzy sets to represent vagueness by the use degree of membership values. While fuzzy sets represent graded truth ( µ \(\:ϵ\:\left[\text{0,1}\right]\) ) and can handle vague terms, they do not distinguish between partial truth and lack of knowledge [ 27 ]. Atanassov et al. [ 28 ] further extended the FSs theory to Intuitionistic fuzzy sets (IFS) introduced a hesitation based on both the degree of membership ( T) and non-membership ( F) , expressed as 1-T-F , they restrict the sum ( T + I + F = 1); however, it is often diluted because different kinds of indeterminacy are combined into the same residual term. This makes these frameworks unable to capture the indeterminacy as an independent, first-class component. Neutrosophic statistics as a solution To address these limitations, neutrosophic statistics (NS) emerge as a powerful generalization of Intuitionistic fuzzy sets (IFS), specifically designed to handle uncertain, indeterminate, and inconsistent information [ 22 , 29 – 35 ]. Neutrosophic set is a mathematical framework developed by Smarandache, designed to handle uncertain, unclear, vague, and incomplete data, addressing the constraints of classical probability and fuzzy sets, the sum can range up to 3 (0 ≤ T + I + F ≤ 3). The idea of neutrosophic sets is a broader platform, building upon the principles of the fuzzy and classical sets [ 36 ]. It differs from previous approaches because neutrosophic sets maintain distinct categories of truth, indeterminacy, and falsity. It can represent the real-world agricultural data where data is often conflicting or vague. Soil moisture, pH, temperature and humidity sensors may fail, drift or transmit inconsistent readings, whereas neutrosophic logic distinguishes each value into T (how believable), F (evidence against it) and I (how uncertain it is), rather than depending on a single crisp or fuzzy value. In the precision agriculture mechanism model, neutrosophic logic is integrated with IoT and cloud computing to automate geometric soil analysis and environmental monitoring while directly using uncertainty in calculation. Neutrosophic logic expands to other forms of neutrosophic statistical techniques, many of which have been proposed, including multiple regression analysis [ 37 ], analysis of variance [ 38 ], forecasting [ 39 ], and acceptance sampling plans [ 40 ]. Moreover, neutrosophic techniques have been applied to unsupervised learning tasks including cluster analysis along distance and similarity metrics [ 41 ]. This review synthesizes a wide range of previous studies, with an emphasis on how neutrosophic sets improve Multi-Criteria Decision-Making (MCDM) frameworks for resolving conflicting agricultural parameters. It highlights how neutrosophic approaches to decision-making are enhanced by addressing uncertainties inherent in agricultural data, including those from soil conditions to market dynamics. Furthermore, the efficiency of neutrosophic models in handling ambiguous or contradictory situations is compared with classical statistical methods and represents an advanced computational intelligence paradigm extending fuzzy reasoning for intelligent decision-making under deep uncertainty.. Finally, the article examines the current challenges of applying neutrosophic statistics in agriculture, paving the way for future research in this interdisciplinary field. 2. Bibliometric Overview of Neutrosophic Research in Smart Agriculture 2.1 Data Source and Analysis Tools This review used the Scopus database as its bibliometric source due to its comprehensive coverage of peer-reviewed sources in all fields of engineering, agricultural sciences, and interdisciplinary studies. TITLE-ABS-KEY field was used to conduct the search to achieve high topical relevance. A search was made with TITLE-ABS-KEY (("neutrosophic" OR "neutrosophic logic" OR "neutrosophic set" OR "indeterminacy") AND ("agriculture" OR "farming" OR "crop" OR "soil" OR "irrigation" OR "smart agriculture" OR "precision agriculture")). The initial searched yielded 223 records. There were no restrictions on the publication year so as to fully encompass the temporal development of neutrosophic research in the agricultural sector. The records recovered were directly exported out of Scopus in CSV format and imported into the biblioshiny web interface of the bibliometrix R package to analyse. Descriptive statistics and annual scientific production trends and source dynamics were generated with the help of Biblioshiny, whereas network analyses, such as country collaboration and keyword co-occurrence, were used to study the intellectual and thematic structure of the area. The combination of these tools made it possible to conduct a systematic and reproducible bibliometric evaluation of neutrosophic logic applications in smart agriculture. 2.2. Publication Trends Figure 1 . shows the scientific output concerning neutrosophic research in the field of agriculture annually. These findings suggest that the publication activity was very low before 2017 and since then, it has gradually risen between 2018 and 2021. There is a sharp growth peak after 2022 and the highest number of publications are found between 2024–2025. The apparent decline in 2026 is attributed to the indexing lag typical of real-time database access, rather than a reduction in scholarly interest. In general, the identified tendency defines neutrosophic applications in agriculture as a research area with a swift rise in academic interest. 2.3. Country-wise Collaboration Figure 2 . shows the network of international co-authorship of countries participating in the research of neutrosophic in smart agriculture. The network also emphasizes the geographical dispersion of research output and the strength of the collaborative links. India and China are significant contributors, which means the active research in the area of neutrosophic decision-making and uncertainty modelling of agricultural systems. Such countries also share a wide range of collaborative relationships with scholars in the Middle East, Europe and North America. The United States and some European nations show a moderate yet steady involvement which suggests increasing interdisciplinary involvement. Contrastingly, the low representation of Africa and South America indicates research gaps in the region. In general, the collaboration network demonstrates a skewed yet growing international research environment with the necessity to collaborate on a larger international level. This regional concentration in Asia reflects the high priority given to Agriculture 4.0 and computational intelligence in these developing countries. 2.4. Keyword Co-occurrence and Research Themes The thematic form of neutrosophic research in agriculture is captured by the keyword co-occurrence network in Fig. 3. The main focus of the methodological approach of the field is represented by a dominant central cluster around neutrosophic decision-support systems and uncertainty-aware modelling. The keywords closely related are those that involve decision-making, optimization and handling of indeterminacy, as applied in the agricultural environment. Secondary clusters are related to application-based themes, such as crop management, soil assessment, irrigation planning, and decision models related to sustainability. Peripheral clusters are new or niche areas of research, which mean that it is at an initial stage of diversification with respect to application areas. The inter-cluster connectivity is rather low, which indicates an emerging field of research where theoretic and practical contributions are still in their early stages of integration. This shows the necessity of the enhanced methodological integration between sophisticated neutrosophic models and practical smart agriculture infrastructures. Notably, the keywords co-occurrence network reveals a significant green cluster dedicated specifically to multi-criteria-decision-making (MCDM) and the Analytic Hierarchy Process (AHP), validation the selection of MCDM as the primary analytical lens for this review. 3. Neutrosophic Theory and Modelling Basics 3.1. Neutrosophic set (NS): core concept A neutrosophic set on a universe X is typically written as NS = {( x, T(x), I(x), F(x)) | x \(\:ϵ\) X }, (1) T-I-F triplet; T(x) - level of truth/membership, I(x) - level of indeterminacy, F(x) - level of falsity or membership, with the range of 0 \(\:\le\:\) T(x), I(x), F(x) \(\:\le\:1\) and 0 \(\:\le\:T+I+F\le\:3.\) These functions return values in the open interval of (0, 1), without restrictive sum constraint found in fuzzy or intuitionistic sets ( T + I + F = 1). This generality allows NS to capture inconsistencies commonly found in real datasets [ 22 ]. This tricomponent setup allows for a more nuanced representation of real-world agricultural data compared to traditional binary and even fuzzy logic systems [ 42 ]. 3.2. Single-valued neutrosophic sets (SVNS) For real-world application, single-valued neutrosophic sets restrict T(x), I(x) and F(x) to the unit interval [0,1], while maintaining their independence. Due to the balance expressive power with computational simplicity, SVNS has become widely adopted in MCDM, predictive modelling, and sustainable agriculture assessments. Typical notation is, A = [ x, u(x), r(x), v(x)): x \(\:ϵ\) X ]. (2) where, u(x) – Single-valued truth, r(x) – Indeterminacy, v(x) – Level of falsity, with respect to a mild condition such as 0 \(\:\le\:\) u(x), r(x), v(x) \(\:\le\:3\) . In the case of decision-making processes, neutrosophic logic is a system that allows the inclusion of more dimensions for the analysis. It finds great application in fields such as smart agriculture, where choices have to be derived from sensor data that might be influenced by the noise, be incomplete, or changed by the environment [ 30 ]. For instance, a smart agriculture mechanism model integrated with neutrosophic theory, IoT, and cloud computing has been demonstrated to perform more detailed calculations by considering uncertain situations inherent in neutrosophic numbers and log [ 30 ]. This integration allows for better decision-making in irrigation, pest control, and nutrient management by incorporating the degrees of truth, indeterminacy, and falsity associated with various environmental parameters and crop responses 3.3. Soft, hypersoft and extended neutrosophic sets Let \(\:X\:\) be a universe and \(\:E\:\) a set of parameters. A neutrosophic soft set (NSS) is a parameterized family of neutrosophic sets defined as a mapping: $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:F:E\to\:\mathcal{N}\mathcal{S}\left(X\right),\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$ 3 where each parameter \(\:e\in\:E\) is associated with a neutrosophic set over \(\:X\) . Each object–parameter pair is described by a triplet \(\:\left(T,I,F\right)\) , enabling flexible modelling of uncertain multi-attribute decision problems [ 43 ]. Neutrosophic logic, when combined with a soft set theory, offered by Molodtsov et al. [ 44 ] improves decision-support systems by handling uncertain and imprecise parameters. Within the context of neutrosophic soft sets, suggested by Maji et al. [ 43 ], every pair of an object-parameter is described as a neutrosophic triplet ( T, I, F ). Where T, I and F are the degrees of truth, indeterminacy, and falsity, respectively. In this method, the emphasis is laid on the attribution of neutrosophic membership values to the objects of the universal set to the attribution of the same to parameters, thus providing additional flexibility in modelling uncertainty. As a result, soft neutrosophic sets offer a powerful framework to multi-criteria decision-making (MCDM) issues. An example is when determining the best variety of crop to grow, the yield potential, resistance to disease, and irrigation needs are among the factors that may be weighted with uncertainty, and with this method, a more realistic approach to this problem can be obtained. Neutrosophic hypersoft sets extend neutrosophic soft sets by allowing tuples of sub-parameters. Let $$\:\:\:\:\:\:E={E}_{1}\times\:{E}_{2}\times\:\cdots\:\times\:{E}_{n},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$ 4 where each \(\:{E}_{i}\) represents a sub-attribute (e.g., soil fertility, climatic zone, irrigation availability). An NHSS maps each parameter tuple to a neutrosophic set on \(\:X\) . The neutrosophic hypersoft sets (NHSS) and neutrosophic hypersoft topological structures extend existing from neutrosophic soft and hypersoft models, allowing tuples of sub-parameters, including climatic zone, soil fertility, and water availability, and specifying neutrosophic structures on their Cartesian products. This feature of modelling has been effectively applied to use in advanced agricultural multi-criteria decision-making (MCDM) problems, such as farm site selection. NHSS is able to reflect complex interdependencies of the agricultural decision processes, including choosing the crop depending on the interaction between the climate zone, soil fertility, and availability of irrigation as can be observed in recent research [ 45 , 46 ]. This degree of complexity is particularly vital within the agricultural sector, where the decision factors are commonly of a nested and hierarchical nature. For instance, soil quality which is a critical agricultural parameter that may be sub-divided into sub-attributes like pH, nitrogen content, phosphorus content, and organic matter, each having a neutrosophic measure attached to it. NHSS consequently enables the finer modelling of multi-level hierarchical uncertainty, which promotes the more accurate agricultural planning and optimizes resource allocation. Figure 4 . Schematically illustrates the structural shift from soft neutrosophic sets to neutrosophic hypersofts and further to extended neutrosophic models to manage deep layers of agricultural uncertainty. Extended neutrosophic sets are a generalization of standard neutrosophic sets where T, I , and F can be expressed as intervals and multiple values instead of being expressed as single numerical values. This generalization leads to some forms such as interval-valued neutrosophic sets, multi-valued neutrosophic sets and n-valued neutrosophic sets, that provide broader frameworks for uncertainty. They are useful especially when more specific numerical estimates cannot be made, as is prevalent within agricultural decision problems that require crop yield estimation, price forecasts, and effects of fertilizer in uncertain situations. Consequently, extended neutrosophic models have been successfully integrated into advanced decision-support frameworks, including neutrosophic goal programming and bio-inspired optimization algorithms, to address complex multi-criteria decision-making problems frameworks is in crop land allocation problems that typically maximize profit and output and minimize costs in conditions of uncertainty of yield, market price, and the effectiveness of applied fertilizer [ 47 ]. Such extended sets can be substituted with a neutrosophic goal programming method that may include bio-inspired algorithms to optimize land distribution, and as an effective approach to indeterminate criteria e.g. seed growth response and fertilizer suitability. These enhanced neutrosophic models enable a more detailed computation, through an explicit consideration of subtle uncertainty in agricultural data to enhance the accuracy and reliability of agriculture decision-making in smart agriculture applications, such as IoT-based monitoring systems, predictive modelling, and risk assessment [ 30 , 48 ]. 3.4. Neutrosophic Relations and Cognitive Maps Neutrosophic Cognitive Maps (NCMs) are extension of fuzzy cognitive maps by including indeterminate relationship represented by the value I. Vertex in NCM may have states; 1 (active), 0 (inactive), I (indeterminate). Each vertex (nodes) in NCM indicate a factor, variable or indicator that influence in agriculture. Edges are weighted from the set {-1, 0, 1, I}, that shows the possibility of positive, negative, neutral or uncertain influence, NCMs represent a powerful tool to model agricultural sustainability, especially when the interactions between variables are not completely known. Figure 5 . Shows a neutrosophic cognitive map of agricultural decision variables as state nodes {1, 0, 1} interconnected by directed edges of weight {-1, 0, 1, I} to characterize positive, negative, neutral and indeterminate casual relationships. Zulqarnain et al. [ 49 ] introduce generalized aggregate operators on NHSS, including extended union, extended intersection, AND/OR operations, and necessity operators, and study their properties for multi-criteria decision making (MCDM). These operators are designed to aggregate evaluations from multiple experts and multiple sub-attributes, supporting selection and planning in complex decision problems. In a smart-agriculture context, the same operators can be interpreted as neutrosophic logic operators that fuse heterogeneous sensor readings and expert assessments such as combining soil, crop and weather sub-criteria into a single neutrosophic decision score for tasks such as crop variety selection, irrigation scheduling, fertilizer recommendation, or disease risk assessment. 3.5. Neutrosophic Logic operators Neutrosophic logic extends classical logic operators AND, OR, and NOT to represent three-dimensional uncertainty. These operators have been applied effectively in anomaly detection for smart farming to handle ambiguous sensor data [ 50 ]. Neutrosophic AND: A ∧ N B = (min ( T A ​, T B ​), max ( I A ​, I B ​) , max ( F A ​, F B ​ )) (5) In the case of two neutrosophic sets A and B, the truth value of A AND B is given by the minimum of the truth values, the indeterminacy value is given by the maximum of the indeterminacy values, while the falsity value is given by the maximum of the two falsity values. This operator represents a model of situations where multiple conditions have to be simultaneously met, and the uncertainty in one condition raises the overall uncertainty. Neutrosophic OR: A ∨ N B = (max ( T A ​, T B ​), min ( I A ​, I B ​), min ( F A ​, F B ​)) (6) The truth degree of A OR B is the maximum of their truth degrees, the indeterminacy degree is the least of their indeterminacy degrees, and the falsity degree is the minimum of their falsity degrees. This operator is used when any one of several conditions can fulfil a requirement. Neutrosophic NOT: ¬ N A = ( F A ​, I A ​, T A ​) (7) The complement of a neutrosophic set A changes its truth and falsity degrees and keeps the indeterminacy. This operator stands for the negation of a proposition. Figure 6 . demonstrates the operational workflow of netrosophic logic in agricultural decision support, where sensor inputs are transformed into ( T, I. F ) triplets and synthesized using AND, OR, and NOT operators. These operators are very essential to decision support systems that are used in agriculture. As an example, in a smart irrigation system, decisions might be influenced by several factors such as soil moisture ( T 1 , I 1 , F 1 ), weather forecast ( T 2 , I 2 , F 2 ), and crop growth stage ( T 3 , I 3 , F 3 ) [ 30 ]. Neutrosophic operators may merge these uncertain sensor readings and expert knowledge to find out the best irrigation action while at the same time they recognize the environmental data indeterminacy [ 30 ]. In the case of crop yield prediction, they have the capability of integrating various uncertain inputs such as rainfall, temperature, and soil nutrient levels in order to forecast future yields while also being very clear about the indeterminacy for each factor [ 48 ]. 3.6. Cubic Spherical Neutrosophic Sets (CSNS) Cubic Spherical Neutrosophic sets represents a high-level extension of classical neutrosophic sets. Their purpose is to enhance the modelling of multi-level and geometrically structured uncertainty. Correspondingly, each element in CSNS is represented not only by the neutrosophic membership degree of truth (T), indeterminacy (I), and falsity (F) but also by the additional radius parameter (r) describing the spatial interpretation of uncertainty. It expressed as, A = {( x , [ T L ( x ), T U ( x )], [ I L ( x ), I U ( x )], [ F L ( x ), F U ( x )], ( T ( x ), I ( x ), F ( x )))} (8) Where the membership values are subject to the following constraints: { T ( x ), I ( x ), F ( x ), r ( x )}, 0 ≤ T 2 + I 2 + F 2 ≤ 1 (8a) r(x) = \(\:\surd\:\) 1- ( T 2 ( x )+ I 2 ( x )+ F 2 ( x )) (8b) CSNS would generally extend this concept by integrating cubic sets with spherical neutrosophic sets. Spherical neutrosophic sets enable decision-makers to separately assign grades for truth, indeterminacy, and falsity such that their total is less than or equal to one. The term "cubic" usually refers to the combination of interval-valued information with fuzzy numbers, thus allowing a more detailed depiction of uncertain data. In the case of agriculture, where sensor data might be inaccurate for instance, soil moisture levels varying within a certain range and expert opinions might be unclear like "the crop is moderately healthy", CSNS could provide a high-level technique for the aggregation and data analysis. As an example, determining the health of the crop might mean that not only single values for truth, indeterminacy, and falsity are considered, but also intervals for these values, thus indicating a deeper level of imprecision in diagnosis or prediction. This would, therefore, enable more dependable decision, making in precision agriculture areas, such as the detection of the earliest symptoms of disease or the efficient use of irrigation when it is difficult to establish exact thresholds. In particular, this improvement adds to geometric robustness and considers multi-level uncertainty. The CSNS has broad applicability in agriculture, especially for crop ranking under climatic variability, risk evaluation in crop planning, assessing risk under fluctuating climatic conditions and resource allocation and sustainability assessment [ 51 ]. 4. Current neutrosophic application in smart agriculture The wide range of application of neutrosophic logic to smart agriculture are summarised in Fig. 7 , illustrating its incorporation into decision-support systems for land allocation, soil assessment, yield forecasting, and intelligent anomaly detection under uncertainty. 4.1. IoT- Enabled Smart Farming The combination of neutrosophic logic and IoT smart farming systems provides a reliable way to deal with uncertainty in real-time farming systems. Sensor data regarding soil analysis, climate, GPS farming, and crop analysis coordinates are often incomplete or noisy. Neutrosophic-IoT systems can effectively overcome this problem by representing raw data as neutrosophic triplets before processing. The core components of the Neutrosophic Inference Engine (NIED) and the corresponding smart agriculture applications are summarized in Table 1 . Table 1 Core Neutrosophic Inference Engine (NIED) Components and Their Smart Agriculture application Component Core Technique Key Innovation Smart Agriculture Application Reference NIED Neutrosophication and de-neutrosophication Transformation of pentagonal and trapezoidal neutrosophic numbers using area-based and mean-based methods IoT data acquisition and pre-processing [ 52 ] NIED Neutrosophic clustering and analysis Outlier and boundary handling using Lagrange multipliers and G-metrics on single-valued neutrosophic set Data classification and big data analytics [ 53 ] NIED Neutrosophic IF-THEN rules Rule-based inference under indeterminate conditions Real-time decision support in smart farming [ 30 ] Recently, studies have shown that cloud-assisted and edge-enabled IoT systems in which neutrosophic inferences are incorporated enhance reliability of irrigational decision, nutrient scheduling as well as environmental monitoring. These platforms are capable of increasing the flexibility and scalability of a precision agriculture system to dynamic field conditions through the explicit modelling of indeterminacy of data. 4.2. Decision support and Crop recommendation systems Kaviyarasu et al. [ 54 ] have proposed “Algorithm 1”, using neutrosophic hypersoft sets (NFHSs) for farm site selection, define variables with double sets ( S 1, Γ1) and \(\:\left({S}_{2},{{\Gamma\:}}_{2}\right)\) , their combination through “resultant union,” and ranking sites based on the final score ( \(\:{O}_{i}={r}_{i}-{c}_{i}\) ), which is obtained through summation of rows( r i ) and columns ( c i ), selecting the one with highest score ( \(\:{y}_{j}=\text{a}\text{r}\text{g}{\text{m}\text{a}\text{x}}_{i}\left\{{O}_{i}\right\}\) ) to handle uncertainty. Kaviyarasu et al. [ 54 ] continued to advance the usage of neutrosophic hypersoft sets in “Algorithm 2”, incorporating topology with the integration of open sets based on the location and decision parameters, along with integration of data based on advanced operations, and site selection based on net scores ( \(\:{O}_{i}={r}_{i}-{c}_{i}\) )- achieving consistent results like identifying site \(\:{y}_{2}\) optimal across more than 12 parameters for robust uncertainty management. The effectiveness of hypersoft and cubic neutrosophic models for capturing interdependencies among multiple criteria and expert assessments. Neutrosophic DSS offer greater robustness, and their outcomes are more explainable compared to traditional MCDM approaches, particularly for regions facing climatic uncertainty and resource constraints [ 51 , 54 ]. Angammal and Grace. [ 55 ] model crop selection for medium farm holders in Ariyalur as a multi-objective, multi-attribute neutrosophic optimization problem, where truth, indeterminacy and falsity membership functions explicitly represent uncertainty in yield, prices, seed growth, fertilizer suitability and other agri-inputs. By minimizing under-deviation in truth and over-deviation in indeterminacy and falsity, the neutrosophic goal programming models simultaneously optimize production, profit and expenditure under constraints of land, labour, water and food requirements. This demonstrates that neutrosophic decision-support systems can provide practical, field-validated crop allocation and crop choice recommendations for specific regions such as Ariyalur district. 4.3. Soil, Water, and Land Suitability assessment Soils and land evaluation processes are based on a set of physical, chemical, and biological indicators showing spatial variability, which are often measured with a certain degree of imprecision. To overcome these challenges, the Neutrosophic Fuzzy–Analytic Hierarchy Process (NF-AHP) and similar hybrid models have been applied in soil quality indexing and land suitability analysis. By incorporating neutrosophic judgments into pairwise comparisons, these approaches explicit model expert uncertainty and conflicting assessments. From a methodological perspective, the criteria for soil and land evaluation are first hierarchically organized, and expert judgments are elicited through linguistic terms that are converted to neutrosophic numbers. Neutrosophic pairwise comparison matrices are then set up for each criterion relationship, capturing the truth, indeterminacy, and falsity. Criterion weights are determined via neutrosophic aggregation and normalization processes, continuing with consistency analysis adapted to the neutrosophic format. Weighted criteria are eventually combined with spatial or quantitative indicators of soil to calculate the composite soil quality or land suitability indices. Empirical results show that neutrosophic-enhanced soil and land evaluation models outperform classical AHP and fuzzy-AHP in selecting suitable zones for cultivation and determining land degradation risk, especially in the case of climate-sensitive agricultural systems [ 56 ]. 4.4. Yield Prediction and agriculture risk assessment Neutrosophic logic has emerged as a vital tool for modelling yield and risk under climate variability, incomplete data, and expert vagueness, where classical probability and even fuzzy logic struggle. Recent literature integrates neutrosophic logic with statistical and deep learning models for crop-yield prediction under climate stress. A recent framework combines neutrosophic logic with least squares regression and an independence test to estimate crop-loss functions and classify crops by profitability and environmental risk, focus specifically on extreme-weather events. Deep learning, particularly restricted Boltzmann machines (RBM), is used to capture complex nonlinear relations between climate, management variables, and yield, while neutrosophic representations encode truth, falsity, and indeterminacy in expert and sensor inputs [ 48 ]. The model is demonstrated gains in estimation of yield damage and provides farmers with functional risk indicators to support adaptation decisions such as diversification and input adjustment [ 48 ]. At the planning level, multi-objective neutrosophic fuzzy linear programming has been applied to optimize seasonal crop portfolios such as wheat and rice in canal-irrigated systems under uncertain water availability and climate shocks. Here, yield, water requirements, storage limits, and canal capacities are modelled as neutrosophic–fuzzy parameters so that both randomness and imprecision like expert scenarios rather than hard data are reflected. The optimization aims to maximize net profit and total production while addressing to hydrological and infrastructural limitations, demonstrating that neutrosophic fuzzy algorithms can handle yield uncertainty more effectively than conventional fuzzy models when parameters are susceptible to sudden, climate-driven changes [ 57 ]. Neutrosophic approaches are also being embedded in probabilistic sequence models for yield forecasting. A single-valued neutrosophic hidden Markov model (HMM) has been proposed to represent long-run weather regimes and their transitions, with neutrosophic probability capturing indeterminate states. This model is used to forecast crop yields and notify farmers about likely favourable and unfavourable yield states under evolving weather conditions [ 58 ]. In addition to forecasting, neutrosophic logic supports risk assessment in crop selection. Quadripartitioned single-valued neutrosophic sets and associated entropy/similarity measures have been used to transform expert linguistic assessments of multiple risks (climate, soil, pest, market) into interpretable risk levels for alternative crops. A case study on mustard and paddy shows how final risk levels such as “absolutely high” vs “very low” can be robustly derived from imprecise, multi-expert inputs, improving strategic crop choice under uncertainty [ 59 ]. Neutrosophic goal programming has likewise been used to determine optimal land allocation under uncertain yields, prices, and agronomic factors, leveraging separate truth, indeterminacy, and falsity membership functions and bio-inspired optimization to maximize profit and production under resource constraints [ 47 ]. 4.5. Anomaly Detection and edge intelligence in smart farming Anomaly detection has grown in importance in the agricultural field with sensors networks and edge or fog computing systems being installed to assist in smart farming. The sensor measurements are prone to noise, missing values, and variation in the environment making traditional anomaly detectors to have missed detection or false alarm [ 60 ]. In reaction, edge-based deep learning systems, including CNN-LSTM based and LSTM (Convolutional Neural Network- Long Short-Term Memory) autoencoders, have shown that intelligence pushed to sensors can be highly detected and low latency in smart farms settings [ 50 , 61 ]. The neutrosophic logic provides a complementary model in that it explicitly models truth, falsity, and indeterminacy in both data and decisions. Neutrosophic multivariate time-series models together with graph learning have been applied in the context of Industrial IoT to improve the performance of the anomaly detector when the dimensionality is high and the sensor data is distorted [ 62 ]. Likewise, neutrosophic-enhanced ensemble methods to detect intrusion in the IoT break down prediction confidence into truth, falsity, and indeterminacy and allow systems to avoid making uncertain decisions, which is a valuable feature of edge deployments that demand trust in autonomous actions [ 63 ]. Even though the majority of anomaly detection methods in smart agriculture still utilize probabilistic or deep learning models like GANs (Generative Adversarial Network), autoencoders, CNN-LSTM models, and ensemble outlier detectors instead of neutrosophic logic [ 50 , 60 , 64 , 65 ], neutrosophic modelling has already been used in agricultural decision-support systems to operate with uncertain soil and environmental data [ 30 ]. This suggests a potential future direction of research: namely, the incorporation of neutrosophic representations into edge-based anomaly detection in smart farming, wherein edge nodes should be able to distinguish sensor behaviour as normal or abnormal, but should in addition be able to describe indeterminate states that humans may choose to inspect or conserve via conservative control. This can improve the reliability of systems, minimize unnecessary alarms, and facilitate the open human-in-the-loop decision-making at the network edge [ 30 , 62 , 63 ]. Table 2 . Provides a consolidated comparative overview of recent neutroosphic methodological applied across various smart agriculture domains, highlighting the modelling approaches, evaluation criteria, and practical outcomes. 4.6. Implication of agriculture statistics and practice The neutrosophic approaches fill a significant interface between agricultural statistics and decision science by looking at indeterminacy as a first-class statistical object instead of noise to be discarded or pushed to traditional probabilistic models [ 33 ]. Neutrosophic statistics is based on classical methodologies by breaking down the observations into determinate and indeterminate parts, thus allowing the analysis of experimental data, soil measurements, and yield records that naturally incorporate vagueness and does not arbitrarily treat these as completely precise. Furthermore, model output is not limited to single point estimates or confidence interval, but instead can be presented as neutrosophic triplets ( T , I , F ) which are naturally related to action-based decision criteria like accept, review, or intervene. This model resembles the decisions made by agronomists and farmers in a real situation when they are uncertain [ 66 ]. Although regression analysis, geostatistical modelling, and machine learning are crucial in large-scale agriculture prediction processes, neutrosophic logic improves the trustworthiness of decisions in scenarios where data is incomplete, measurement uncertainty, or expert judgments are deployed [ 56 ]. Neutrosophic methods are typically best applied in conjunction with conventional statistical and machine learning predictors, working at the decision-support and interpretation tiers of smart agriculture systems rather than substituting existing predictive pipelines [ 67 ]. Design and analysis Neutrosophic analysis of experimental data enables the expression of treatment effects that demonstrate indeterminacy components. It is especially useful in cases where field replicas are few, measurement errors are large, and expert-based assessments, including disease severity scales or visual soil ratings, are subjective or ambiguous in nature [ 68 ]. Risk-sensitive advisory Neutrosophic yield and soil fertility models should be used to detect borderline cases with high indeterminacy, and hence provide advice to do further sampling or expert evaluation instead of making overconfident advisories. This knowledge-based risk management guidance increases the safety and reliability of agricultural advisory services particularly in climate-sensitive areas [ 66 ]. Table 2 Key neutrosophic logic in smart-agriculture studies Application domain Neutrosophic method Factors considered Main outcome for smart agriculture Reference Crop land allocation and optimal crop mix Neutrosophic Goal Programming + bio-inspired algorithms (GWO, SGO, PSO) Yield, prices, seed growth, fertilizer suitability; land, labour, water, food demand Maximizes profit and production, minimizes expenditure; neutrosophic–bio-inspired solution outperforms fuzzy methods [ 47 ] Land allocation & resource planning Neutrosophic linear programming Regions A_j (60,150,20,10 ha), demands b_i (800,200,600,1000,2500 tons), productivity Na_ij [wheat A1= {4,6} tons/ha], profit Np_i [wheat={1400,1600}/ton] Maximizes neutrosophic profit under constraints, robust to yield/price uncertainty [ 69 ] Carbon emission reduction policy Fermatean neutrosophic using WINGS with AHP-EWM 9 factors (τ4 = carbon policy, τ6 = tech adoption, τ8 = sustainable management) Policy prioritization tool (τ₄=carbon policy 0.220 top) [ 70 ] Maize silage soil quality NF-AHP weights using MLR and RFR prediction 89 samples, 28 indicators (slope 0.0746, MBC 0.0787) MLR > RFR (R²=0.99), precision soil assessment [ 56 ] IoT anomaly detection SVNS with decision matrices using correlation scoring Sensor streams (uncertainty, missingness) Real-time edge anomaly detection, fewer false alarms [ 50 ] Farm site selection Neutrosophic hypersoft topological MCDM Soil, climate, water, economics + sub-attributes Robust farm selection despite contradictory judgments [ 54 ] Sugar beet soil quality assessment in semi-arid soils Neutrosophic Fuzzy-AHP (NF-AHP) for SQI; predicted with multi-class logistic regression, random forest, one-against-all SVM Physical, chemical, fertility, biological indicators under semi-arid conditions; linked to NDVI from Sentinel-2A NF-AHP-based SQI framework with ML classifier accuracy for data-driven soil/crop management in semi-arid agriculture [ 71 ] Crop yield & risk assessment Neutrosophic least squares with RBM (Restricted Boltzmann Machine) Rice/banana yields, weather extremes, 160 farmers Risk-aware yield prediction with damage categories under uncertainty [ 48 ] Soil quality assessment in sub-humid ecosystem Neutrosophic fuzzy-AHP using support vector machine Soil indicators scored via linear/nonlinear functions in sub-humid mountain areas Hybrid SQI model for accurate soil quality evaluation aiding sustainable land management [ 72 ] Crop recommendation under uncertainty Neutrosophic–paraconsistent uncertainty expert system with Butterfly Optimization Algorithm (UES-BOA) Soil fertility and climate parameters: Nitrogen (N), Phosphorus (P), Potassium (K), temperature, relative humidity, soil pH, rainfall; 2200 instances, 22 crop classes; certainty degree (µ) and contradiction degree (λ) via neutrosophic and paraconsistent logic Robust crop recommendation under uncertainty with optimized rules, achieving 95.8% accuracy and outperforming ANN, MLP, and SVM. [ 73 ] Multi-criteria decision-making in agriculture (farmer performance selection) Neutrosophic Soft Matrices (NSM) with score and value functions Farmer performance indicators including crop productivity, input use, and resource management, evaluated using truth, indeterminacy, and falsity degrees. Reliable farmer selection under uncertainty using score-based neutrosophic soft matrices. . [ 74 ] 5. Advanced neutrosophic frameworks for smart agriculture Modern farmework evolve from classic neutrosophic methods by integrating complex mathematical structures capable of addressing complex agricultural decision-making defined by interacting criteria and deep uncertainty. Broadly, the literature on neutrosophic logic-based decision-making in agriculture is dominated by two primary branches: (i) neutrosophic hypersoft and topological models, (ii) hybrid neutrosophic-fuzzy MCDM frameworks. 5.1. Neutrosophic hypersoft and Topological frameworks Advanced neutrosophic hypersoft and topological structures extend classical neutrosophic sets to represent multi-attribute, hierarchically structured, and highly uncertain information typical of smart agriculture. Neutrosophic hypersoft sets generalize soft and neutrosophic sets by allowing each parameter such as soil type, climate and input type to be partitioned into sub-parameters and handled as multi-argument tuples, enabling precision modelling of complex agronomic criteria under truth, indeterminacy and falsity membership degrees [ 75 , 76 , 77 ]. In a 2025 study Kaviyarasu et al. [ 54 ] proposed neutrosophic hypersoft topological framework for agricultural decision-making constructs a neutrosophic agricultural topology in which open sets are generated from a neutrosophic sub-base and standard topological notions like basis, subspace, interior and closure are adapted to hypersoft neutrosophic spaces [ 54 ]. The research introduces two algorithms, one directly on neutrosophic hypersoft sets and another operating on neutrosophic hypersoft topological spaces. Numerical case studies using real agricultural data included crop alternatives evaluated under multiple agronomic and economic factors show that this topology-based MCDM approach improves the efficiency and reliability of decision strategies when the number of variables is large and uncertainty is high. Topological variants, such as neutrosophic semi-open and semi-closed hypersoft sets, further refine this framework. By defining semi-open and semi-closed neutrosophic hypersoft sets and constructing corresponding topologies, decision algorithms have been developed for multi-attribute group decision-making. Although these models were demonstrated using COVID-19 case studies, the authors explicitly indicate that similar MAGDM (Multi-Attribute Group Decision-Making) schemes can be adapted to agricultural yield optimization and related planning problems [ 78 , 79 ]. Beyond pure topology, hypersoft hybrids extensions such as possibility neutrosophic hypersoft sets, interval-valued complex neutrosophic hypersoft sets, fermatean neutrosophic hypersoft provide enhanced decision- capabilities by incorporating possibility degrees, phase information and higher-order uncertainty [ 46 , 75 , 79 , 80 ]. These models have been applied to sustainable agriculture case studies in which environmental, social, and economic criteria and their sub-attributes are evaluated under indeterminate and conflicting evidence, demonstrating improved handling of ambiguity and trade-offs compared to conventional MCDM methods [ 46 ]. 5.2. Hybrid Neutrosophic-Fuzzy and MCDM models Hybrid neutrosophic–fuzzy and MCDM models provide structured decision support in smart agriculture by combining rich representations of uncertainty with powerful ranking and weighting procedures. Neutrosophic and advanced fuzzy sets such as fermatean, q-rung orthopair, t-spherical, hypersoft allow expert opinions, sensor data, and qualitative assessments to be expressed with degrees of truth, falsity, and indeterminacy rather than crisp numbers, capturing hesitation and conflicting evidence typical of climate, market- and soil-driven decisions [ 46 , 81 – 83 ]. These uncertainty models are then embedded in MCDM frameworks such as AHP, TOPSIS, CODAS, GRA, SPOTIS, MACBETH, or new hybrid schemes to weigh criteria and rank alternatives, for example when comparing agricultural production techniques, smart farming modes, UAV platforms, or vertical-farm technologies under multiple economic, environmental and social criteria [ 84 , 85 ]. In practice, such hybrid models have been used to analyse sustainable agriculture and water-demand strategies with fuzzy AHP–TOPSIS variants, to optimize green supplier selection using Z-numbers with fuzzy LMAW–CRADIS, to evaluate Agriculture 4.0 decision support systems with hyperbolic fuzzy weighting and CODAS, and to select smart farming or robotic agri-farming modes under (p, q)-rung or q-rung orthopair fuzzy environments [ 81 , 84 , 86 , 87 ]. They also support specialized problems like designing sustainable weed-management strategies in a t-spherical probabilistic hesitant fuzzy setting or ranking agri-food waste-valorization solutions with fermatean fuzzy SWARA–DEMATEL–QFD [ 88 , 89 ]. Across these applications, hybrid neutrosophic–fuzzy MCDM models consistently aim to improve realism of expert input, integrate heterogeneous criteria, and deliver stable rankings checked by sensitivity and comparative analyses, making them a core advanced framework for smart-agriculture decision-making under deep uncertainty. Table 3 . is a summary of representative hybrid neutrosophic-fuzzy MCDM frameworks and their applications in agriculture. The NF-AHP weighting of 28 soil indicators enabled more nuanced handling of ambiguous field measurements and expert judgments, and produced stable, interpretable importance scores for key physical, chemical, productivity, and biological indicators in a climate-sensitive region [ 56 ]. Complementary work on land allocation for medium farm holders proposed a bi-level TOPSIS-based neutrosophic programming technique, showing higher net profit and better risk handling than fuzzy and intuitionistic fuzzy optimization approaches under uncertain water supply, labour, and yield conditions [ 47 ]. In sustainable agriculture, fermatean neutrosophic hypersoft MCDM algorithms further demonstrate that integrating neutrosophic structures with soft sets yields more flexible and realistic evaluations of agricultural techniques and inputs than conventional fuzzy-only schemes [ 46 ]. Table 3 Neutrosophic–Based Hybrid MCDM Models Applied to Agricultural Planning and Sustainability Hybrid model Agricultural application Reference Neutrosophic–fuzzy AHP and TOPSIS Soil quality indexing and suitability ranking under uncertain indicators [ 56 , 90 ] Neutrosophic TOPSIS and programming (bi-level) Land allocation and farm planning with profit–risk trade-offs [ 47 ] Fermatean neutrosophic hypersoft MCDM Sustainable practice and input selection using environmental, social–economic criteria [ 46 ] 6. Unified neutrosophic Intelligent Decision Framework for Smart Agriculture To effectively incorporate neutrosophic intelligence in smart agricultural decision environments, this review proposes a Unified Neutrosophic Intelligent Decision Framework that incorporates five interconnected layers that provide deep uncertainty management and intelligent decision-making. The Data Layer will obtain real-time agricultural data via IoT-powered sensors installed in farming fields, where they will monitor soil, climatic, and crop-related data that are vital in precision agriculture [ 30 ]. The Uncertainty Representation Layer leverages neutrosophic modelling to explicitly describe truth, falsity, and indeterminacy related to heterogeneous agricultural data to facilitate the successful manipulation of incomplete, inconsistent and noisy data [ 30 , 54 ]. In the Reasoning Layer, neutrosophic aggreagation operators combine multi-source uncertain data into analysable representations, which are robust to conflicting or partially missing data [ 54 , 85 ]. The Decision Layer integrates neutrosophic Multi-Criteria Decision-Making (MCDM) models to evaluate the alternatives across economic, environmental, and operating criteria to assist in optimized agricultural planning and resource allocation [ 46 ]. Finally, the Application Layer translates the framework into the real world by implementing smart farming management with the help of intelligent Decision Support Systems (DSS), which transforms the results of analysis into recommendations and action. The proposed layered architecture defines a unified interface between IoT-based data acquisition, uncertainty-sensitive reasoning, and intelligent decision-making, hence presenting a conceptual foundation for next-generation smart agricultural systems working on deep uncertainty. In order to present a systematized understanding of uncertainty-aware decision-making in smart agriculture, Unified Neutrosophic Intelligent Decision Framework is proposed, consisting of interrelated layers such as data acquisition, uncertainty representation, reasoning, decision-making, and implementation deployment, as shown in Fig. 8 . 7. Limitations and critical assessment 7.1. Methodological limitations 7.1.1. Parameter selection and subjectivity: Defining the neutrosophic triple ( T, I, F ), mapping of linguistic terms to membership values and selection of aggregation operators remains predominantly expert-driven and usually ad hoc. These choices can directly influence outcomes crop ranking, land suitability, and yield risks estimation. As a result, decision outcomes shift significantly when alternative parametrization or mapping schemes are applied. Despite this sensitivity, systematic sensitivity analyses are reported in the existing literature, a limitation that has been consistently cited in both the application-based research and methodological reviews [91, 92]. 7.1.2. Lack of standardized metrics and benchmarks: Currently, no standardized set of evaluation metrics exists that simultaneously accounts for predictive accuracy and uncertainty calibration for neutrosophic predictions. This lack of standardisation hinders comparative analysis comparison and meta-analysis across studies report only task-specific measures such as classification accuracy or MCDM ranking scores. According to recent surveys, it is necessary to have shared benchmark and standardized evaluation protocols to facilitate a fair comparison among neutrosophic, fuzzy, and ML-based approach, and XAI-driven models [67, 93]. 7.2. Practical implementation limitations; 7.2.1. Limited software tools and packages: Software support for neutrosophic modelling lacks a unified framework contrast to the robust ecosystem of fuzzy logic and mainstream machine learning systems (scikit-learn, TensorFlow). Although prototype libraries such as PyIVNS (Python Interval-Valued Neutrosophic Set) prove the viability of inter-valued neutrosophic operations, they are not yet widely integrated into standard data-science work-flows. This limitation hinders reproducibility and slows the transition of neutrosophic methods into practical agricultural decision-support system [91]. 7.2.2. Computational complexity of hypersoft and topological variants: Hypersoft sets and hypersoft topologies are advanced neutrosophic frameworks that offer significant expressive power for multi-subattribute MCDM by enabling robust topological operations and cartesian products of multiple sub-attributes. However, this increased modelling flexibility is paired with large computational complexity especially when applied to large-scale spatial or remote sensing datasets. Developers of hypersoft topologies model identify challenges related to dimensionality growth and algorithmic scalability, which may limit real-world utility in data-intensive agricultural applications [54, 78]. 8. Research gaps 8.1. Few extensive field validations: Multi-site and multi-season experiments across a wide range of agro-ecological conditions are notably scarce, and most neutrosophic research studies in agriculture have been restricted to localized pilot projects, or on simulated data. Lack of field evaluation on a large scale fails to validate that these approaches are robust to real-world farming systems, in heterogenous climatic and management conditions [67, 93]. 8.2. Scarce comparison with strong ML baselines: Most neutrosophic works are limited in their comparison with fuzzy or Intuitionistic fuzzy variants. Insufficient benchmarking against good machine learning baselines like Random forests, XGBoost and deep neural networks, is usually missing, undermining statements about performance improvements. Evidence suggests that tree-based ensembles and deep learning models are already very strong in predicting factors such as crop yield prediction and remote sensing. In the absence of systematic comparisons, it remains difficult to distinguish between the benefits of explicitly uncertainty modelling and the improvements due to more complex models or feature engineering [56, 94]. 9. Future research direction for Smart agriculture Future research directions in smart agriculture, particularly through the lens of neutrosophic sets, highlight the necessity of a methodological roadmap. Primary research must pivot to the systematic integration of neutrosophic intelligence with machine learning and deep learning models, emphasizing neutrosophic feature encoding for yield, price, and risk forecasting, and transforming sensor observations into ( T, I, F ) triplets prior to learning. Neutrosophic logic is well-positioned for widely adopted in noise-robust learning, yet it is not thoroughly explored within regression models and deep architectures [ 30 ]. Targeted efforts should focus on neuro-neutrosophic hybrid models, neutrosophic-based regularization strategies, and uncertainty-aware loss function designed to enhance generalization in the presence of missing, biased, or heterogeneous agricultural data [ 95 ]. Additionally, the development of neutrosophic explainable-AI (XAI) framework is critical, as interpretability remains a key challenge in data-driven agricultural decision-support systems. Hence, in the coming years, researchers should prioritize integrate neutrosophic logic theories along with other XAI techniques such as SHAP (SHapley Additive exPlanations) [ 96 ] and LIME (Local Interpretable Model-agnostic Explanations) [97] may enhance transparency and trust in decision-making processes. Furthermore, employing neutrosophic logic tasks in IoT-based edge clouds and cloud infrastructures for support real-time anomaly identification offers significant potential [ 30 ]. Future studies should also investigate scaling neutrosophic models to satellite, UAV (Unmanned Aerial Vehicle), hyperspectral, and other multi-source big-data platforms using cloud-edge collaborative architectures. On the other hand, normalization processes along with the development of common datasets should be executed to facilitate appropriate deployment in policy-focused tasks. Conclusion The integration of neutrosophic logic in smart agriculture is a critical evolution in the response to the complexities and uncertainties of agricultural decision-making. Neutrosophic techniques that incorporate neutrosophic linear programming, clustering and IF-THEN rule offers a resilient architecture in optimization of land allocation, resource planning and real-time farming decision. These approaches are effective in mitigating inherent uncertaunty in the agricultural variables, such as the yield, price and environmental factors. To illustrate, interval-valued complex neutrosophic hypersoft sets (IV-CNHS) have been developed, allowing labels to be partitioned into multi-sub parametric tuples, which offers a more detailed and mathematically adequate treatment of the complex, interdependent variables of agricultural systems. Although these developments are encouraging, yet persistent several limitations in its methodology. The subjectivity involved in the selection of parameters based on expert judgment and the manipulation of linguistic words into a value based on membership compromise the integrity of outcomes which may include crop ranking and land suitability assessment. This variability explains why sensitivity analyses are essential, and it is not reported in existing studies often. Furthermore, the absence of standardized measures of assessing neutrosophic outputs makes it complicated to assess the predictive accuracy and uncertainty calibration, which needs for unified standards in this area. The development of advanced neutrosophic systems, such as neutrosophic hypersoft sets also improves the ability to manage intricate interdependencies between decision parameters especially in areas with uncertain climatic conditions. These frameworks enable incorporation of various variables in the decision-making process like soil quality and climatic conditions thus enhancing the robustness of the agricultural practices. In conclusion, the neutrosophic logic does propose to improve the decision-making in the smart farming, but it is important to address identified limitations to make it as effective as possible. The further studies and collaboration among experts are required to refining these approaches, establishing the metrics of the standard evaluation, and eventually enhance the productivity and sustainability in an increasingly uncertain climatic- agriculture. Declarations Acknowledgment The authors would like to thank the Department of Physical Science and Information Technology, Tamil Nadu Agricultural University, Coimbatore, for providing the necessary academic facilities and institutional support that facilitated this review work Authors Contribution DevaDharshini: writing original draft, collection of literatures, conceptualization, Editing; Kalpana Muthuswamy: Supervision, review and editing; M Vijayabhama: Supervision; P Vasanthi: Supervision; R Parimalarangan: Supervision. Ethical Approval The article does not contain any studies involving human participants or animal performed by any of the authors. Consent to participate: Not applicable Consent to publish: Not applicable Funding Declaration This research did not receive any specific grant from funding agencies. Data availability statement Data sharing is not applicable to this article as no datasets were generated or analysed during the current study. Conflict of interest No potential competing interest was reported by the author(s). References Fischer RA, Byerlee D, Edmeades G (2009) Can technology deliver on the yield challenge to 2050? Agecon Search, Misc. Pap. https://www.fao.org/4/ak542e/ak542e12a.pdf Zhang J, Trautman D, Liu Y, Bi C, Chen W, Ou L, Goebel R (2024) Achieving the rewards of smart agriculture. Agronomy 14:452. https://doi.org/10.3390/agronomy14030452 Musajan A, Lin Q, Wei D, Mao S (2024) Unveiling the mechanisms of digital technology in driving farmers' green production transformation: Evidence from China's watermelon and muskmelon sector. Foods 13:3926. https://doi.org/10.3390/foods13233926 Patel PN, Padaliya M, Sanjay VC, Anand B (2024) Internet of Things: A way of transforming conventional agriculture. Int J Sci Res Sci Eng Technol 11:281–292. https://doi.org/10.32628/ijsrset24115120 Huo D, Malik AW, Ravana SD, Rahman AU, Ahmedy I (2024) Mapping smart farming: Addressing agricultural challenges in data-driven era. Renew Sustain Energy Rev 189:113858. https://doi.org/10.1016/j.rser.2023.113858 Mansoor S, Iqbal S, Popescu SM, Kim SL, Chung YS, Baek J-H (2025) Integration of smart sensors and IoT in precision agriculture: Trends, challenges and future perspectives. Front Plant Sci 16. https://doi.org/10.3389/fpls.2025.1587869 Raj R, Ghosh A, Pal A, Kundu SK, Karmakar S (2025) A brief review on smart farming technologies for precision agriculture. In: 2025 8th Int. Conf. Electron. Mater. Eng. Nano-Technol. (IEMENTech), pp. 1–5 https://doi.org/10.1109/iementech65115.2025.10959551 Alahmad T, Neményi M, Nyéki A (2023) Applying IoT sensors and big data to improve precision crop production: A review. Agronomy 13:2603. https://doi.org/10.3390/agronomy13102603 Kamilaris A, Prenafeta-Boldú FX (2018) Deep learning in agriculture: A survey. Comput Electron Agric 147:70–90. https://doi.org/10.1016/j.compag.2018.02.016 Manogna RL, Dharmaji V, Sarang S (2025) Enhancing agricultural commodity price forecasting with deep learning. Sci Rep 15:20903. https://doi.org/10.1038/s41598-025-05103-z Jabed MA, Murad MAA (2024) Crop yield prediction in agriculture: A comprehensive review of machine learning and deep learning approaches. Artif Intell Agric 8:100–123. https://doi.org/10.1016/j.heliyon.2024.e40836 Wani JA et al (2022) Machine learning and deep learning based computational techniques in automatic agricultural diseases detection: Methodologies, applications, and challenges. Arch Comput Methods Eng 29:641–677. https://doi.org/10.1007/s11831-021-09588-5 Zhao X, Tang W, Liu Q et al (2025) Impact of agricultural industry transformation based on deep learning model evaluation and metaheuristic algorithms under dual carbon strategy. Sci Rep 15:27929. https://doi.org/10.1038/s41598-025-14073-1 Martin N, White J (2024) Water resources’ AI–ML data uncertainty risk and mitigation using data assimilation. Water 16:2758. https://doi.org/10.3390/w16192758 Heinicke S, Frieler K, Jägermeyr J, Mengel M (2022) Global gridded crop models underestimate yield responses to droughts and heatwaves. Environ Res Lett 12:4938. https://doi.org/10.1088/1748-9326/ac592e Teh HY, Kempa-Liehr AW, Wang KI-K (2020) Sensor data quality: A systematic review. J Big Data 7:11. https://doi.org/10.1186/s40537-020-0285-1 Ustun TS, Hussain SMS, Kirchhoff H, Ghaddar B, Strunz K, Lestas I (2019) Data standardization for smart infrastructure in first-access electricity systems. Proc. IEEE 107, 1790–1802 https://doi.org/10.1109/JPROC.2019.2929621 Karmakar P, Teng SW, Murshed M, Pang S, Li Y, Lin H (2024) Crop monitoring by multimodal remote sensing: A review. Remote Sens Appl Soc Environ 33:101093. https://doi.org/10.1016/j.rsase.2023.101093 Ureña R, Kou G, Wu J, Chiclana F, Herrera-Viedma E (2019) Dealing with incomplete information in linguistic group decision making using interval type-2 fuzzy sets. Int J Intell Syst 34:2982–3014. https://doi.org/10.1002/int.22095 Dubois D, Prade H (2009) An introduction to bipolar representations of information and preference. Int J Intell Syst 24:843–873. https://doi.org/10.1002/int.20297 Lele SR (2020) How should we quantify uncertainty in statistical inference? Stat Sci 35:191–206. https://doi.org/10.3389/fevo.2020.00035 Smarandache F (2014) Introduction to neutrosophic statistics. arXiv https://doi.org/10.48550/ARXIV.1406.2000 Der Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct. Saf 31:105–112. https://doi.org/10.1016/j.strusafe.2008.06.020 Lombardi AM (2017) The epistemic and aleatory uncertainties of the ETAS-type models: An application to the Central Italy seismicity. Sci Rep 7:11812. https://doi.org/10.1038/s41598-017-11925-3 Klir GJ, Folger TA (1988) Fuzzy Sets, Uncertainty, and Information. Prentice Hall, New Jersey. https://doi.org/10.1002/sres.3850050411 Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353. https://doi.org/10.1016/S0019-9958(65)90241-X Das S, Roy B, Kar M, Kar S, Pamucar D (2020) Neutrosophic fuzzy set and its application in decision making. J Ambient Intell Humaniz Comput 11. https://doi.org/10.1007/s12652-020-01808-3 Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 Singh R, Tiwari SN (2025) Improved estimator for population mean utilizing known medians of two auxiliary variables under neutrosophic framework. Neutrosophic Syst Appl 25:38–52. https://doi.org/10.61356/j.nswa.2025.25443 Topal S, Taş F, Broumi S, Kirecci O (2020) Applications of neutrosophic logic of smart agriculture via Internet of Things. 12:105–115. https://doi.org/10.5281/zenodo.4281345 Salama AA, Alhabib R (2024) Unveiling uncertainty: Exploring the potential of neutrosophic statistics for artificial intelligence. Plithogenic Log Comput 2:73–85. https://doi.org/10.61356/j.plc.2024.2393 Tahir Z, Khan H, Aslam M, Shabbir J, Mahmood Y, Smarandache F (2021) Neutrosophic ratio-type estimators for estimating the population mean. Complex Intell Syst 7:2991–3001. https://doi.org/10.1007/s40747-021-00439-1 Smarandache F (2019) Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), Pythagorean fuzzy set, q-rung orthopair fuzzy set, spherical fuzzy set, etc. arXiv https://doi.org/10.48550/ARXIV.1911.07333 Alomair AM, Shahzad U (2023) Neutrosophic mean estimation of sensitive and non-sensitive variables with robust Hartley–Ross-type estimators. Axioms 12:578. https://doi.org/10.3390/axioms12060578 Kumar S, Kour SP, Choudhary M, Sharma V (2022) Determination of population mean using neutrosophic, exponential-type estimator. Lobachevskii J Math 43:3359–3367. https://doi.org/10.1134/s1995080222140219 Khan Z, Gulistan M, Kausar N, Park C (2021) Neutrosophic Rayleigh model with some basic characteristics and engineering applications. IEEE Access 9:71277–71283. https://doi.org/10.1109/ACCESS.2021.3078150 Aslam M, Arif OH (2024) Neutrosophic regression modeling with dummy variables: Applications and simulations. Int J Anal Appl 22:114. https://doi.org/10.28924/2291-8639-22-2024-114 Miari M, Anan MT, Zeina MB (2022) Neutrosophic two way ANOVA. Int J Neutrosophic Sci 18:72–83. https://doi.org/10.54216/IJNS.180306 Singh S (2025) A neutrosophic set theory based approach for time series forecasting. Int J Res Trends Innov. http://www.ijrti.org/papers/IJRTI2512113.pdf Aslam M, Raza MA, Ahmad L (2019) Acceptance sampling plans for two-stage process for multiple manufacturing lines under neutrosophic statistics. J Intell Fuzzy Syst 36:7839–7850. https://doi.org/10.3233/JIFS-182849 Ye J (2014) Clustering methods using distance-based similarity measures of single-valued neutrosophic sets. J Intell Syst. https://doi.org/10.1515/jisys-2013-0091 Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562. https://doi.org/10.1016/S0898-1221(03)00016-6 Molodtsov D (1999) Soft set theory—First results. Comput Math Appl 37:19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 Fujita T, Smarandache F (2025) Hyperneutrosophic set and forest hyperneutrosophic set with practical applications in agriculture. Optim Agric. https://doi.org/10.61356/j.oia.2025.2478 Saeed M, Shafique I (2024) Relation on Fermatean neutrosophic soft set with application to sustainable agriculture. HyperSoft Set Methods Eng. https://doi.org/10.61356/j.hsse.2024.18250 Angammal S, Grace G (2024) Neutrosophic goal programming technique with bio inspired algorithms for crop land allocation problem. Sci Rep 14. https://doi.org/10.1038/s41598-024-69487-0 Srikanth M, Mohan R, Naik M (2024) Neutrosophic logic-based crop yield prediction and risk assessment using least squares regression. Neutrosophic Syst Appl. https://doi.org/10.61356/j.nswa.2024.23362 Zulqarnain RM, Xin XL, Saqlain M, Smarandache F (2020) Generalized aggregate operators on neutrosophic hypersoft set. Neutrosophic Sets Syst 36:271–281. https://digitalrepository.unm.edu/nss_journal/vol36/iss1/20 Alanazi BA, Alrashdi I (2023) A neutrosophic approach to edge-based anomaly detection in smart farming systems. Neutrosophic Sets Syst 58:211–224. https://fs.unm.edu/nss8/index.php/111/article/view/3541 Gomathi S, Karpagadevi M, Krishnaprakash S, Revathy A, Broumi S (2024) Cubic spherical neutrosophic sets for advanced decision-making. Neutrosophic Sets Syst 73:24. https://digitalrepository.unm.edu/nss_journal/vol73/iss1/24 Chakraborty A, Mondal S, Broumi S (2019) De-neutrosophication technique of pentagonal neutrosophic number and application in minimal spanning tree. Neutrosophic Sets Syst 29:1–18. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1431&context=nss_journal Rashno E, Minaei-Bidgoli B, Guo Y (2020) An effective clustering method based on data indeterminacy in neutrosophic set domain. Eng Appl Artif Intell 89:103411. https://doi.org/10.1016/j.engappai.2019.103411 Kaviyarasu M, Rajeshwari M, Alqahtani M (2025) Neutrosophic hypersoft topological framework for agricultural decision-making. Eur J Pure Appl Math 18:590–615. https://doi.org/10.29020/nybg.ejpam.v18i2.5905 Angammal S, Grace HG, Martin N, Smarandache F (2024) Multi attribute neutrosophic optimization technique for optimal crop selection in Ariyalur district. Neutrosophic Sets Syst 73:1. https://digitalrepository.unm.edu/nss_journal/vol73/iss1/16 Kaya NS, Dengiz O (2024) Assessment of the neutrosophic fuzzy-AHP and predictive power of soil quality indicators for maize silage. Comput Electron Agric 218:109446. https://doi.org/10.1016/j.compag.2024.109446 Kousar S, Sangi M, Kausar N, Pamucar D, Ozbilge E, Cagin T (2023) Multi-objective optimization model for uncertain crop production under neutrosophic fuzzy environment: A case study. AIMS Math. https://doi.org/10.3934/math.2023380 Sudha S, Lathamaheswari M, Broumi S (2024) Long run behaviour of single valued neutrosophic hidden Markov model. In: 12th Int. Conf. Mech. Eng. (TSME-ICoME 2022) https://doi.org/10.1063/5.0209796 Borah G, Dutta P (2024) Fuzzy risk analysis in crop selection using information measures on quadripartitioned single-valued neutrosophic sets. Expert Syst Appl 255:124750. https://doi.org/10.1016/j.eswa.2024.124750 Cheng W, Ma T, Wang X, Wang G (2022) Anomaly detection for Internet of Things time series data using generative adversarial networks with attention mechanism in smart agriculture. Front Plant Sci 13:890563. https://doi.org/10.3389/fpls.2022.890563 Goyal V, Yadav A, Kumar S, Mukherjee R (2024) Lightweight LAE for anomaly detection with sound-based architecture in smart poultry farm. IEEE Internet Things J 11:8199–8209. https://doi.org/10.1109/jiot.2023.3318298 Liu P, Han Q, Wu T, Tao W (2023) Anomaly detection in industrial multivariate time-series data with neutrosophic theory. IEEE Internet Things J 10:13458–13473. https://doi.org/10.1109/jiot.2023.3262612 Al-Masri E (2025) Deciding when not to decide: Indeterminacy-aware intrusion detection with NeutroSENSE. In: 2025 IEEE World AI IoT Congress (AIIoT), pp. 0142–0148 https://doi.org/10.1109/aiiot65859.2025.11105216 Catalano C, Paiano L, Calabrese F, Cataldo M, Mancarella L, Tommasi F (2022) Anomaly detection in smart agriculture systems. Comput Ind 143:103750. https://doi.org/10.1016/j.compind.2022.103750 Benameur R, Dahane A, Kechar B, Benyamina A (2024) An innovative smart and sustainable low-cost irrigation system for anomaly detection using deep learning. Sensors 24. https://doi.org/10.3390/s24041162 Mohanraj I, Ashokumar K, Naren J (2016) Field monitoring and automation using IoT in agriculture domain. Procedia Comput Sci 93:931–939. https://doi.org/10.1016/j.procs.2016.07.275 Benos L, Tagarakis AC, Dolias G, Berruto R, Kateris D, Bochtis D (2021) Machine learning in agriculture: A comprehensive review. Sensors 21:3758. https://doi.org/10.3390/s21113758 Kodati S, Selvaraj J (2019) Smart agricultural using Internet of Things, cloud and big data. Int J Innov Technol Explor Eng 8:3718–3722. https://doi.org/10.35940/ijitee.J9671.0881019 Jdid M, Smarandache F (2023) Optimal agricultural land use: An efficient neutrosophic linear programming method. Neutrosophic Syst Appl. https://doi.org/10.61356/j.nswa.2023.76 Zhang K, Chen Z, Wang Y (2025) A novel approach for agricultural carbon emission reduction by integrating fermatean neutrosophic set with WINGS and AHP-EWM. Sci Rep 15:391. https://doi.org/10.1038/s41598-024-84423-y Mutlu N, Dengiz O, Kaya N, Saygın F, Pacci S, Demirkaya S, Ay A, Mutlu A, Arslan B, Kaya Y, Başaran B, Bozdağ M, Özer E, Çini E (2025) Assessing the neutrosophic fuzzy-AHP based soil quality index for sugar beet: A comparative study of multi-class logistic regression, random forest, and one-against-all support vector machine models. Expert Syst Appl 295:128862. https://doi.org/10.1016/j.eswa.2025.128862 Özkan B, Dengiz O, Alaboz P, Kaya NS (2023) A new hybrid approach to assessing soil quality using neutrosophic fuzzy-AHP and support vector machine algorithm in sub-humid ecosystem. J Mt Sci 20. https://doi.org/10.1007/s11629-022-7749-z Veerasamy K, Fredrik T (2023) Intelligent farming based on uncertainty expert system with butterfly optimization algorithm for crop recommendation. J Internet Serv Inf Secur 13:158–169. 10.58346/JISIS.2023.I4.011 Jafar M, Saqlain M, Shafiq A, Khalid M, Akbar H, Naveed A (2020) New technology in agriculture using neutrosophic soft matrices with the help of score function. https://doi.org/10.5281/ZENODO.3742406 Rahman A, Saeed M, Alburaikan A, Khalifa H (2022) (2022) An intelligent multiattribute decision-support framework based on parameterization of neutrosophic hypersoft set. Comput. Intell. Neurosci. https://doi.org/10.1155/2022/6229947 Saeed M, Rahman A, Arshad M (2021) A study on some operations and products of neutrosophic hypersoft graphs. J Appl Math Comput 68:2187–2214. https://doi.org/10.1007/s12190-021-01614-w Zulqarnain R, Siddique I, Ali R, Jarad F, Samad A, Abdeljawad T (2021) Neutrosophic hypersoft matrices with application to solve multiattributive decision-making problems. Complexity 5589874 (2021). https://doi.org/10.1155/2021/5589874 Ajay D, Charisma J, Boonsatit N, Hammachukiattikul P, Rajchakit G (2021) (2021) Neutrosophic semiopen hypersoft sets with an application to MAGDM under the COVID-19 scenario. J. Math. https://doi.org/10.1155/2021/5583218 Rahman A, Saeed M, Arshad M, El-Morsy S (2021) Multi-attribute decision-support system based on aggregations of interval-valued complex neutrosophic hypersoft set. Appl. Comput. Intell. Soft Comput. 4368770 (2021). https://doi.org/10.1155/2021/4368770 Saeed M, Shafique I, Günerhan H (2025) Fundamentals of fermatean neutrosophic soft set with application in decision making problem. Int J Math Stat Comput Sci. https://doi.org/10.59543/ijmscs.v3i.10625 Yiarayong P (2024) Enhancing multi-criteria decision-making in smart farming using (p, q)-rung orthopair fuzzy hypersoft sets and weighted aggregation operators. Int J Inf Technol 17:2695–2700. https://doi.org/10.1007/s41870-024-02266-2 Riaz M, Hamid M, Afzal D, Pamucar D, Chu Y (2021) Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets. PLoS ONE 16. https://doi.org/10.1371/journal.pone.0246485 Banik B, Chakraborty A (2023) Comparative study between GRA and MEREC technique on an agricultural-based MCGDM problem in pentagonal neutrosophic environment. Int J Environ Sci Technol. https://doi.org/10.1007/s13762-023-04768-1 Saqlain M, Kumam P, Kumam W (2025) Optimizing agricultural decision-making with integrated MCDM-MCDA methods: A case study on crop economics. Yugosl J Oper Res. https://doi.org/10.2298/yjor240915008s Mohamed M, Alaa N, Arain B, Sallam K (2025) A hierarchical soft computational model for optimizing agricultural UAVs: Recruiting neutrosophic theory and tree soft sets. Neutrosophic Syst Appl. https://doi.org/10.63689/2993-7159.1275 Puška A, Božanić D, Nedeljković M, Janošević M (2022) Green supplier selection in an uncertain environment in agriculture using a hybrid MCDM model: Z-numbers–fuzzy LMAW–fuzzy CRADIS model. Axioms 11:427. https://doi.org/10.3390/axioms11090427 Alamoodi A, Garfan S, Deveci M, Albahri O, Albahri A, Yussof S, Homod R, Sharaf I, Moslem S (2024) Evaluating agriculture 4.0 decision support systems based on hyperbolic fuzzy-weighted zero-inconsistency combined with combinative distance-based assessment. Comput Electron Agric 227:109618. https://doi.org/10.1016/j.compag.2024.109618 Sandra M, Narayanamoorthy S, Suvitha K, Pamucar D, Simić V, Kang D (2024) A trace to median index based fuzzy decision making technique for weed management in agricultural systems. IEEE Access 12:165185–165202. https://doi.org/10.1109/access.2024.3493605 Zhang Q, Zhang H (2024) Assessing agri-food waste valorization challenges and solutions considering smart technologies: An integrated fermatean fuzzy multi-criteria decision-making approach. Sustainability. https://doi.org/10.3390/su16146169 Rouyendegh B, Savalan Ş (2022) An integrated fuzzy MCDM hybrid methodology to analyze agricultural production. Sustainability. https://doi.org/10.3390/su14084835 Sleem A, Abdel-Basset M, El-Henawy IM (2020) PyIVNS: A Python tool for interval-valued neutrosophic sets. SoftwareX 12:100632. https://doi.org/10.1016/j.softx.2020.100632 Khalifa NEM, Smarandache F, Manogaran G, Loey M (2021) A study of neutrosophic set significance on deep transfer learning models: An experimental case on a limited COVID-19 chest X-ray dataset. Cogn Comput 13:1–16. https://doi.org/10.1007/s12559-020-09802-9 Paudel D, Moran MS, Deines JM (2025) CY-Bench: A benchmark dataset for subnational crop yield forecasting. Earth Syst Sci Data. https://doi.org/10.5194/essd-2025-83 Muruganantham P, Wibowo S, Grandhi S, Samrat NH, Islam N (2022) A systematic literature review on crop yield prediction with deep learning and remote sensing. Remote Sens 14:1990. https://doi.org/10.3390/rs14091990 Mallik S (2024) Recommendation system using neutrosophic logic in agriculture. Int J Intell Syst Appl Eng 12:735–741. https://ijisae.org/index.php/IJISAE/article/view/6279 Lundberg S, Lee S-I (2017) A unified approach to interpreting model predictions. https://doi.org/10.48550/arXiv.1705.07874 . arXiv Ribeiro MT, Singh S, Guestrin C (2016) Why should I trust you? Explaining the predictions of any classifier. In: Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., pp. 1135–1144 https://doi.org/10.1145/2939672.2939778 Additional Declarations The authors declare no competing interests. Supplementary Files floatimage1.png Graphical abstract Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9385567","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Systematic Review","associatedPublications":[],"authors":[{"id":621321204,"identity":"04d40f1b-cf4e-4d13-a0ab-9813999d1641","order_by":0,"name":"Deva dharshini","email":"","orcid":"","institution":"Tamil Nadu Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"Deva","middleName":"","lastName":"dharshini","suffix":""},{"id":621321240,"identity":"d5277d8a-f890-4106-a027-d7663229d7b4","order_by":1,"name":"Kalpana Muthuswamy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACCQbmBjCDHy7ETFALI0SLZBvJWgyOEeswyfaDbQ9+7rCLNr7fe/AzD4OdPAM77wG8WqR5EtsNe88k5247xpcszcOQbNjAzJeAV4scQ2KbBG8bM1ALjwFQC3MCAzOPAX4t/A/bJP+21edubuMx/s3DUE9Yi7REYps0b9vh3A1sPGZAWw4T1iI542G7sWzb8dwZx3LMLOcYHDdsI6RF4nzysYdv26pz+5vPGN94U1Etz89/Br8WIGBDYhugconRMgpGwSgYBaMACwAAU5w6Ys8hRyAAAAAASUVORK5CYII=","orcid":"","institution":"Tamil Nadu Agricultural University","correspondingAuthor":true,"prefix":"","firstName":"Kalpana","middleName":"","lastName":"Muthuswamy","suffix":""}],"badges":[],"createdAt":"2026-04-11 07:28:22","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9385567/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9385567/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106854734,"identity":"46a2bcad-aab2-43d1-ab1b-140c65329ca7","added_by":"auto","created_at":"2026-04-14 07:13:08","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":98798,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnnual Scientific Production\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/4a8f8f27ad8954835a789e76.png"},{"id":106854736,"identity":"655bdb81-d737-4150-b3cb-514e3bb3fd55","added_by":"auto","created_at":"2026-04-14 07:13:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":626001,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGlobal collaboration\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/a2592acb49368913a3858c5f.png"},{"id":106854773,"identity":"3a963083-9659-4d17-b8b1-086ce8255bfc","added_by":"auto","created_at":"2026-04-14 07:13:16","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":135029,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eKeyword Co-occurrence Network\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/af976dd8c8393cc36573b174.png"},{"id":106854769,"identity":"f55fd4a2-a472-491b-b908-4728db4a614f","added_by":"auto","created_at":"2026-04-14 07:13:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":486297,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSoft, hypersoft and extended neutrosophic sets in smart agriculture.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/a1675b3e5db846f0f3c8d2d3.png"},{"id":106854732,"identity":"c7265c42-4771-4795-854b-519696b5f31d","added_by":"auto","created_at":"2026-04-14 07:13:07","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":412727,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNeutrosophic Cognitive Map (NCM)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/70899bb052af6715339c5f52.png"},{"id":106854730,"identity":"f828e7f0-1473-4aed-b0f4-a3f02f44188b","added_by":"auto","created_at":"2026-04-14 07:13:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1763533,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNeutrosophic operators logic-based in irrigation.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/e908c11fcf0aaa5a7d9db6c5.png"},{"id":106854731,"identity":"e614d014-8642-4750-a2f0-0c3b63d5a8d6","added_by":"auto","created_at":"2026-04-14 07:13:07","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":332412,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA schematic figure of decision support of neutrosophic logic-based smart agriculture.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/df1e78954fcb3e7dc09d626d.png"},{"id":106854777,"identity":"c258f05a-daba-4a9f-8548-55a47a196280","added_by":"auto","created_at":"2026-04-14 07:13:21","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":394204,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eUnified Neutrosophic Intelligent Decision Framework for Smart agriculture\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/1a27ae81dd1e07b1892cb4cd.png"},{"id":106960938,"identity":"961f1c81-f28a-4dc9-baf8-e9b602db07ba","added_by":"auto","created_at":"2026-04-15 09:23:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6059226,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/46f3dcf6-8789-4271-8277-0afb77b201f1.pdf"},{"id":106854758,"identity":"be599645-664c-403f-a0c9-4095e1a8fd7c","added_by":"auto","created_at":"2026-04-14 07:13:11","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":280919,"visible":true,"origin":"","legend":"\u003cp\u003eGraphical abstract\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9385567/v1/b2be4e7297b42f70f8401d2c.png"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eNeutrosophic Knowledge-Based Frameworks for Intelligent Decision Support Under Deep Uncertainty: Applications in Smart Agriculture\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe global population is projected to reach 9.7\u0026nbsp;billion by 2050, which means that food production efficiency and security will have to be increased by 60% above their existing levels primarily to fulfil the demand. As a result, the agricultural sector has seen a significant shift, and the idea of smart agriculture and Agriculture 4.0 have emerged [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Smart agriculture is an interdisciplinary subfield of agricultural science, technology, data science, and environmental science, aimed at increasing the efficiency of farming and solving problems like land shortage, climate change, and resource depletion. This transformation shifts farm management toward data-driven decisions that optimize labour, water and fertilizer use while at the same time lowering environmental damage [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. This transformation creates a cyber-physical farm management system, which unites the network infrastructure, powerful hardware, and advanced analytics [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. IoT, artificial intelligence, robotics, big data analytics, and remote sensing are some of the key enabling technologies in smart agriculture. [\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eCore technologies\u003c/h3\u003e\n\u003cp\u003ePrimarily among these technologies is the Internet of Things (IoT), which enables real-time data acquisition and connectivity in real-time. Sensors commonly employed in smart farming include those used for monitoring soil moisture, plant disease detection, pH, temperature. These technologies make possible AI-powered decision tools that leverage the combination of IoT, sensor networks, climate analytics, and machine learning for the provision of climate-informed guidance on crop management. Wireless communication like LoRa, NB-IoT are extensively used in precision agriculture to transfer data to processing systems, thereby improving crop quality and agricultural production [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Machine learning and deep learning models are used to analyse the acquired data for time-series forecasting [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], yield prediction [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], disease detection [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], and resource optimization using spatial data [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eData uncertainties\u003c/h3\u003e\n\u003cp\u003eWhile these are promising technologies with vast benefits, there is often a limitation to their performance because of the uncertainties inherently existing in the data [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Research indicates global crop models, has shown that models trained using historical data could be susceptible to biased responses in extreme climatic conditions, highlighting the systematic difficulty regarding uncertainty in crop growth data due to drought conditions, warming, rainfall, and seasonality [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Field sensors often suffer from calibration drift, communication loss, and physical damage, leading to biased and missing readings in IoT networks [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Power connectivity problems and lack of historical records make its datasets incomplete and diverse [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], and issues in integrating diverse agricultural datasets such as weather data, soil, and market data into multiple scales and resolutions also increase heterogeneity in datasets [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Qualitative insights provided through linguistic terms, such as qualitative classifications and rankings, can be heavily influenced by uncertainty and incomplete information [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFurthermore, classical probability struggles to capture the nuanced thresholds and risk levels that agronomists and policy experts often face. Classical statistics usually assumes that observations are realized around a single true value, and uncertainty is mainly due to sampling variability [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. However, alternative uncertainty frameworks are motivated by the chance that these representations fail to adequately capture epistemic and internal uncertainty [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo better understand these limitations, distinguishing between aleatory and epistemic types of uncertainty in agricultural data is essential [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Aleatory uncertainty is caused by inherent randomness in the world, while epistemic uncertainty is due to a lack of knowledge [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Both types affect predictions and forecasting in agriculture datasets, but they are conceptually different, one is irreducible randomness, and the other is ignorance. Indeterminacy caused by incomplete and vague data specifically challenges Bayesian statistics, classical statistics, probability and fuzzy or intuitionistic fuzzy sets (IFS) [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Even Bayesian methods tend to give only one predictive distribution, which restricts the explicit modelling of indeterminacy (p (Y | data)). Classical sets and probability only consider aleatory uncertainty, mainly as random variation around true value and treat data as precise value. Zadeh et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] implemented fuzzy sets to represent vagueness by the use degree of membership values. While fuzzy sets represent graded truth (\u003cem\u003e\u0026micro;\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ϵ\\:\\left[\\text{0,1}\\right]\\)\u003c/span\u003e\u003c/span\u003e) and can handle vague terms, they do not distinguish between partial truth and lack of knowledge [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Atanassov et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] further extended the FSs theory to Intuitionistic fuzzy sets (IFS) introduced a hesitation based on both the degree of membership (\u003cem\u003eT)\u003c/em\u003e and non-membership (\u003cem\u003eF)\u003c/em\u003e, expressed as \u003cem\u003e1-T-F\u003c/em\u003e, they restrict the sum (\u003cem\u003eT\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eI\u003c/em\u003e + \u003cem\u003eF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1); however, it is often diluted because different kinds of indeterminacy are combined into the same residual term. This makes these frameworks unable to capture the indeterminacy as an independent, first-class component.\u003c/p\u003e\n\u003ch3\u003eNeutrosophic statistics as a solution\u003c/h3\u003e\n\u003cp\u003eTo address these limitations, neutrosophic statistics (NS) emerge as a powerful generalization of Intuitionistic fuzzy sets (IFS), specifically designed to handle uncertain, indeterminate, and inconsistent information [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan additionalcitationids=\"CR30 CR31 CR32 CR33 CR34\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Neutrosophic set is a mathematical framework developed by Smarandache, designed to handle uncertain, unclear, vague, and incomplete data, addressing the constraints of classical probability and fuzzy sets, the sum can range up to 3 (0\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eT\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eI\u003c/em\u003e+ \u003cem\u003eF\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;3). The idea of neutrosophic sets is a broader platform, building upon the principles of the fuzzy and classical sets [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. It differs from previous approaches because neutrosophic sets maintain distinct categories of truth, indeterminacy, and falsity. It can represent the real-world agricultural data where data is often conflicting or vague. Soil moisture, pH, temperature and humidity sensors may fail, drift or transmit inconsistent readings, whereas neutrosophic logic distinguishes each value into T (how believable), F (evidence against it) and I (how uncertain it is), rather than depending on a single crisp or fuzzy value. In the precision agriculture mechanism model, neutrosophic logic is integrated with IoT and cloud computing to automate geometric soil analysis and environmental monitoring while directly using uncertainty in calculation. Neutrosophic logic expands to other forms of neutrosophic statistical techniques, many of which have been proposed, including multiple regression analysis [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], analysis of variance [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], forecasting [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], and acceptance sampling plans [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Moreover, neutrosophic techniques have been applied to unsupervised learning tasks including cluster analysis along distance and similarity metrics [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis review synthesizes a wide range of previous studies, with an emphasis on how neutrosophic sets improve Multi-Criteria Decision-Making (MCDM) frameworks for resolving conflicting agricultural parameters. It highlights how neutrosophic approaches to decision-making are enhanced by addressing uncertainties inherent in agricultural data, including those from soil conditions to market dynamics. Furthermore, the efficiency of neutrosophic models in handling ambiguous or contradictory situations is compared with classical statistical methods and represents an advanced computational intelligence paradigm extending fuzzy reasoning for intelligent decision-making under deep uncertainty.. Finally, the article examines the current challenges of applying neutrosophic statistics in agriculture, paving the way for future research in this interdisciplinary field.\u003c/p\u003e"},{"header":"2. Bibliometric Overview of Neutrosophic Research in Smart Agriculture","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Data Source and Analysis Tools\u003c/h2\u003e \u003cp\u003eThis review used the Scopus database as its bibliometric source due to its comprehensive coverage of peer-reviewed sources in all fields of engineering, agricultural sciences, and interdisciplinary studies. TITLE-ABS-KEY field was used to conduct the search to achieve high topical relevance. A search was made with TITLE-ABS-KEY ((\"neutrosophic\" OR \"neutrosophic logic\" OR \"neutrosophic set\" OR \"indeterminacy\") AND (\"agriculture\" OR \"farming\" OR \"crop\" OR \"soil\" OR \"irrigation\" OR \"smart agriculture\" OR \"precision agriculture\")). The initial searched yielded 223 records. There were no restrictions on the publication year so as to fully encompass the temporal development of neutrosophic research in the agricultural sector. The records recovered were directly exported out of Scopus in CSV format and imported into the biblioshiny web interface of the bibliometrix R package to analyse. Descriptive statistics and annual scientific production trends and source dynamics were generated with the help of Biblioshiny, whereas network analyses, such as country collaboration and keyword co-occurrence, were used to study the intellectual and thematic structure of the area. The combination of these tools made it possible to conduct a systematic and reproducible bibliometric evaluation of neutrosophic logic applications in smart agriculture.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Publication Trends\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. shows the scientific output concerning neutrosophic research in the field of agriculture annually. These findings suggest that the publication activity was very low before 2017 and since then, it has gradually risen between 2018 and 2021. There is a sharp growth peak after 2022 and the highest number of publications are found between 2024\u0026ndash;2025. The apparent decline in 2026 is attributed to the indexing lag typical of real-time database access, rather than a reduction in scholarly interest. In general, the identified tendency defines neutrosophic applications in agriculture as a research area with a swift rise in academic interest.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Country-wise Collaboration\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. shows the network of international co-authorship of countries participating in the research of neutrosophic in smart agriculture. The network also emphasizes the geographical dispersion of research output and the strength of the collaborative links. India and China are significant contributors, which means the active research in the area of neutrosophic decision-making and uncertainty modelling of agricultural systems. Such countries also share a wide range of collaborative relationships with scholars in the Middle East, Europe and North America. The United States and some European nations show a moderate yet steady involvement which suggests increasing interdisciplinary involvement. Contrastingly, the low representation of Africa and South America indicates research gaps in the region. In general, the collaboration network demonstrates a skewed yet growing international research environment with the necessity to collaborate on a larger international level. This regional concentration in Asia reflects the high priority given to Agriculture 4.0 and computational intelligence in these developing countries.\u003c/p\u003e \u003cp\u003e \u003cb\u003e2.4. Keyword Co-occurrence and Research Themes\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe thematic form of neutrosophic research in agriculture is captured by the keyword co-occurrence network in Fig.\u0026nbsp;3. The main focus of the methodological approach of the field is represented by a dominant central cluster around neutrosophic decision-support systems and uncertainty-aware modelling. The keywords closely related are those that involve decision-making, optimization and handling of indeterminacy, as applied in the agricultural environment. Secondary clusters are related to application-based themes, such as crop management, soil assessment, irrigation planning, and decision models related to sustainability. Peripheral clusters are new or niche areas of research, which mean that it is at an initial stage of diversification with respect to application areas. The inter-cluster connectivity is rather low, which indicates an emerging field of research where theoretic and practical contributions are still in their early stages of integration. This shows the necessity of the enhanced methodological integration between sophisticated neutrosophic models and practical smart agriculture infrastructures. Notably, the keywords co-occurrence network reveals a significant green cluster dedicated specifically to multi-criteria-decision-making (MCDM) and the Analytic Hierarchy Process (AHP), validation the selection of MCDM as the primary analytical lens for this review.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Neutrosophic Theory and Modelling Basics","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Neutrosophic set (NS): core concept\u003c/h2\u003e \u003cp\u003eA neutrosophic set on a universe X is typically written as\u003c/p\u003e \u003cp\u003eNS = {(\u003cem\u003ex, T(x), I(x), F(x)) | x\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ϵ\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eX\u003c/em\u003e}, (1)\u003c/p\u003e \u003cp\u003eT-I-F triplet; \u003cem\u003eT(x)\u003c/em\u003e - level of truth/membership, \u003cem\u003eI(x) -\u003c/em\u003e level of indeterminacy, \u003cem\u003eF(x) -\u003c/em\u003e level of falsity or membership, with the range of \u003cem\u003e0\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\le\\:\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003eT(x), I(x), F(x)\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\le\\:1\\)\u003c/span\u003e\u003c/span\u003e and 0\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\le\\:T+I+F\\le\\:3.\\)\u003c/span\u003e\u003c/span\u003e These functions return values in the open interval of (0, 1), without restrictive sum constraint found in fuzzy or intuitionistic sets (\u003cem\u003eT\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eI\u003c/em\u003e + \u003cem\u003eF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1). This generality allows NS to capture inconsistencies commonly found in real datasets [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. This tricomponent setup allows for a more nuanced representation of real-world agricultural data compared to traditional binary and even fuzzy logic systems [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Single-valued neutrosophic sets (SVNS)\u003c/h2\u003e \u003cp\u003eFor real-world application, single-valued neutrosophic sets restrict \u003cem\u003eT(x), I(x)\u003c/em\u003e and \u003cem\u003eF(x)\u003c/em\u003e to the unit interval [0,1], while maintaining their independence. Due to the balance expressive power with computational simplicity, SVNS has become widely adopted in MCDM, predictive modelling, and sustainable agriculture assessments. Typical notation is,\u003c/p\u003e \u003cp\u003eA = [\u003cem\u003ex, u(x), r(x), v(x)): x\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ϵ\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eX\u003c/em\u003e]. (2)\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eu(x)\u003c/em\u003e \u0026ndash; Single-valued truth, \u003cem\u003er(x)\u003c/em\u003e \u0026ndash; Indeterminacy, \u003cem\u003ev(x)\u003c/em\u003e \u0026ndash; Level of falsity, with respect to a mild condition such as \u003cem\u003e0\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\le\\:\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003eu(x), r(x), v(x)\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\le\\:3\\)\u003c/span\u003e\u003c/span\u003e. In the case of decision-making processes, neutrosophic logic is a system that allows the inclusion of more dimensions for the analysis. It finds great application in fields such as smart agriculture, where choices have to be derived from sensor data that might be influenced by the noise, be incomplete, or changed by the environment [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. For instance, a smart agriculture mechanism model integrated with neutrosophic theory, IoT, and cloud computing has been demonstrated to perform more detailed calculations by considering uncertain situations inherent in neutrosophic numbers and log [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. This integration allows for better decision-making in irrigation, pest control, and nutrient management by incorporating the degrees of truth, indeterminacy, and falsity associated with various environmental parameters and crop responses\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Soft, hypersoft and extended neutrosophic sets\u003c/h2\u003e \u003cp\u003eLet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\:\\)\u003c/span\u003e\u003c/span\u003ebe a universe and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\:\\)\u003c/span\u003e\u003c/span\u003ea set of parameters. A neutrosophic soft set (NSS) is a parameterized family of neutrosophic sets defined as a mapping:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:F:E\\to\\:\\mathcal{N}\\mathcal{S}\\left(X\\right),\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere each parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:e\\in\\:E\\)\u003c/span\u003e\u003c/span\u003eis associated with a neutrosophic set over \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e. Each object\u0026ndash;parameter pair is described by a triplet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(T,I,F\\right)\\)\u003c/span\u003e\u003c/span\u003e, enabling flexible modelling of uncertain multi-attribute decision problems [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNeutrosophic logic, when combined with a soft set theory, offered by Molodtsov et al. [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] improves decision-support systems by handling uncertain and imprecise parameters. Within the context of neutrosophic soft sets, suggested by Maji et al. [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], every pair of an object-parameter is described as a neutrosophic triplet (\u003cem\u003eT, I, F\u003c/em\u003e). Where T, I and F are the degrees of truth, indeterminacy, and falsity, respectively. In this method, the emphasis is laid on the attribution of neutrosophic membership values to the objects of the universal set to the attribution of the same to parameters, thus providing additional flexibility in modelling uncertainty. As a result, soft neutrosophic sets offer a powerful framework to multi-criteria decision-making (MCDM) issues. An example is when determining the best variety of crop to grow, the yield potential, resistance to disease, and irrigation needs are among the factors that may be weighted with uncertainty, and with this method, a more realistic approach to this problem can be obtained.\u003c/p\u003e \u003cp\u003eNeutrosophic hypersoft sets extend neutrosophic soft sets by allowing tuples of sub-parameters. Let\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\:\\:\\:\\:\\:E={E}_{1}\\times\\:{E}_{2}\\times\\:\\cdots\\:\\times\\:{E}_{n},\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere each \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{i}\\)\u003c/span\u003e\u003c/span\u003erepresents a sub-attribute (e.g., soil fertility, climatic zone, irrigation availability). An NHSS maps each parameter tuple to a neutrosophic set on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e. The neutrosophic hypersoft sets (NHSS) and neutrosophic hypersoft topological structures extend existing from neutrosophic soft and hypersoft models, allowing tuples of sub-parameters, including climatic zone, soil fertility, and water availability, and specifying neutrosophic structures on their Cartesian products. This feature of modelling has been effectively applied to use in advanced agricultural multi-criteria decision-making (MCDM) problems, such as farm site selection. NHSS is able to reflect complex interdependencies of the agricultural decision processes, including choosing the crop depending on the interaction between the climate zone, soil fertility, and availability of irrigation as can be observed in recent research [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. This degree of complexity is particularly vital within the agricultural sector, where the decision factors are commonly of a nested and hierarchical nature. For instance, soil quality which is a critical agricultural parameter that may be sub-divided into sub-attributes like pH, nitrogen content, phosphorus content, and organic matter, each having a neutrosophic measure attached to it. NHSS consequently enables the finer modelling of multi-level hierarchical uncertainty, which promotes the more accurate agricultural planning and optimizes resource allocation. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Schematically illustrates the structural shift from soft neutrosophic sets to neutrosophic hypersofts and further to extended neutrosophic models to manage deep layers of agricultural uncertainty.\u003c/p\u003e \u003cp\u003eExtended neutrosophic sets are a generalization of standard neutrosophic sets where \u003cem\u003eT, I\u003c/em\u003e, and \u003cem\u003eF\u003c/em\u003e can be expressed as intervals and multiple values instead of being expressed as single numerical values. This generalization leads to some forms such as interval-valued neutrosophic sets, multi-valued neutrosophic sets and n-valued neutrosophic sets, that provide broader frameworks for uncertainty. They are useful especially when more specific numerical estimates cannot be made, as is prevalent within agricultural decision problems that require crop yield estimation, price forecasts, and effects of fertilizer in uncertain situations. Consequently, extended neutrosophic models have been successfully integrated into advanced decision-support frameworks, including neutrosophic goal programming and bio-inspired optimization algorithms, to address complex multi-criteria decision-making problems frameworks is in crop land allocation problems that typically maximize profit and output and minimize costs in conditions of uncertainty of yield, market price, and the effectiveness of applied fertilizer [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Such extended sets can be substituted with a neutrosophic goal programming method that may include bio-inspired algorithms to optimize land distribution, and as an effective approach to indeterminate criteria e.g. seed growth response and fertilizer suitability. These enhanced neutrosophic models enable a more detailed computation, through an explicit consideration of subtle uncertainty in agricultural data to enhance the accuracy and reliability of agriculture decision-making in smart agriculture applications, such as IoT-based monitoring systems, predictive modelling, and risk assessment [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Neutrosophic Relations and Cognitive Maps\u003c/h2\u003e \u003cp\u003eNeutrosophic Cognitive Maps (NCMs) are extension of fuzzy cognitive maps by including indeterminate relationship represented by the value I. Vertex in NCM may have states; 1 (active), 0 (inactive), I (indeterminate). Each vertex (nodes) in NCM indicate a factor, variable or indicator that influence in agriculture. Edges are weighted from the set {-1, 0, 1, I}, that shows the possibility of positive, negative, neutral or uncertain influence, NCMs represent a powerful tool to model agricultural sustainability, especially when the interactions between variables are not completely known. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Shows a neutrosophic cognitive map of agricultural decision variables as state nodes {1, 0, 1} interconnected by directed edges of weight {-1, 0, 1, I} to characterize positive, negative, neutral and indeterminate casual relationships.\u003c/p\u003e \u003cp\u003eZulqarnain et al. [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] introduce generalized aggregate operators on NHSS, including extended union, extended intersection, AND/OR operations, and necessity operators, and study their properties for multi-criteria decision making (MCDM). These operators are designed to aggregate evaluations from multiple experts and multiple sub-attributes, supporting selection and planning in complex decision problems. In a smart-agriculture context, the same operators can be interpreted as neutrosophic logic operators that fuse heterogeneous sensor readings and expert assessments such as combining soil, crop and weather sub-criteria into a single neutrosophic decision score for tasks such as crop variety selection, irrigation scheduling, fertilizer recommendation, or disease risk assessment.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.5. Neutrosophic Logic operators\u003c/h2\u003e \u003cp\u003eNeutrosophic logic extends classical logic operators AND, OR, and NOT to represent three-dimensional uncertainty. These operators have been applied effectively in anomaly detection for smart farming to handle ambiguous sensor data [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eNeutrosophic AND:\u003c/h3\u003e\n\u003cp\u003e \u003cem\u003eA\u003c/em\u003e \u0026and;\u003csub\u003e\u003cem\u003eN\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eB\u003c/em\u003e= (min (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, T\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e​), max (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, I\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​)\u003c/em\u003e, max (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, F\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​\u003c/em\u003e)) (5)\u003c/p\u003e \u003cp\u003eIn the case of two neutrosophic sets A and B, the truth value of A AND B is given by the minimum of the truth values, the indeterminacy value is given by the maximum of the indeterminacy values, while the falsity value is given by the maximum of the two falsity values. This operator represents a model of situations where multiple conditions have to be simultaneously met, and the uncertainty in one condition raises the overall uncertainty.\u003c/p\u003e\n\u003ch3\u003eNeutrosophic OR:\u003c/h3\u003e\n\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e \u003cem\u003eA\u003c/em\u003e \u0026or;\u003csub\u003e\u003cem\u003eN\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eB\u003c/em\u003e= (max (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, T\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e​), min (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, I\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e​), min (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, F\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e​)) (6)\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe truth degree of A OR B is the maximum of their truth degrees, the indeterminacy degree is the least of their indeterminacy degrees, and the falsity degree is the minimum of their falsity degrees. This operator is used when any one of several conditions can fulfil a requirement.\u003c/p\u003e\n\u003ch3\u003eNeutrosophic NOT:\u003c/h3\u003e\n\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e\u0026not;\u003csub\u003e\u003cem\u003eN\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eA\u003c/em\u003e= (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, I\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​, T\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e​) (7)\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe complement of a neutrosophic set A changes its truth and falsity degrees and keeps the indeterminacy. This operator stands for the negation of a proposition. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. demonstrates the operational workflow of netrosophic logic in agricultural decision support, where sensor inputs are transformed into (\u003cem\u003eT, I. F\u003c/em\u003e) triplets and synthesized using AND, OR, and NOT operators. These operators are very essential to decision support systems that are used in agriculture. As an example, in a smart irrigation system, decisions might be influenced by several factors such as soil moisture (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e), weather forecast (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e), and crop growth stage (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Neutrosophic operators may merge these uncertain sensor readings and expert knowledge to find out the best irrigation action while at the same time they recognize the environmental data indeterminacy [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. In the case of crop yield prediction, they have the capability of integrating various uncertain inputs such as rainfall, temperature, and soil nutrient levels in order to forecast future yields while also being very clear about the indeterminacy for each factor [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.6. Cubic Spherical Neutrosophic Sets (CSNS)\u003c/h2\u003e \u003cp\u003eCubic Spherical Neutrosophic sets represents a high-level extension of classical neutrosophic sets. Their purpose is to enhance the modelling of multi-level and geometrically structured uncertainty. Correspondingly, each element in CSNS is represented not only by the neutrosophic membership degree of truth (T), indeterminacy (I), and falsity (F) but also by the additional radius parameter (r) describing the spatial interpretation of uncertainty. It expressed as,\u003c/p\u003e \u003cp\u003eA = {(\u003cem\u003ex\u003c/em\u003e, [\u003cem\u003eT\u003c/em\u003e\u003csup\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eT\u003c/em\u003e\u003csup\u003e\u003cem\u003eU\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e)], [\u003cem\u003eI\u003c/em\u003e\u003csup\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eI\u003c/em\u003e\u003csup\u003e\u003cem\u003eU\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e)], [\u003cem\u003eF\u003c/em\u003e\u003csup\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eF\u003c/em\u003e\u003csup\u003e\u003cem\u003eU\u003c/em\u003e\u003c/sup\u003e (\u003cem\u003ex\u003c/em\u003e)], (\u003cem\u003eT\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eI\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eF\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)))} (8)\u003c/p\u003e \u003cp\u003eWhere the membership values are subject to the following constraints:\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e{\u003cem\u003eT\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eI\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e), \u003cem\u003eF\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e), \u003cem\u003er\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)}, 0\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eT\u003c/em\u003e \u003csup\u003e2\u003c/sup\u003e +\u003cem\u003eI\u003c/em\u003e \u003csup\u003e2\u003c/sup\u003e +\u003cem\u003eF\u003c/em\u003e \u003csup\u003e2\u003c/sup\u003e \u0026le; 1 (8a)\u003c/p\u003e\u003cp\u003er(x) = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\surd\\:\\)\u003c/span\u003e\u003c/span\u003e1- (\u003cem\u003eT\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(\u003cem\u003ex\u003c/em\u003e)+ \u003cem\u003eI\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(\u003cem\u003ex\u003c/em\u003e)+ \u003cem\u003eF\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(\u003cem\u003ex\u003c/em\u003e)) (8b)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eCSNS would generally extend this concept by integrating cubic sets with spherical neutrosophic sets. Spherical neutrosophic sets enable decision-makers to separately assign grades for truth, indeterminacy, and falsity such that their total is less than or equal to one. The term \"cubic\" usually refers to the combination of interval-valued information with fuzzy numbers, thus allowing a more detailed depiction of uncertain data. In the case of agriculture, where sensor data might be inaccurate for instance, soil moisture levels varying within a certain range and expert opinions might be unclear like \"the crop is moderately healthy\", CSNS could provide a high-level technique for the aggregation and data analysis. As an example, determining the health of the crop might mean that not only single values for truth, indeterminacy, and falsity are considered, but also intervals for these values, thus indicating a deeper level of imprecision in diagnosis or prediction. This would, therefore, enable more dependable decision, making in precision agriculture areas, such as the detection of the earliest symptoms of disease or the efficient use of irrigation when it is difficult to establish exact thresholds. In particular, this improvement adds to geometric robustness and considers multi-level uncertainty. The CSNS has broad applicability in agriculture, especially for crop ranking under climatic variability, risk evaluation in crop planning, assessing risk under fluctuating climatic conditions and resource allocation and sustainability assessment [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Current neutrosophic application in smart agriculture","content":"\u003cp\u003eThe wide range of application of neutrosophic logic to smart agriculture are summarised\u003c/p\u003e \u003cp\u003ein Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e, illustrating its incorporation into decision-support systems for land allocation, soil assessment, yield forecasting, and intelligent anomaly detection under uncertainty.\u003c/p\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.1. IoT- Enabled Smart Farming\u003c/h2\u003e \u003cp\u003eThe combination of neutrosophic logic and IoT smart farming systems provides a reliable way to deal with uncertainty in real-time farming systems. Sensor data regarding soil analysis, climate, GPS farming, and crop analysis coordinates are often incomplete or noisy. Neutrosophic-IoT systems can effectively overcome this problem by representing raw data as neutrosophic triplets before processing. The core components of the Neutrosophic Inference Engine (NIED) and the corresponding smart agriculture applications are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCore Neutrosophic Inference Engine (NIED) Components and Their Smart Agriculture application\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComponent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCore Technique\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKey Innovation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSmart Agriculture Application\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNIED\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophication and de-neutrosophication\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTransformation of pentagonal and trapezoidal neutrosophic numbers using area-based and mean-based methods\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIoT data acquisition and pre-processing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNIED\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic clustering and analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOutlier and boundary handling using Lagrange multipliers and G-metrics on single-valued neutrosophic set\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eData classification and big data analytics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNIED\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic IF-THEN rules\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRule-based inference under indeterminate conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReal-time decision support in smart farming\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eRecently, studies have shown that cloud-assisted and edge-enabled IoT systems in which neutrosophic inferences are incorporated enhance reliability of irrigational decision, nutrient scheduling as well as environmental monitoring. These platforms are capable of increasing the flexibility and scalability of a precision agriculture system to dynamic field conditions through the explicit modelling of indeterminacy of data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Decision support and Crop recommendation systems\u003c/h2\u003e \u003cp\u003eKaviyarasu et al. [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e] have proposed \u0026ldquo;Algorithm 1\u0026rdquo;, using neutrosophic hypersoft sets (NFHSs) for farm site selection, define variables with double sets (\u003cem\u003eS\u003c/em\u003e1, Γ1) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({S}_{2},{{\\Gamma\\:}}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e, their combination through \u0026ldquo;resultant union,\u0026rdquo; and ranking sites based on the final score (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{O}_{i}={r}_{i}-{c}_{i}\\)\u003c/span\u003e\u003c/span\u003e), which is obtained through summation of rows(\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) and columns (\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), selecting the one with highest score (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{j}=\\text{a}\\text{r}\\text{g}{\\text{m}\\text{a}\\text{x}}_{i}\\left\\{{O}_{i}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e) to handle uncertainty.\u003c/p\u003e \u003cp\u003eKaviyarasu et al. [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e] continued to advance the usage of neutrosophic hypersoft sets in \u0026ldquo;Algorithm 2\u0026rdquo;, incorporating topology with the integration of open sets based on the location and decision parameters, along with integration of data based on advanced operations, and site selection based on net scores (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{O}_{i}={r}_{i}-{c}_{i}\\)\u003c/span\u003e\u003c/span\u003e)- achieving consistent results like identifying site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{2}\\)\u003c/span\u003e\u003c/span\u003e optimal across more than 12 parameters for robust uncertainty management. The effectiveness of hypersoft and cubic neutrosophic models for capturing interdependencies among multiple criteria and expert assessments. Neutrosophic DSS offer greater robustness, and their outcomes are more explainable compared to traditional MCDM approaches, particularly for regions facing climatic uncertainty and resource constraints [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAngammal and Grace. [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e] model crop selection for medium farm holders in Ariyalur as a multi-objective, multi-attribute neutrosophic optimization problem, where truth, indeterminacy and falsity membership functions explicitly represent uncertainty in yield, prices, seed growth, fertilizer suitability and other agri-inputs. By minimizing under-deviation in truth and over-deviation in indeterminacy and falsity, the neutrosophic goal programming models simultaneously optimize production, profit and expenditure under constraints of land, labour, water and food requirements. This demonstrates that neutrosophic decision-support systems can provide practical, field-validated crop allocation and crop choice recommendations for specific regions such as Ariyalur district.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Soil, Water, and Land Suitability assessment\u003c/h2\u003e \u003cp\u003eSoils and land evaluation processes are based on a set of physical, chemical, and biological indicators showing spatial variability, which are often measured with a certain degree of imprecision. To overcome these challenges, the Neutrosophic Fuzzy\u0026ndash;Analytic Hierarchy Process (NF-AHP) and similar hybrid models have been applied in soil quality indexing and land suitability analysis.\u003c/p\u003e \u003cp\u003eBy incorporating neutrosophic judgments into pairwise comparisons, these approaches explicit model expert uncertainty and conflicting assessments. From a methodological perspective, the criteria for soil and land evaluation are first hierarchically organized, and expert judgments are elicited through linguistic terms that are converted to neutrosophic numbers. Neutrosophic pairwise comparison matrices are then set up for each criterion relationship, capturing the truth, indeterminacy, and falsity. Criterion weights are determined via neutrosophic aggregation and normalization processes, continuing with consistency analysis adapted to the neutrosophic format. Weighted criteria are eventually combined with spatial or quantitative indicators of soil to calculate the composite soil quality or land suitability indices. Empirical results show that neutrosophic-enhanced soil and land evaluation models outperform classical AHP and fuzzy-AHP in selecting suitable zones for cultivation and determining land degradation risk, especially in the case of climate-sensitive agricultural systems [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Yield Prediction and agriculture risk assessment\u003c/h2\u003e \u003cp\u003eNeutrosophic logic has emerged as a vital tool for modelling yield and risk under climate variability, incomplete data, and expert vagueness, where classical probability and even fuzzy logic struggle. Recent literature integrates neutrosophic logic with statistical and deep learning models for crop-yield prediction under climate stress. A recent framework combines neutrosophic logic with least squares regression and an independence test to estimate crop-loss functions and classify crops by profitability and environmental risk, focus specifically on extreme-weather events. Deep learning, particularly restricted Boltzmann machines (RBM), is used to capture complex nonlinear relations between climate, management variables, and yield, while neutrosophic representations encode truth, falsity, and indeterminacy in expert and sensor inputs [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. The model is demonstrated gains in estimation of yield damage and provides farmers with functional risk indicators to support adaptation decisions such as diversification and input adjustment [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAt the planning level, multi-objective neutrosophic fuzzy linear programming has been applied to optimize seasonal crop portfolios such as wheat and rice in canal-irrigated systems under uncertain water availability and climate shocks. Here, yield, water requirements, storage limits, and canal capacities are modelled as neutrosophic\u0026ndash;fuzzy parameters so that both randomness and imprecision like expert scenarios rather than hard data are reflected. The optimization aims to maximize net profit and total production while addressing to hydrological and infrastructural limitations, demonstrating that neutrosophic fuzzy algorithms can handle yield uncertainty more effectively than conventional fuzzy models when parameters are susceptible to sudden, climate-driven changes [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNeutrosophic approaches are also being embedded in probabilistic sequence models for yield forecasting. A single-valued neutrosophic hidden Markov model (HMM) has been proposed to represent long-run weather regimes and their transitions, with neutrosophic probability capturing indeterminate states. This model is used to forecast crop yields and notify farmers about likely favourable and unfavourable yield states under evolving weather conditions [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. In addition to forecasting, neutrosophic logic supports risk assessment in crop selection. Quadripartitioned single-valued neutrosophic sets and associated entropy/similarity measures have been used to transform expert linguistic assessments of multiple risks (climate, soil, pest, market) into interpretable risk levels for alternative crops. A case study on mustard and paddy shows how final risk levels such as \u0026ldquo;absolutely high\u0026rdquo; vs \u0026ldquo;very low\u0026rdquo; can be robustly derived from imprecise, multi-expert inputs, improving strategic crop choice under uncertainty [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. Neutrosophic goal programming has likewise been used to determine optimal land allocation under uncertain yields, prices, and agronomic factors, leveraging separate truth, indeterminacy, and falsity membership functions and bio-inspired optimization to maximize profit and production under resource constraints [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Anomaly Detection and edge intelligence in smart farming\u003c/h2\u003e \u003cp\u003eAnomaly detection has grown in importance in the agricultural field with sensors networks and edge or fog computing systems being installed to assist in smart farming. The sensor measurements are prone to noise, missing values, and variation in the environment making traditional anomaly detectors to have missed detection or false alarm [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e]. In reaction, edge-based deep learning systems, including CNN-LSTM based and LSTM (Convolutional Neural Network- Long Short-Term Memory) autoencoders, have shown that intelligence pushed to sensors can be highly detected and low latency in smart farms settings [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e]. The neutrosophic logic provides a complementary model in that it explicitly models truth, falsity, and indeterminacy in both data and decisions. Neutrosophic multivariate time-series models together with graph learning have been applied in the context of Industrial IoT to improve the performance of the anomaly detector when the dimensionality is high and the sensor data is distorted [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. Likewise, neutrosophic-enhanced ensemble methods to detect intrusion in the IoT break down prediction confidence into truth, falsity, and indeterminacy and allow systems to avoid making uncertain decisions, which is a valuable feature of edge deployments that demand trust in autonomous actions [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e]. Even though the majority of anomaly detection methods in smart agriculture still utilize probabilistic or deep learning models like GANs (Generative Adversarial Network), autoencoders, CNN-LSTM models, and ensemble outlier detectors instead of neutrosophic logic [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e], neutrosophic modelling has already been used in agricultural decision-support systems to operate with uncertain soil and environmental data [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. This suggests a potential future direction of research: namely, the incorporation of neutrosophic representations into edge-based anomaly detection in smart farming, wherein edge nodes should be able to distinguish sensor behaviour as normal or abnormal, but should in addition be able to describe indeterminate states that humans may choose to inspect or conserve via conservative control. This can improve the reliability of systems, minimize unnecessary alarms, and facilitate the open human-in-the-loop decision-making at the network edge [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e]. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Provides a consolidated comparative overview of recent neutroosphic methodological applied across various smart agriculture domains, highlighting the modelling approaches, evaluation criteria, and practical outcomes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e4.6. Implication of agriculture statistics and practice\u003c/h2\u003e \u003cp\u003eThe neutrosophic approaches fill a significant interface between agricultural statistics and decision science by looking at indeterminacy as a first-class statistical object instead of noise to be discarded or pushed to traditional probabilistic models [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Neutrosophic statistics is based on classical methodologies by breaking down the observations into determinate and indeterminate parts, thus allowing the analysis of experimental data, soil measurements, and yield records that naturally incorporate vagueness and does not arbitrarily treat these as completely precise. Furthermore, model output is not limited to single point estimates or confidence interval, but instead can be presented as neutrosophic triplets (\u003cem\u003eT\u003c/em\u003e, \u003cem\u003eI\u003c/em\u003e, \u003cem\u003eF\u003c/em\u003e) which are naturally related to action-based decision criteria like accept, review, or intervene. This model resembles the decisions made by agronomists and farmers in a real situation when they are uncertain [\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e]. Although regression analysis, geostatistical modelling, and machine learning are crucial in large-scale agriculture prediction processes, neutrosophic logic improves the trustworthiness of decisions in scenarios where data is incomplete, measurement uncertainty, or expert judgments are deployed [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. Neutrosophic methods are typically best applied in conjunction with conventional statistical and machine learning predictors, working at the decision-support and interpretation tiers of smart agriculture systems rather than substituting existing predictive pipelines [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eDesign and analysis\u003c/strong\u003e \u003cp\u003eNeutrosophic analysis of experimental data enables the expression of treatment effects that demonstrate indeterminacy components. It is especially useful in cases where field replicas are few, measurement errors are large, and expert-based assessments, including disease severity scales or visual soil ratings, are subjective or ambiguous in nature [\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e].\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eRisk-sensitive advisory\u003c/strong\u003e \u003cp\u003eNeutrosophic yield and soil fertility models should be used to detect borderline cases with high indeterminacy, and hence provide advice to do further sampling or expert evaluation instead of making overconfident advisories. This knowledge-based risk management guidance increases the safety and reliability of agricultural advisory services particularly in climate-sensitive areas [\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e].\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKey neutrosophic logic in smart-agriculture studies\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApplication domain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFactors considered\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMain outcome for smart agriculture\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrop land allocation and optimal crop mix\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic Goal Programming\u0026thinsp;+\u0026thinsp;bio-inspired algorithms (GWO, SGO, PSO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYield, prices, seed growth, fertilizer suitability; land, labour, water, food demand\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMaximizes profit and production, minimizes expenditure; neutrosophic\u0026ndash;bio-inspired solution outperforms fuzzy methods\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLand allocation \u0026amp; resource planning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic linear programming\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRegions A_j (60,150,20,10 ha), demands b_i (800,200,600,1000,2500 tons), productivity Na_ij [wheat A1= {4,6} tons/ha], profit Np_i [wheat={1400,1600}/ton]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMaximizes neutrosophic profit under constraints, robust to yield/price uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCarbon emission reduction policy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFermatean neutrosophic using WINGS with AHP-EWM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9 factors (τ4\u0026thinsp;=\u0026thinsp;carbon policy, τ6\u0026thinsp;=\u0026thinsp;tech adoption, τ8\u0026thinsp;=\u0026thinsp;sustainable management)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePolicy prioritization tool (τ₄=carbon policy 0.220 top)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaize silage soil quality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNF-AHP weights using MLR and RFR prediction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89 samples, 28 indicators (slope 0.0746, MBC 0.0787)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMLR\u0026thinsp;\u0026gt;\u0026thinsp;RFR (R\u0026sup2;=0.99), precision soil assessment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIoT anomaly detection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSVNS with decision matrices using correlation scoring\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSensor streams (uncertainty, missingness)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReal-time edge anomaly detection, fewer false alarms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFarm site selection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic hypersoft topological MCDM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSoil, climate, water, economics\u0026thinsp;+\u0026thinsp;sub-attributes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRobust farm selection despite contradictory judgments\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSugar beet soil quality assessment in semi-arid soils\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic Fuzzy-AHP (NF-AHP) for SQI; predicted with multi-class logistic regression, random forest, one-against-all SVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePhysical, chemical, fertility, biological indicators under semi-arid conditions; linked to NDVI from Sentinel-2A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNF-AHP-based SQI framework with ML classifier accuracy for data-driven soil/crop management in semi-arid agriculture\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrop yield \u0026amp; risk assessment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic least squares with RBM (Restricted Boltzmann Machine)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRice/banana yields, weather extremes, 160 farmers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRisk-aware yield prediction with damage categories under uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoil quality assessment in sub-humid ecosystem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic fuzzy-AHP using support vector machine\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSoil indicators scored via linear/nonlinear functions in sub-humid mountain areas\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHybrid SQI model for accurate soil quality evaluation aiding sustainable land management\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCrop recommendation under uncertainty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic\u0026ndash;paraconsistent uncertainty expert system with Butterfly Optimization Algorithm (UES-BOA)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSoil fertility and climate parameters: Nitrogen (N), Phosphorus (P), Potassium (K), temperature, relative humidity, soil pH, rainfall; 2200 instances, 22 crop classes; certainty degree (\u0026micro;) and contradiction degree (λ) via neutrosophic and paraconsistent logic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRobust crop recommendation under uncertainty with optimized rules, achieving 95.8% accuracy and outperforming ANN, MLP, and SVM.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMulti-criteria decision-making in agriculture (farmer performance selection)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutrosophic Soft Matrices (NSM) with score and value functions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFarmer performance indicators including crop productivity, input use, and resource management, evaluated using truth, indeterminacy, and falsity degrees.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReliable farmer selection under uncertainty using score-based neutrosophic soft matrices.\u003c/p\u003e \u003cp\u003e.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Advanced neutrosophic frameworks for smart agriculture","content":"\u003cp\u003eModern farmework evolve from classic neutrosophic methods by integrating complex mathematical structures capable of addressing complex agricultural decision-making defined by interacting criteria and deep uncertainty. Broadly, the literature on neutrosophic logic-based decision-making in agriculture is dominated by two primary branches: (i) neutrosophic hypersoft and topological models, (ii) hybrid neutrosophic-fuzzy MCDM frameworks.\u003c/p\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Neutrosophic hypersoft and Topological frameworks\u003c/h2\u003e \u003cp\u003eAdvanced neutrosophic hypersoft and topological structures extend classical neutrosophic sets to represent multi-attribute, hierarchically structured, and highly uncertain information typical of smart agriculture. Neutrosophic hypersoft sets generalize soft and neutrosophic sets by allowing each parameter such as soil type, climate and input type to be partitioned into sub-parameters and handled as multi-argument tuples, enabling precision modelling of complex agronomic criteria under truth, indeterminacy and falsity membership degrees [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e]. In a 2025 study Kaviyarasu et al. [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e] proposed neutrosophic hypersoft topological framework for agricultural decision-making constructs a neutrosophic agricultural topology in which open sets are generated from a neutrosophic sub-base and standard topological notions like basis, subspace, interior and closure are adapted to hypersoft neutrosophic spaces [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. The research introduces two algorithms, one directly on neutrosophic hypersoft sets and another operating on neutrosophic hypersoft topological spaces. Numerical case studies using real agricultural data included crop alternatives evaluated under multiple agronomic and economic factors show that this topology-based MCDM approach improves the efficiency and reliability of decision strategies when the number of variables is large and uncertainty is high.\u003c/p\u003e \u003cp\u003eTopological variants, such as neutrosophic semi-open and semi-closed hypersoft sets, further refine this framework. By defining semi-open and semi-closed neutrosophic hypersoft sets and constructing corresponding topologies, decision algorithms have been developed for multi-attribute group decision-making. Although these models were demonstrated using COVID-19 case studies, the authors explicitly indicate that similar MAGDM (Multi-Attribute Group Decision-Making) schemes can be adapted to agricultural yield optimization and related planning problems [\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e, \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBeyond pure topology, hypersoft hybrids extensions such as possibility neutrosophic hypersoft sets, interval-valued complex neutrosophic hypersoft sets, fermatean neutrosophic hypersoft provide enhanced decision- capabilities by incorporating possibility degrees, phase information and higher-order uncertainty [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e, \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e, \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e]. These models have been applied to sustainable agriculture case studies in which environmental, social, and economic criteria and their sub-attributes are evaluated under indeterminate and conflicting evidence, demonstrating improved handling of ambiguity and trade-offs compared to conventional MCDM methods [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Hybrid Neutrosophic-Fuzzy and MCDM models\u003c/h2\u003e \u003cp\u003eHybrid neutrosophic\u0026ndash;fuzzy and MCDM models provide structured decision support in smart agriculture by combining rich representations of uncertainty with powerful ranking and weighting procedures. Neutrosophic and advanced fuzzy sets such as fermatean, q-rung orthopair, t-spherical, hypersoft allow expert opinions, sensor data, and qualitative assessments to be expressed with degrees of truth, falsity, and indeterminacy rather than crisp numbers, capturing hesitation and conflicting evidence typical of climate, market- and soil-driven decisions [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan additionalcitationids=\"CR82\" citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e]. These uncertainty models are then embedded in MCDM frameworks such as AHP, TOPSIS, CODAS, GRA, SPOTIS, MACBETH, or new hybrid schemes to weigh criteria and rank alternatives, for example when comparing agricultural production techniques, smart farming modes, UAV platforms, or vertical-farm technologies under multiple economic, environmental and social criteria [\u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e, \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn practice, such hybrid models have been used to analyse sustainable agriculture and water-demand strategies with fuzzy AHP\u0026ndash;TOPSIS variants, to optimize green supplier selection using Z-numbers with fuzzy LMAW\u0026ndash;CRADIS, to evaluate Agriculture 4.0 decision support systems with hyperbolic fuzzy weighting and CODAS, and to select smart farming or robotic agri-farming modes under (p, q)-rung or q-rung orthopair fuzzy environments [\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e, \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e]. They also support specialized problems like designing sustainable weed-management strategies in a t-spherical probabilistic hesitant fuzzy setting or ranking agri-food waste-valorization solutions with fermatean fuzzy SWARA\u0026ndash;DEMATEL\u0026ndash;QFD [\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e, \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e]. Across these applications, hybrid neutrosophic\u0026ndash;fuzzy MCDM models consistently aim to improve realism of expert input, integrate heterogeneous criteria, and deliver stable rankings checked by sensitivity and comparative analyses, making them a core advanced framework for smart-agriculture decision-making under deep uncertainty. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. is a summary of representative hybrid neutrosophic-fuzzy MCDM frameworks and their applications in agriculture.\u003c/p\u003e \u003cp\u003eThe NF-AHP weighting of 28 soil indicators enabled more nuanced handling of ambiguous field measurements and expert judgments, and produced stable, interpretable importance scores for key physical, chemical, productivity, and biological indicators in a climate-sensitive region [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. Complementary work on land allocation for medium farm holders proposed a bi-level TOPSIS-based neutrosophic programming technique, showing higher net profit and better risk handling than fuzzy and intuitionistic fuzzy optimization approaches under uncertain water supply, labour, and yield conditions [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. In sustainable agriculture, fermatean neutrosophic hypersoft MCDM algorithms further demonstrate that integrating neutrosophic structures with soft sets yields more flexible and realistic evaluations of agricultural techniques and inputs than conventional fuzzy-only schemes [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNeutrosophic\u0026ndash;Based Hybrid MCDM Models Applied to Agricultural Planning and Sustainability\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAgricultural application\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeutrosophic\u0026ndash;fuzzy AHP and TOPSIS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoil quality indexing and suitability ranking under uncertain indicators\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeutrosophic TOPSIS and programming (bi-level)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLand allocation and farm planning with profit\u0026ndash;risk trade-offs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFermatean neutrosophic hypersoft MCDM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSustainable practice and input selection using environmental, social\u0026ndash;economic criteria\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6. Unified neutrosophic Intelligent Decision Framework for Smart Agriculture","content":"\u003cp\u003eTo effectively incorporate neutrosophic intelligence in smart agricultural decision environments, this review proposes a Unified Neutrosophic Intelligent Decision Framework that incorporates five interconnected layers that provide deep uncertainty management and intelligent decision-making. The Data Layer will obtain real-time agricultural data via IoT-powered sensors installed in farming fields, where they will monitor soil, climatic, and crop-related data that are vital in precision agriculture [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The Uncertainty Representation Layer leverages neutrosophic modelling to explicitly describe truth, falsity, and indeterminacy related to heterogeneous agricultural data to facilitate the successful manipulation of incomplete, inconsistent and noisy data [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. In the Reasoning Layer, neutrosophic aggreagation operators combine multi-source uncertain data into analysable representations, which are robust to conflicting or partially missing data [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e, \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e]. The Decision Layer integrates neutrosophic Multi-Criteria Decision-Making (MCDM) models to evaluate the alternatives across economic, environmental, and operating criteria to assist in optimized agricultural planning and resource allocation [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Finally, the Application Layer translates the framework into the real world by implementing smart farming management with the help of intelligent Decision Support Systems (DSS), which transforms the results of analysis into recommendations and action. The proposed layered architecture defines a unified interface between IoT-based data acquisition, uncertainty-sensitive reasoning, and intelligent decision-making, hence presenting a conceptual foundation for next-generation smart agricultural systems working on deep uncertainty. In order to present a systematized understanding of uncertainty-aware decision-making in smart agriculture, Unified Neutrosophic Intelligent Decision Framework is proposed, consisting of interrelated layers such as data acquisition, uncertainty representation, reasoning, decision-making, and implementation deployment, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"7. Limitations and critical assessment","content":"\u003cp\u003e\u003cstrong\u003e7.1.\u0026nbsp;Methodological limitations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.1.1.\u0026nbsp; \u0026nbsp; \u0026nbsp; Parameter selection and subjectivity:\u0026nbsp;\u003c/strong\u003eDefining the neutrosophic triple (\u003cem\u003eT, I, F\u003c/em\u003e), mapping of linguistic terms to membership values and selection of aggregation operators remains predominantly expert-driven and usually ad hoc. These choices can directly influence outcomes crop ranking, land suitability, and yield risks estimation. As a result, decision outcomes shift significantly when alternative parametrization or mapping schemes are applied. Despite this sensitivity, systematic sensitivity analyses are reported in the existing literature, a limitation that has been consistently cited in both the application-based research and methodological reviews [91, 92].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.1.2.\u0026nbsp; \u0026nbsp; \u0026nbsp;Lack of standardized metrics and benchmarks:\u003c/strong\u003e Currently, no standardized set of evaluation metrics exists that simultaneously accounts for predictive accuracy and uncertainty calibration for neutrosophic predictions. This lack of standardisation hinders comparative analysis comparison and meta-analysis across studies report only task-specific measures such as classification accuracy or MCDM ranking scores. According to recent surveys, it is necessary to have shared benchmark and standardized evaluation protocols to facilitate a fair comparison among neutrosophic, fuzzy, and ML-based approach, and XAI-driven models [67, 93].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.2.\u0026nbsp;Practical implementation limitations;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.2.1.\u0026nbsp; \u0026nbsp; \u0026nbsp;Limited software tools and packages:\u003c/strong\u003e Software support for neutrosophic modelling lacks a unified framework contrast to the robust ecosystem of fuzzy logic and mainstream machine learning systems (scikit-learn, TensorFlow). Although prototype libraries such as PyIVNS (Python Interval-Valued Neutrosophic Set) prove the viability of inter-valued neutrosophic operations, they are not yet widely integrated into standard data-science work-flows. This limitation hinders reproducibility and slows the transition of neutrosophic methods into practical agricultural decision-support system [91].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e7.2.2.\u0026nbsp; \u0026nbsp; \u0026nbsp;Computational complexity of hypersoft and topological variants:\u0026nbsp;\u003c/strong\u003eHypersoft sets and hypersoft topologies are advanced neutrosophic frameworks that offer significant expressive power for multi-subattribute MCDM by enabling robust topological operations and cartesian products of multiple sub-attributes. However, this increased modelling flexibility is paired with large computational complexity especially when applied to large-scale spatial or remote sensing datasets. Developers of hypersoft topologies model identify challenges related to dimensionality growth and algorithmic scalability, which may limit real-world utility in data-intensive agricultural applications [54, 78].\u003c/p\u003e"},{"header":"8. Research gaps","content":"\u003cp\u003e\u003cstrong\u003e8.1.\u0026nbsp;Few extensive field validations:\u0026nbsp;\u003c/strong\u003eMulti-site and multi-season experiments across a wide range of agro-ecological conditions are notably scarce, and most neutrosophic research studies in agriculture have been restricted to localized pilot projects, or on simulated data. Lack of field evaluation on a large scale fails to validate that these approaches are robust to real-world farming systems, in heterogenous climatic and management conditions [67, 93].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e8.2.\u0026nbsp;Scarce comparison with strong ML baselines:\u0026nbsp;\u003c/strong\u003eMost neutrosophic works are limited in their comparison with fuzzy or Intuitionistic fuzzy variants. Insufficient benchmarking against good machine learning baselines like Random forests, XGBoost and deep neural networks, is usually missing, undermining statements about performance improvements. Evidence suggests that tree-based ensembles and deep learning models are already very strong in predicting factors such as crop yield prediction and remote sensing. In the absence of systematic comparisons, it remains difficult to distinguish between the benefits of explicitly uncertainty modelling and the improvements due to more complex models or feature engineering [56, 94].\u003c/p\u003e"},{"header":"9. Future research direction for Smart agriculture","content":"\u003cp\u003eFuture research directions in smart agriculture, particularly through the lens of neutrosophic sets, highlight the necessity of a methodological roadmap. Primary research must pivot to the systematic integration of neutrosophic intelligence with machine learning and deep learning models, emphasizing neutrosophic feature encoding for yield, price, and risk forecasting, and transforming sensor observations into (\u003cem\u003eT, I, F\u003c/em\u003e) triplets prior to learning. Neutrosophic logic is well-positioned for widely adopted in noise-robust learning, yet it is not thoroughly explored within regression models and deep architectures [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Targeted efforts should focus on neuro-neutrosophic hybrid models, neutrosophic-based regularization strategies, and uncertainty-aware loss function designed to enhance generalization in the presence of missing, biased, or heterogeneous agricultural data [\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e95\u003c/span\u003e]. Additionally, the development of neutrosophic explainable-AI (XAI) framework is critical, as interpretability remains a key challenge in data-driven agricultural decision-support systems. Hence, in the coming years, researchers should prioritize integrate neutrosophic logic theories along with other XAI techniques such as SHAP (SHapley Additive exPlanations) [\u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e96\u003c/span\u003e] and LIME (Local Interpretable Model-agnostic Explanations) [97] may enhance transparency and trust in decision-making processes. Furthermore, employing neutrosophic logic tasks in IoT-based edge clouds and cloud infrastructures for support real-time anomaly identification offers significant potential [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Future studies should also investigate scaling neutrosophic models to satellite, UAV (Unmanned Aerial Vehicle), hyperspectral, and other multi-source big-data platforms using cloud-edge collaborative architectures. On the other hand, normalization processes along with the development of common datasets should be executed to facilitate appropriate deployment in policy-focused tasks.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe integration of neutrosophic logic in smart agriculture is a critical evolution in the response to the complexities and uncertainties of agricultural decision-making. Neutrosophic techniques that incorporate neutrosophic linear programming, clustering and IF-THEN rule offers a resilient architecture in optimization of land allocation, resource planning and real-time farming decision. These approaches are effective in mitigating inherent uncertaunty in the agricultural variables, such as the yield, price and environmental factors. To illustrate, interval-valued complex neutrosophic hypersoft sets (IV-CNHS) have been developed, allowing labels to be partitioned into multi-sub parametric tuples, which offers a more detailed and mathematically adequate treatment of the complex, interdependent variables of agricultural systems.\u003c/p\u003e \u003cp\u003eAlthough these developments are encouraging, yet persistent several limitations in its methodology. The subjectivity involved in the selection of parameters based on expert judgment and the manipulation of linguistic words into a value based on membership compromise the integrity of outcomes which may include crop ranking and land suitability assessment. This variability explains why sensitivity analyses are essential, and it is not reported in existing studies often. Furthermore, the absence of standardized measures of assessing neutrosophic outputs makes it complicated to assess the predictive accuracy and uncertainty calibration, which needs for unified standards in this area.\u003c/p\u003e \u003cp\u003eThe development of advanced neutrosophic systems, such as neutrosophic hypersoft sets also improves the ability to manage intricate interdependencies between decision parameters especially in areas with uncertain climatic conditions. These frameworks enable incorporation of various variables in the decision-making process like soil quality and climatic conditions thus enhancing the robustness of the agricultural practices. In conclusion, the neutrosophic logic does propose to improve the decision-making in the smart farming, but it is important to address identified limitations to make it as effective as possible. The further studies and collaboration among experts are required to refining these approaches, establishing the metrics of the standard evaluation, and eventually enhance the productivity and sustainability in an increasingly uncertain climatic- agriculture.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank the Department of Physical Science and Information Technology, Tamil Nadu Agricultural University, Coimbatore, for providing the necessary academic facilities and institutional support that facilitated this review work\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors Contribution\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDevaDharshini: writing original draft, collection of literatures, conceptualization, Editing; Kalpana Muthuswamy: Supervision, review and editing; M Vijayabhama: Supervision; P Vasanthi: Supervision; R Parimalarangan: Supervision.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe article does not contain any studies involving human participants or animal performed by any of the authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate:\u003c/strong\u003e Not applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to publish:\u0026nbsp;\u003c/strong\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData sharing is not applicable to this article as no datasets were generated or analysed during the current study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo potential competing interest was reported by the author(s).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eFischer RA, Byerlee D, Edmeades G (2009) Can technology deliver on the yield challenge to 2050? Agecon Search, Misc. Pap. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.fao.org/4/ak542e/ak542e12a.pdf\u003c/span\u003e\u003cspan address=\"https://www.fao.org/4/ak542e/ak542e12a.pdf\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang J, Trautman D, Liu Y, Bi C, Chen W, Ou L, Goebel R (2024) Achieving the rewards of smart agriculture. Agronomy 14:452. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/agronomy14030452\u003c/span\u003e\u003cspan address=\"10.3390/agronomy14030452\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMusajan A, Lin Q, Wei D, Mao S (2024) Unveiling the mechanisms of digital technology in driving farmers' green production transformation: Evidence from China's watermelon and muskmelon sector. Foods 13:3926. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/foods13233926\u003c/span\u003e\u003cspan address=\"10.3390/foods13233926\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePatel PN, Padaliya M, Sanjay VC, Anand B (2024) Internet of Things: A way of transforming conventional agriculture. Int J Sci Res Sci Eng Technol 11:281\u0026ndash;292. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.32628/ijsrset24115120\u003c/span\u003e\u003cspan address=\"10.32628/ijsrset24115120\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuo D, Malik AW, Ravana SD, Rahman AU, Ahmedy I (2024) Mapping smart farming: Addressing agricultural challenges in data-driven era. Renew Sustain Energy Rev 189:113858. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rser.2023.113858\u003c/span\u003e\u003cspan address=\"10.1016/j.rser.2023.113858\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMansoor S, Iqbal S, Popescu SM, Kim SL, Chung YS, Baek J-H (2025) Integration of smart sensors and IoT in precision agriculture: Trends, challenges and future perspectives. Front Plant Sci 16. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/fpls.2025.1587869\u003c/span\u003e\u003cspan address=\"10.3389/fpls.2025.1587869\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRaj R, Ghosh A, Pal A, Kundu SK, Karmakar S (2025) A brief review on smart farming technologies for precision agriculture. In: 2025 8th Int. Conf. Electron. Mater. Eng. Nano-Technol. (IEMENTech), pp. 1\u0026ndash;5 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/iementech65115.2025.10959551\u003c/span\u003e\u003cspan address=\"10.1109/iementech65115.2025.10959551\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlahmad T, Nem\u0026eacute;nyi M, Ny\u0026eacute;ki A (2023) Applying IoT sensors and big data to improve precision crop production: A review. Agronomy 13:2603. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/agronomy13102603\u003c/span\u003e\u003cspan address=\"10.3390/agronomy13102603\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKamilaris A, Prenafeta-Bold\u0026uacute; FX (2018) Deep learning in agriculture: A survey. Comput Electron Agric 147:70\u0026ndash;90. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2018.02.016\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2018.02.016\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eManogna RL, Dharmaji V, Sarang S (2025) Enhancing agricultural commodity price forecasting with deep learning. Sci Rep 15:20903. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-025-05103-z\u003c/span\u003e\u003cspan address=\"10.1038/s41598-025-05103-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJabed MA, Murad MAA (2024) Crop yield prediction in agriculture: A comprehensive review of machine learning and deep learning approaches. Artif Intell Agric 8:100\u0026ndash;123. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.heliyon.2024.e40836\u003c/span\u003e\u003cspan address=\"10.1016/j.heliyon.2024.e40836\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWani JA et al (2022) Machine learning and deep learning based computational techniques in automatic agricultural diseases detection: Methodologies, applications, and challenges. Arch Comput Methods Eng 29:641\u0026ndash;677. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11831-021-09588-5\u003c/span\u003e\u003cspan address=\"10.1007/s11831-021-09588-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao X, Tang W, Liu Q et al (2025) Impact of agricultural industry transformation based on deep learning model evaluation and metaheuristic algorithms under dual carbon strategy. Sci Rep 15:27929. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-025-14073-1\u003c/span\u003e\u003cspan address=\"10.1038/s41598-025-14073-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMartin N, White J (2024) Water resources\u0026rsquo; AI\u0026ndash;ML data uncertainty risk and mitigation using data assimilation. Water 16:2758. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/w16192758\u003c/span\u003e\u003cspan address=\"10.3390/w16192758\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeinicke S, Frieler K, J\u0026auml;germeyr J, Mengel M (2022) Global gridded crop models underestimate yield responses to droughts and heatwaves. Environ Res Lett 12:4938. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/1748-9326/ac592e\u003c/span\u003e\u003cspan address=\"10.1088/1748-9326/ac592e\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTeh HY, Kempa-Liehr AW, Wang KI-K (2020) Sensor data quality: A systematic review. J Big Data 7:11. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s40537-020-0285-1\u003c/span\u003e\u003cspan address=\"10.1186/s40537-020-0285-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUstun TS, Hussain SMS, Kirchhoff H, Ghaddar B, Strunz K, Lestas I (2019) Data standardization for smart infrastructure in first-access electricity systems. Proc. IEEE 107, 1790\u0026ndash;1802 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/JPROC.2019.2929621\u003c/span\u003e\u003cspan address=\"10.1109/JPROC.2019.2929621\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKarmakar P, Teng SW, Murshed M, Pang S, Li Y, Lin H (2024) Crop monitoring by multimodal remote sensing: A review. Remote Sens Appl Soc Environ 33:101093. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rsase.2023.101093\u003c/span\u003e\u003cspan address=\"10.1016/j.rsase.2023.101093\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUre\u0026ntilde;a R, Kou G, Wu J, Chiclana F, Herrera-Viedma E (2019) Dealing with incomplete information in linguistic group decision making using interval type-2 fuzzy sets. Int J Intell Syst 34:2982\u0026ndash;3014. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/int.22095\u003c/span\u003e\u003cspan address=\"10.1002/int.22095\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDubois D, Prade H (2009) An introduction to bipolar representations of information and preference. Int J Intell Syst 24:843\u0026ndash;873. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/int.20297\u003c/span\u003e\u003cspan address=\"10.1002/int.20297\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLele SR (2020) How should we quantify uncertainty in statistical inference? Stat Sci 35:191\u0026ndash;206. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/fevo.2020.00035\u003c/span\u003e\u003cspan address=\"10.3389/fevo.2020.00035\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSmarandache F (2014) Introduction to neutrosophic statistics. arXiv \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.48550/ARXIV.1406.2000\u003c/span\u003e\u003cspan address=\"10.48550/ARXIV.1406.2000\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDer Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct. Saf 31:105\u0026ndash;112. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.strusafe.2008.06.020\u003c/span\u003e\u003cspan address=\"10.1016/j.strusafe.2008.06.020\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLombardi AM (2017) The epistemic and aleatory uncertainties of the ETAS-type models: An application to the Central Italy seismicity. Sci Rep 7:11812. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-017-11925-3\u003c/span\u003e\u003cspan address=\"10.1038/s41598-017-11925-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKlir GJ, Folger TA (1988) Fuzzy Sets, Uncertainty, and Information. Prentice Hall, New Jersey. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/sres.3850050411\u003c/span\u003e\u003cspan address=\"10.1002/sres.3850050411\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZadeh LA (1965) Fuzzy sets. Inf Control 8:338\u0026ndash;353. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0019-9958(65)90241-X\u003c/span\u003e\u003cspan address=\"10.1016/S0019-9958(65)90241-X\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDas S, Roy B, Kar M, Kar S, Pamucar D (2020) Neutrosophic fuzzy set and its application in decision making. J Ambient Intell Humaniz Comput 11. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12652-020-01808-3\u003c/span\u003e\u003cspan address=\"10.1007/s12652-020-01808-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAtanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u0026ndash;96. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0165-0114(86)80034-3\u003c/span\u003e\u003cspan address=\"10.1016/S0165-0114(86)80034-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSingh R, Tiwari SN (2025) Improved estimator for population mean utilizing known medians of two auxiliary variables under neutrosophic framework. Neutrosophic Syst Appl 25:38\u0026ndash;52. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.nswa.2025.25443\u003c/span\u003e\u003cspan address=\"10.61356/j.nswa.2025.25443\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTopal S, Taş F, Broumi S, Kirecci O (2020) Applications of neutrosophic logic of smart agriculture via Internet of Things. 12:105\u0026ndash;115. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/zenodo.4281345\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.4281345\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSalama AA, Alhabib R (2024) Unveiling uncertainty: Exploring the potential of neutrosophic statistics for artificial intelligence. Plithogenic Log Comput 2:73\u0026ndash;85. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.plc.2024.2393\u003c/span\u003e\u003cspan address=\"10.61356/j.plc.2024.2393\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTahir Z, Khan H, Aslam M, Shabbir J, Mahmood Y, Smarandache F (2021) Neutrosophic ratio-type estimators for estimating the population mean. Complex Intell Syst 7:2991\u0026ndash;3001. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s40747-021-00439-1\u003c/span\u003e\u003cspan address=\"10.1007/s40747-021-00439-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSmarandache F (2019) Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), Pythagorean fuzzy set, q-rung orthopair fuzzy set, spherical fuzzy set, etc. arXiv \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.48550/ARXIV.1911.07333\u003c/span\u003e\u003cspan address=\"10.48550/ARXIV.1911.07333\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlomair AM, Shahzad U (2023) Neutrosophic mean estimation of sensitive and non-sensitive variables with robust Hartley\u0026ndash;Ross-type estimators. Axioms 12:578. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/axioms12060578\u003c/span\u003e\u003cspan address=\"10.3390/axioms12060578\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar S, Kour SP, Choudhary M, Sharma V (2022) Determination of population mean using neutrosophic, exponential-type estimator. Lobachevskii J Math 43:3359\u0026ndash;3367. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1134/s1995080222140219\u003c/span\u003e\u003cspan address=\"10.1134/s1995080222140219\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhan Z, Gulistan M, Kausar N, Park C (2021) Neutrosophic Rayleigh model with some basic characteristics and engineering applications. IEEE Access 9:71277\u0026ndash;71283. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/ACCESS.2021.3078150\u003c/span\u003e\u003cspan address=\"10.1109/ACCESS.2021.3078150\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAslam M, Arif OH (2024) Neutrosophic regression modeling with dummy variables: Applications and simulations. Int J Anal Appl 22:114. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.28924/2291-8639-22-2024-114\u003c/span\u003e\u003cspan address=\"10.28924/2291-8639-22-2024-114\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMiari M, Anan MT, Zeina MB (2022) Neutrosophic two way ANOVA. Int J Neutrosophic Sci 18:72\u0026ndash;83. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.54216/IJNS.180306\u003c/span\u003e\u003cspan address=\"10.54216/IJNS.180306\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSingh S (2025) A neutrosophic set theory based approach for time series forecasting. Int J Res Trends Innov. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.ijrti.org/papers/IJRTI2512113.pdf\u003c/span\u003e\u003cspan address=\"http://www.ijrti.org/papers/IJRTI2512113.pdf\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAslam M, Raza MA, Ahmad L (2019) Acceptance sampling plans for two-stage process for multiple manufacturing lines under neutrosophic statistics. J Intell Fuzzy Syst 36:7839\u0026ndash;7850. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3233/JIFS-182849\u003c/span\u003e\u003cspan address=\"10.3233/JIFS-182849\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYe J (2014) Clustering methods using distance-based similarity measures of single-valued neutrosophic sets. J Intell Syst. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1515/jisys-2013-0091\u003c/span\u003e\u003cspan address=\"10.1515/jisys-2013-0091\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555\u0026ndash;562. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0898-1221(03)00016-6\u003c/span\u003e\u003cspan address=\"10.1016/S0898-1221(03)00016-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMolodtsov D (1999) Soft set theory\u0026mdash;First results. Comput Math Appl 37:19\u0026ndash;31. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0898-1221(99)00056-5\u003c/span\u003e\u003cspan address=\"10.1016/S0898-1221(99)00056-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFujita T, Smarandache F (2025) Hyperneutrosophic set and forest hyperneutrosophic set with practical applications in agriculture. Optim Agric. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.oia.2025.2478\u003c/span\u003e\u003cspan address=\"10.61356/j.oia.2025.2478\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaeed M, Shafique I (2024) Relation on Fermatean neutrosophic soft set with application to sustainable agriculture. HyperSoft Set Methods Eng. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.hsse.2024.18250\u003c/span\u003e\u003cspan address=\"10.61356/j.hsse.2024.18250\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAngammal S, Grace G (2024) Neutrosophic goal programming technique with bio inspired algorithms for crop land allocation problem. Sci Rep 14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-024-69487-0\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-69487-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSrikanth M, Mohan R, Naik M (2024) Neutrosophic logic-based crop yield prediction and risk assessment using least squares regression. Neutrosophic Syst Appl. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.nswa.2024.23362\u003c/span\u003e\u003cspan address=\"10.61356/j.nswa.2024.23362\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZulqarnain RM, Xin XL, Saqlain M, Smarandache F (2020) Generalized aggregate operators on neutrosophic hypersoft set. Neutrosophic Sets Syst 36:271\u0026ndash;281. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://digitalrepository.unm.edu/nss_journal/vol36/iss1/20\u003c/span\u003e\u003cspan address=\"https://digitalrepository.unm.edu/nss_journal/vol36/iss1/20\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlanazi BA, Alrashdi I (2023) A neutrosophic approach to edge-based anomaly detection in smart farming systems. Neutrosophic Sets Syst 58:211\u0026ndash;224. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://fs.unm.edu/nss8/index.php/111/article/view/3541\u003c/span\u003e\u003cspan address=\"https://fs.unm.edu/nss8/index.php/111/article/view/3541\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGomathi S, Karpagadevi M, Krishnaprakash S, Revathy A, Broumi S (2024) Cubic spherical neutrosophic sets for advanced decision-making. Neutrosophic Sets Syst 73:24. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://digitalrepository.unm.edu/nss_journal/vol73/iss1/24\u003c/span\u003e\u003cspan address=\"https://digitalrepository.unm.edu/nss_journal/vol73/iss1/24\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChakraborty A, Mondal S, Broumi S (2019) De-neutrosophication technique of pentagonal neutrosophic number and application in minimal spanning tree. Neutrosophic Sets Syst 29:1\u0026ndash;18. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1431\u0026amp;context=nss_journal\u003c/span\u003e\u003cspan address=\"https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1431\u0026amp;context=nss_journal\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRashno E, Minaei-Bidgoli B, Guo Y (2020) An effective clustering method based on data indeterminacy in neutrosophic set domain. Eng Appl Artif Intell 89:103411. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.engappai.2019.103411\u003c/span\u003e\u003cspan address=\"10.1016/j.engappai.2019.103411\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKaviyarasu M, Rajeshwari M, Alqahtani M (2025) Neutrosophic hypersoft topological framework for agricultural decision-making. Eur J Pure Appl Math 18:590\u0026ndash;615. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.29020/nybg.ejpam.v18i2.5905\u003c/span\u003e\u003cspan address=\"10.29020/nybg.ejpam.v18i2.5905\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAngammal S, Grace HG, Martin N, Smarandache F (2024) Multi attribute neutrosophic optimization technique for optimal crop selection in Ariyalur district. Neutrosophic Sets Syst 73:1. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://digitalrepository.unm.edu/nss_journal/vol73/iss1/16\u003c/span\u003e\u003cspan address=\"https://digitalrepository.unm.edu/nss_journal/vol73/iss1/16\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKaya NS, Dengiz O (2024) Assessment of the neutrosophic fuzzy-AHP and predictive power of soil quality indicators for maize silage. Comput Electron Agric 218:109446. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2024.109446\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2024.109446\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKousar S, Sangi M, Kausar N, Pamucar D, Ozbilge E, Cagin T (2023) Multi-objective optimization model for uncertain crop production under neutrosophic fuzzy environment: A case study. AIMS Math. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3934/math.2023380\u003c/span\u003e\u003cspan address=\"10.3934/math.2023380\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSudha S, Lathamaheswari M, Broumi S (2024) Long run behaviour of single valued neutrosophic hidden Markov model. In: 12th Int. Conf. Mech. Eng. (TSME-ICoME 2022) \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/5.0209796\u003c/span\u003e\u003cspan address=\"10.1063/5.0209796\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBorah G, Dutta P (2024) Fuzzy risk analysis in crop selection using information measures on quadripartitioned single-valued neutrosophic sets. Expert Syst Appl 255:124750. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.eswa.2024.124750\u003c/span\u003e\u003cspan address=\"10.1016/j.eswa.2024.124750\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCheng W, Ma T, Wang X, Wang G (2022) Anomaly detection for Internet of Things time series data using generative adversarial networks with attention mechanism in smart agriculture. Front Plant Sci 13:890563. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/fpls.2022.890563\u003c/span\u003e\u003cspan address=\"10.3389/fpls.2022.890563\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGoyal V, Yadav A, Kumar S, Mukherjee R (2024) Lightweight LAE for anomaly detection with sound-based architecture in smart poultry farm. IEEE Internet Things J 11:8199\u0026ndash;8209. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/jiot.2023.3318298\u003c/span\u003e\u003cspan address=\"10.1109/jiot.2023.3318298\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu P, Han Q, Wu T, Tao W (2023) Anomaly detection in industrial multivariate time-series data with neutrosophic theory. IEEE Internet Things J 10:13458\u0026ndash;13473. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/jiot.2023.3262612\u003c/span\u003e\u003cspan address=\"10.1109/jiot.2023.3262612\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAl-Masri E (2025) Deciding when not to decide: Indeterminacy-aware intrusion detection with NeutroSENSE. In: 2025 IEEE World AI IoT Congress (AIIoT), pp. 0142\u0026ndash;0148 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/aiiot65859.2025.11105216\u003c/span\u003e\u003cspan address=\"10.1109/aiiot65859.2025.11105216\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCatalano C, Paiano L, Calabrese F, Cataldo M, Mancarella L, Tommasi F (2022) Anomaly detection in smart agriculture systems. Comput Ind 143:103750. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compind.2022.103750\u003c/span\u003e\u003cspan address=\"10.1016/j.compind.2022.103750\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBenameur R, Dahane A, Kechar B, Benyamina A (2024) An innovative smart and sustainable low-cost irrigation system for anomaly detection using deep learning. Sensors 24. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/s24041162\u003c/span\u003e\u003cspan address=\"10.3390/s24041162\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMohanraj I, Ashokumar K, Naren J (2016) Field monitoring and automation using IoT in agriculture domain. Procedia Comput Sci 93:931\u0026ndash;939. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procs.2016.07.275\u003c/span\u003e\u003cspan address=\"10.1016/j.procs.2016.07.275\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBenos L, Tagarakis AC, Dolias G, Berruto R, Kateris D, Bochtis D (2021) Machine learning in agriculture: A comprehensive review. Sensors 21:3758. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/s21113758\u003c/span\u003e\u003cspan address=\"10.3390/s21113758\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKodati S, Selvaraj J (2019) Smart agricultural using Internet of Things, cloud and big data. Int J Innov Technol Explor Eng 8:3718\u0026ndash;3722. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.35940/ijitee.J9671.0881019\u003c/span\u003e\u003cspan address=\"10.35940/ijitee.J9671.0881019\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJdid M, Smarandache F (2023) Optimal agricultural land use: An efficient neutrosophic linear programming method. Neutrosophic Syst Appl. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.61356/j.nswa.2023.76\u003c/span\u003e\u003cspan address=\"10.61356/j.nswa.2023.76\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang K, Chen Z, Wang Y (2025) A novel approach for agricultural carbon emission reduction by integrating fermatean neutrosophic set with WINGS and AHP-EWM. Sci Rep 15:391. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-024-84423-y\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-84423-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMutlu N, Dengiz O, Kaya N, Saygın F, Pacci S, Demirkaya S, Ay A, Mutlu A, Arslan B, Kaya Y, Başaran B, Bozdağ M, \u0026Ouml;zer E, \u0026Ccedil;ini E (2025) Assessing the neutrosophic fuzzy-AHP based soil quality index for sugar beet: A comparative study of multi-class logistic regression, random forest, and one-against-all support vector machine models. Expert Syst Appl 295:128862. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.eswa.2025.128862\u003c/span\u003e\u003cspan address=\"10.1016/j.eswa.2025.128862\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Ouml;zkan B, Dengiz O, Alaboz P, Kaya NS (2023) A new hybrid approach to assessing soil quality using neutrosophic fuzzy-AHP and support vector machine algorithm in sub-humid ecosystem. J Mt Sci 20. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11629-022-7749-z\u003c/span\u003e\u003cspan address=\"10.1007/s11629-022-7749-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVeerasamy K, Fredrik T (2023) Intelligent farming based on uncertainty expert system with butterfly optimization algorithm for crop recommendation. J Internet Serv Inf Secur 13:158\u0026ndash;169. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.58346/JISIS.2023.I4.011\u003c/span\u003e\u003cspan address=\"10.58346/JISIS.2023.I4.011\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJafar M, Saqlain M, Shafiq A, Khalid M, Akbar H, Naveed A (2020) New technology in agriculture using neutrosophic soft matrices with the help of score function. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/ZENODO.3742406\u003c/span\u003e\u003cspan address=\"10.5281/ZENODO.3742406\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRahman A, Saeed M, Alburaikan A, Khalifa H (2022) (2022) An intelligent multiattribute decision-support framework based on parameterization of neutrosophic hypersoft set. Comput. Intell. Neurosci. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2022/6229947\u003c/span\u003e\u003cspan address=\"10.1155/2022/6229947\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaeed M, Rahman A, Arshad M (2021) A study on some operations and products of neutrosophic hypersoft graphs. J Appl Math Comput 68:2187\u0026ndash;2214. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12190-021-01614-w\u003c/span\u003e\u003cspan address=\"10.1007/s12190-021-01614-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZulqarnain R, Siddique I, Ali R, Jarad F, Samad A, Abdeljawad T (2021) Neutrosophic hypersoft matrices with application to solve multiattributive decision-making problems. Complexity 5589874 (2021). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2021/5589874\u003c/span\u003e\u003cspan address=\"10.1155/2021/5589874\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAjay D, Charisma J, Boonsatit N, Hammachukiattikul P, Rajchakit G (2021) (2021) Neutrosophic semiopen hypersoft sets with an application to MAGDM under the COVID-19 scenario. J. Math. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2021/5583218\u003c/span\u003e\u003cspan address=\"10.1155/2021/5583218\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRahman A, Saeed M, Arshad M, El-Morsy S (2021) Multi-attribute decision-support system based on aggregations of interval-valued complex neutrosophic hypersoft set. Appl. Comput. Intell. Soft Comput. 4368770 (2021). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2021/4368770\u003c/span\u003e\u003cspan address=\"10.1155/2021/4368770\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaeed M, Shafique I, G\u0026uuml;nerhan H (2025) Fundamentals of fermatean neutrosophic soft set with application in decision making problem. Int J Math Stat Comput Sci. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.59543/ijmscs.v3i.10625\u003c/span\u003e\u003cspan address=\"10.59543/ijmscs.v3i.10625\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYiarayong P (2024) Enhancing multi-criteria decision-making in smart farming using (p, q)-rung orthopair fuzzy hypersoft sets and weighted aggregation operators. Int J Inf Technol 17:2695\u0026ndash;2700. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s41870-024-02266-2\u003c/span\u003e\u003cspan address=\"10.1007/s41870-024-02266-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRiaz M, Hamid M, Afzal D, Pamucar D, Chu Y (2021) Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets. PLoS ONE 16. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0246485\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0246485\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBanik B, Chakraborty A (2023) Comparative study between GRA and MEREC technique on an agricultural-based MCGDM problem in pentagonal neutrosophic environment. Int J Environ Sci Technol. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s13762-023-04768-1\u003c/span\u003e\u003cspan address=\"10.1007/s13762-023-04768-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaqlain M, Kumam P, Kumam W (2025) Optimizing agricultural decision-making with integrated MCDM-MCDA methods: A case study on crop economics. Yugosl J Oper Res. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2298/yjor240915008s\u003c/span\u003e\u003cspan address=\"10.2298/yjor240915008s\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMohamed M, Alaa N, Arain B, Sallam K (2025) A hierarchical soft computational model for optimizing agricultural UAVs: Recruiting neutrosophic theory and tree soft sets. Neutrosophic Syst Appl. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.63689/2993-7159.1275\u003c/span\u003e\u003cspan address=\"10.63689/2993-7159.1275\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePuška A, Božanić D, Nedeljković M, Janošević M (2022) Green supplier selection in an uncertain environment in agriculture using a hybrid MCDM model: Z-numbers\u0026ndash;fuzzy LMAW\u0026ndash;fuzzy CRADIS model. Axioms 11:427. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/axioms11090427\u003c/span\u003e\u003cspan address=\"10.3390/axioms11090427\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlamoodi A, Garfan S, Deveci M, Albahri O, Albahri A, Yussof S, Homod R, Sharaf I, Moslem S (2024) Evaluating agriculture 4.0 decision support systems based on hyperbolic fuzzy-weighted zero-inconsistency combined with combinative distance-based assessment. Comput Electron Agric 227:109618. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2024.109618\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2024.109618\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSandra M, Narayanamoorthy S, Suvitha K, Pamucar D, Simić V, Kang D (2024) A trace to median index based fuzzy decision making technique for weed management in agricultural systems. IEEE Access 12:165185\u0026ndash;165202. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/access.2024.3493605\u003c/span\u003e\u003cspan address=\"10.1109/access.2024.3493605\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Q, Zhang H (2024) Assessing agri-food waste valorization challenges and solutions considering smart technologies: An integrated fermatean fuzzy multi-criteria decision-making approach. Sustainability. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/su16146169\u003c/span\u003e\u003cspan address=\"10.3390/su16146169\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRouyendegh B, Savalan Ş (2022) An integrated fuzzy MCDM hybrid methodology to analyze agricultural production. Sustainability. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/su14084835\u003c/span\u003e\u003cspan address=\"10.3390/su14084835\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSleem A, Abdel-Basset M, El-Henawy IM (2020) PyIVNS: A Python tool for interval-valued neutrosophic sets. SoftwareX 12:100632. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.softx.2020.100632\u003c/span\u003e\u003cspan address=\"10.1016/j.softx.2020.100632\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhalifa NEM, Smarandache F, Manogaran G, Loey M (2021) A study of neutrosophic set significance on deep transfer learning models: An experimental case on a limited COVID-19 chest X-ray dataset. Cogn Comput 13:1\u0026ndash;16. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12559-020-09802-9\u003c/span\u003e\u003cspan address=\"10.1007/s12559-020-09802-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePaudel D, Moran MS, Deines JM (2025) CY-Bench: A benchmark dataset for subnational crop yield forecasting. Earth Syst Sci Data. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5194/essd-2025-83\u003c/span\u003e\u003cspan address=\"10.5194/essd-2025-83\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMuruganantham P, Wibowo S, Grandhi S, Samrat NH, Islam N (2022) A systematic literature review on crop yield prediction with deep learning and remote sensing. Remote Sens 14:1990. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/rs14091990\u003c/span\u003e\u003cspan address=\"10.3390/rs14091990\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMallik S (2024) Recommendation system using neutrosophic logic in agriculture. Int J Intell Syst Appl Eng 12:735\u0026ndash;741. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ijisae.org/index.php/IJISAE/article/view/6279\u003c/span\u003e\u003cspan address=\"https://ijisae.org/index.php/IJISAE/article/view/6279\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLundberg S, Lee S-I (2017) A unified approach to interpreting model predictions. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.48550/arXiv.1705.07874\u003c/span\u003e\u003cspan address=\"10.48550/arXiv.1705.07874\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. arXiv\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRibeiro MT, Singh S, Guestrin C (2016) Why should I trust you? Explaining the predictions of any classifier. In: Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., pp. 1135\u0026ndash;1144 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1145/2939672.2939778\u003c/span\u003e\u003cspan address=\"10.1145/2939672.2939778\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Tamil Nadu Agricultural University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Neutrosophic sets, Multi-criteria Decision Making (MCDM), Uncertainty modelling, Computational intelligence, Decision support systems (DSS), Smart agriculture","lastPublishedDoi":"10.21203/rs.3.rs-9385567/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9385567/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNeutrosophic statistics and logic are generalized Fuzzy logic models of uncertainty via an explicit account of terms of truth, indeterminacy and falsity, as extensions of classical probability, fuzzy sets and intuitionistic fuzzy sets. Over recent years, many neutrosophic extensions and hybrid models have been suggested in response to complex decision-making problems involving incomplete, imprecise, and conflicting information. This paper provides a summary of neutrosophic statistical and logical methods, focus on high-level structures, including single-valued, hypersoft, topological, cubic and spherical neutrosophic sets. Mathematical foundations, aggregation operators, and multi-criteria decision-making (MCDM) mechanisms within these frameworks are critically analysed and comparatively discussed. Rapidly evolving formulations in applications, such as multi-criteria and hybrid neutrosophic-learning models are overviewed to demonstrate the ability of neutrosophic models to model hierarchical, multi-attribute, and indeterminate information systems. Smart agriculture has been taken as a representative area of application to illustrate real-world modelling situations without limiting the generality of the offered frameworks. This study proposes a unified conceptual framework integrating neutrosophic theory and multi-criteria decision-making for intelligent decision support under deep uncertainty. The review also presents the major implementation and methodological issues such as parameterization based on experts, absence of standard benchmarks, insufficient software chains, and complexity. Future research directions are provided, including scalable neuro-neutrosophic models, explainable artificial intelligence (XAI) integration, and large-scale decision-support systems.\u003c/p\u003e","manuscriptTitle":"Neutrosophic Knowledge-Based Frameworks for Intelligent Decision Support Under Deep Uncertainty: Applications in Smart Agriculture","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-14 07:12:49","doi":"10.21203/rs.3.rs-9385567/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"80e867bd-b579-4fd6-8d83-5e3cc1c0f0b0","owner":[],"postedDate":"April 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66124912,"name":"Applied Statistics"}],"tags":[],"updatedAt":"2026-04-14T07:12:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-14 07:12:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9385567","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9385567","identity":"rs-9385567","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}