New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings

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Based on this concept, researchers defined the generalised fuzzy soft set and its applications. However, to the best of the author’s knowledge, the generalised fuzzy soft set has not been dealing with in the generalised fuzzy soft code set. In this paper, we introduce the notion of generalised fuzzy soft code set and its application. Methods The theory of fuzzy soft sets and its application, generalised fuzzy soft sets and fuzzy codes in different years were studied with various researchers. To derive a generalised fuzzy soft code set, we apply the concepts of generalised fuzzy soft set and a new view of fuzzy codes and its application. A new aspect of this paper is to introduce the definition of generalised fuzzy soft code sets and its application on medical diagnosis and decision-makings. Results Generalised fuzzy soft code is the most powerful and effective extension of fuzzy soft sets that deal with the choice’s parameterized values. It is an extended model of fuzzy soft sets and a new mathematical tool with significant advantages for handling uncertain information and is proposed by combining the concept of fuzzy soft sets and fuzzy code sets. This paper introduces the concept of generalised fuzzy soft code and its properties. Conclusions In this study, we combine generalised fuzzy soft set and a different approach to coding theory to introduce generalisation of fuzzy soft codes. The paper also considers the relation between generalised fuzzy soft code and its application. We discussed the matrix representation of generalised fuzzy soft code. Furthermore, a demonstration example illustrates how the strategy could be effectively applied to various problems. 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F1000Research 2024, 13 :1461 ( https://doi.org/10.12688/f1000research.158747.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Research Article New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] Masresha Wassie Woldie https://orcid.org/0000-0001-5599-934X 1 , Jejaw Demamu Mebrat 2 , Mihret Alamneh Taye 3 Masresha Wassie Woldie https://orcid.org/0000-0001-5599-934X 1 , Jejaw Demamu Mebrat 2 , Mihret Alamneh Taye 3 PUBLISHED 02 Dec 2024 Author details Author details 1 Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia 2 Debark University, Debark, Amhara, Ethiopia 3 Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia Masresha Wassie Woldie Roles: Conceptualization, Investigation, Methodology, Writing – Original Draft Preparation Jejaw Demamu Mebrat Roles: Methodology, Supervision, Writing – Review & Editing Mihret Alamneh Taye Roles: Conceptualization, Supervision, Writing – Review & Editing OPEN PEER REVIEW DETAILS REVIEWER STATUS This article is included in the Software and Hardware Engineering gateway. Abstract Background Several scholars defined the concepts of fuzzy soft set theory and their application on decision-making problem. Based on this concept, researchers defined the generalised fuzzy soft set and its applications. However, to the best of the author’s knowledge, the generalised fuzzy soft set has not been dealing with in the generalised fuzzy soft code set. In this paper, we introduce the notion of generalised fuzzy soft code set and its application. Methods The theory of fuzzy soft sets and its application, generalised fuzzy soft sets and fuzzy codes in different years were studied with various researchers. To derive a generalised fuzzy soft code set, we apply the concepts of generalised fuzzy soft set and a new view of fuzzy codes and its application. A new aspect of this paper is to introduce the definition of generalised fuzzy soft code sets and its application on medical diagnosis and decision-makings. Results Generalised fuzzy soft code is the most powerful and effective extension of fuzzy soft sets that deal with the choice’s parameterized values. It is an extended model of fuzzy soft sets and a new mathematical tool with significant advantages for handling uncertain information and is proposed by combining the concept of fuzzy soft sets and fuzzy code sets. This paper introduces the concept of generalised fuzzy soft code and its properties. Conclusions In this study, we combine generalised fuzzy soft set and a different approach to coding theory to introduce generalisation of fuzzy soft codes. The paper also considers the relation between generalised fuzzy soft code and its application. We discussed the matrix representation of generalised fuzzy soft code. Furthermore, a demonstration example illustrates how the strategy could be effectively applied to various problems. READ ALL READ LESS Keywords Fuzzy Soft set, Fuzzy code, interval-valued fuzzy soft code, generalised fuzzy soft set, Generalised fuzzy soft code. Corresponding Author(s) Masresha Wassie Woldie ( [email protected] ) Close Corresponding author: Masresha Wassie Woldie Competing interests: No competing interests were disclosed. Grant information: The author(s) declared that no grants were involved in supporting this work. Copyright: © 2024 Woldie MW et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Woldie MW, Mebrat JD and Taye MA. New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.12688/f1000research.158747.1 ) First published: 02 Dec 2024, 13 :1461 ( https://doi.org/10.12688/f1000research.158747.1 ) Latest published: 09 Apr 2025, 13 :1461 ( https://doi.org/10.12688/f1000research.158747.2 )  There is a newer version of this article available. Suppress this message for one day. 1. Introduction Zadeh (1965) established the notion of a “fuzzy set” as a way to represent a class of objects with different membership grades. A membership function, also known as a characteristic function, describes such a set, with each item’s membership degree ranging from 0 to 1. Molodtsov (1999) presented the theory of soft sets as a novel mathematical technique for handling uncertainties that are outside the scope of current mathematical techniques. In order to address complicated issues including ambiguity and uncertainty, Molodtsov created a universal mathematical tool that may be applied to both conventional and some modern mathematical methods. Fuzzy sets are conceptualized in a way that makes their methods intuitively clear. Maji, Biswas, and Roy (2003) developed the theory of soft sets. Gogoi, Kr. Dutta, and Chutia (2014) introduced an application of fuzzy soft set theory in day to day problems; Roy and Maji (2007) presented the application of fuzzy soft set theory to decision-making problems. Amudhambigai and Neeraja (2019) discussed a new view of fuzzy codes and its application. Ozkan and Mehmet (2002) introduced different approaches of fuzzy codes and their properties. Malik, Mordeson, and Nair (1992) defined the concept of a fuzzy generating set and describe the fuzzy subgroup which it generates and introduced the notion of a minimal fuzzy generating set. Ali et al. (2018) designed and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. They also discussed some algebraic properties of soft codes. Garg and Arora (2018) describe the concept of generalized IFSS. Kong, Wang, and Wu (2011) studied the implementation of grey theory-based fuzzy soft sets in decision-making situations. Lin et al. (2018) a set of code words from the cyclic code are decoded using a binary parity-check matrix in a soft-joint manner. Gereme, Demamu, and Alaba (2023) , Hamming distance of fuzzy codes and other features of binary fuzzy codes. ( Lin et al. 2018 ) a novel coding technique for the Galois-Fourier transform domain that is intended for collective encoding and collective iterative soft-decision decoding of cyclic codes of prime lengths. Kamble (2017) examined the codes that emerged from soft sets and fuzzy sets, and using fuzzy linear space, explained the properties of fuzzy linear codes. Kim (2023) developed a fuzzy linear code description based on linear algebraic codes. Tsafack et al. (2018) established the concepts of fuzzy cyclic and linear codes over a Galois ring. Majumdar and Samanta (2010) established generalized fuzzy soft sets and investigated a few of their characteristics. It has been demonstrated that generalized fuzzy soft sets can be used to diagnose medical conditions and decision-making problem. Adde, Toro, and Jego (2012) examined linear block code of maximum likelihood soft-decision decoding. Dauda, Mamat, and Waziri (2015) an application of fuzzy soft sets based on a thorough theoretical analysis of the fundamental operations of soft sets and a definition of soft sets. Kané (2021) suggested a different method for figuring out the fuzzy optimal solution to a semi-fully fuzzy linear programming issue. Ali et al. (2023) discussed the generalized intuitionistic decision-theoretic rough set, a combination of intuitionistic fuzzy sets and decision-theoretic rough sets. However, as far as the author’s awared, no studied pertaining to the fundamentals of generalised fuzzy soft code have been released. Thus, motivated by the formationed works, the current study seeks to introduce this idea. To derive a generalised fuzzy soft code and its properties, we integrate the concepts of a generalised fuzzy soft set ( Majumdar and Samanta 2010 ) and a different approaches of coding theory ( Ozkan & Mehmet 2002 ). A new aspect of this paper is to introduce and develop the definition and application of generalised fuzzy soft code by combining the concepts of fuzzy soft set and fuzzy codes. The definition and features of relations on generalised fuzzy soft codes are proposed. The organization of this study as follows: Section 2 included fundamental notions and properties of preliminary concepts, Section 3 , Generalised fuzzy soft code, and some of their characteristics, whereas, Section 4 takes into consider relation on generalised fuzzy soft codes and its application. 2 Methods In this section, we review a few fundamental concepts that we utilize to get our outcomes. Definition 1. Ozkan & Mehmet (2002) The notion F q = ( a 1 , a 2 , … , a q ) , is a q-ary code which is a collection of symbol sequences in which each symbol is chosen from a set of q different components. The set F q is sometimes referred to as the alphabet and is defined as the set F q = { 0 ¯ , 1 ¯ , 2 ¯ , … , q − 1 ¯ } Definition 2. ( Amudhambigai & Neeraja 2019 ) F n is the collection of all ordered n − tuples p = p 1 , p 2 , … , p k , Where each p i in F q . The elements of F n are referred to as words or vectors. Definition 3. Ozkan & Mehmet (2002) Let us assume that C has a as a code word. The relative weight of a code word a , denoted as R w ( a ) , is the sum of p 1 , p 2 , … , p k if p 1 , p 2 , … , p k are defined as the positions of 1 s in a . For instance, R w ( a ) = 1 + 3 + 4 + 5 = 13 if a = 10111 is a code word of C in F 5 . 1 + 2 + 3 + … + n is the relative weight of 111…1 , which is a code word of C in F 2 n . This can be articulated as the sum of the first n positive integers. The largest relative weight of code C in F 2 n is referred to as this matter. Where n is the length of a code word, where R wr is a mapping defined as R wr : C → [ 0 , 1 ] for C ∈ F 2 n and R wr ( a ) ∈ [ 0 , 1 ] , for any a ∈ C . Definition 4. ( Ozkan & Mehmet 2002 ) Let { c 1 , c 2 , … , c n } is the code word of C with length n. Let C be a code. For each i = 1 , 2 , … , n , let R wr ( c i ) be a fuzzy code word related to the code words c i , c j in C . Then the fuzzy code intersection and union of any two fuzzy codes R wr ( c i ) and R wr ( c j ) , respectively, are given as follows: R wr ( c i ) ⋂ R wr ( c j ) = min { R wr ( c i ) , R wr ( c j ) } R wr ( c i ) ⋃ R wr ( c j ) = max { Rwr ( ci ) , Rwr ( cj ) } Definition 5. ( Amudhambigai and Neeraja 2019 ) For any fuzzy code R wr ( c i ) , the complement is c ( R wr ( c i ) ) is calculated by subtracting from 1 the relative weight of each member of C . That is, (1) c ( R wr ( c i ) ) = 1 − R wr ( c i ) Definition 6. ( Kong, Wang, and Wu 2011 ) Consider the idea of a set of parameters represented by E and U be the notion of a starting universe of items. P ( U ) be represents the power set of U and A ⊆ E . A pair ( F , A ) is a soft set over U if and only if F is a mapping given by F : A → P ( U ) In other words, the soft set is a parameterized family of subjects from the set U . Consider the set of e elements of the set ( F , A ) , or the set of e − approximate components of the soft set, where F ( e ) can be arbitrary, some of which can have nonempty intersection, and some of which can be empty. This applies to every F ( e ) from this family for e in A . where the attributes, traits, or properties of objects are usually the arguments. We might consider Zadeh’s fuzzy set as a subset of the soft set. Given a fuzzy set A , its membership function is μ A , that is, μ A is a mapping from U into [ 0 , 1 ] , that is μ A : U → [ 0 , 1 ] Definition 7. ( Majumdar & Samanta, 2010 ) The set of all fuzzy subsets within a universal set U is denoted by I U . Assume A ⊆ E and that E is a parameter set. Then, a pair ( F , A ) is a fuzzy soft set over U , where F is a mapping denoted by F : A → I U Definition 8. ( Ali et al. 2018 ) Assume that a vector space of size n over the field K is represented by W = K n . ( F , E ) is as of t algebraic linear code over K . For every F ( e i ) ; 1 ≤ i ≤ t , the symbol F ( E ) = F ( e 1 ) , … , F ( et ) in x indicates a linear algebraic code of W . The number of linearly independent elements of F ( e i ) is denoted by d i , which is the dimension of F ( e i ) . Each F ( e i ) ∈ F ( E ) in this instance represents a linear algebraic code. The soft dimension of ( F , E ) is ( F , E ) = { d 1 , d 2 … , d t } and the number of soft code words of ( F , E ) is given by: (2) n ( F , E ) = | F ( e 1 ) | × | F ( e 2 ) | × … × | F ( e t ) | Where 1 ≤ i ≤ t . Keep in mind that dim ( F , A ) represents the soft dimension ( F , E ) . Definition 9. ( Majumdar & Samanta 2010 ). The universal set of elements is = { x 1 , x 2 , … , x n } , and the universal set of parameters is E = { e 1 , e 2 , … , e m } . We shall refer to the pair ( U , E ) as a soft universe. Let μ be a fuzzy subset of E , that is, μ : E → [ 0 , 1 ] , and let F : E → I U . where the set of all fuzzy subsets of U is represented by I U . Assume that F μ represents the mapping. Let a function Fμ such that Fμ : E → I U × I have the following definition: Fμ ( e ) = F ( e ) , μ ( e ) ) , where ( e ) ∈ I U . A generalised fuzzy soft set (in short GFSS) over the soft universe ( U , E ) is then denoted by Fμ . Here, for every parameter e i , Fμ ( e i ) = ( F ( e i ) , μ ( e i ) ) showed both the degree of belongingness that μ ( e i ) represents and the degree of belongingness of the elements of U in F ( e i ) . Definition 10. ( Majumdar & Samanta 2010 ) Let Fμ and G σ be two generalised fuzzy soft sets over ( U , E ) . Now Fμ is said to be a generalised fuzzy soft subset of G σ if (i) μ ⊆ σ (ii) F ( e ) ⊆ G ( e ) , for all e ∈ E , in this case we write F ( e ) is a fuzzy subset of G ( e ) . Definition 11. ( Majumdar and Samanta 2010 ) Consider a generalised fuzzy soft set over ( U , E ) , denoted by Fμ . Then, F ∁ represents the complement of Fμ , which is defined as F ∁ = G σ , where G ( e ) = F ∁ and σ ( e ) = μ ∁ ( e ) , for all e ∈ E . Definition 12. ( Majumdar & Samanta 2010 ) Fμ ⋃ G σ represents the union of two generalised fuzzy soft sets Fμ and G σ . This results in a generalised fuzzy soft set H ν , which is defined as H ν : E → I U × I such that H ν ( e ) = ( H ( e ) , ν ( e ) ) where H ( e ) = F ( e ) ° G ( e ) , ν ( e ) = μ ( e ) ° σ ( e ) , and ° denotes a t-norm . Definition 13. ( Majumdar & Samanta 2010 ) Fμ ⋃ G σ represents the intersection of two generalised fuzzy soft sets, Fμ and G σ . This leads to a generalised fuzzy soft set H ν , which is defined as H ν : E → I U × I such that H ν ( e ) = ( H ( e ) , ν ( e ) ) , where ∗ is a t-co norm and H ( e ) = F ( e ) ∗ G ( e ) and ν ( e ) = μ ( e ) ∗ σ ( e ) . Definition 14. ( Majumdar & Samanta 2010 ) ∅ θ : E → I U × I indicates a generalised null fuzzy soft set, which is referred to as a generalised fuzzy soft set, such that ∅ θ ( e ) = ( F ( e ) , θ ( e ) ) , where ∅ ( e ) = 0 ¯ , and θ ( e ) = 0 , for all e ∈ E . Definition 15. ( Majumdar & Samanta 2010 ) A generalised absolute fuzzy soft set, represented by A α : E → I U × I , is refered to as a generalised fuzzy soft set, where A α ( e ) = F ( e ) , α ( e ) is defined by A ( e ) = 1 ¯ , and α ( e ) = 1 , for all e ∈ E . 3. Results 3.1 Generalised Fuzzy Soft Code (GFSC) In this subsection, we introduce generalised fuzzy soft codes and its properties. Definition 16. Let U = R wr ( a i ) for which C is the universal element, consider the set of parameters be E , and a i is an element of a code vector. The fuzzy soft code universe is a pair ( F , E ) . Let F : E → P ( R wr ( a i ) ) , where all fuzzy code subsets of R wr ( a i ) ∈ [ 0 , 1 ] are collected as P ( R wr ( a i ) ) . And consider a mapping μ and F μ such that (12) μ : E → R wr ( a i ) is a fuzzy subset of E and (13) F μ : E → P ( R wr ( a i ) ) × R wr ( a i ) defined as F μ ( e i ) = ( F ( e i ) , μ ( e i ) ) , ∀ e ∈ E and F ( e i ) ∈ P ( R wr ( a i ) ) . Then, F μ is called a generalised fuzzy soft code (GFSC) over the soft universe ( R wr ( a i ) , E ) . μ ( e i ) is a representation of the possibility of membership, and the degree of belongingness of R wr ( a i ) ∈ F ( e i ) is indicated for each parameter e i by F μ ( e i ) = ( F ( e i ) , μ ( e i ) ) . Example 1. Consider C ⊆ F 2 4 and let R wr ( a ) = { R wr ( 0100 ) , R wr ( 1010 ) , R wr ( 1011 ) , R wr ( 1110 ) , R wr ( 0001 ) , R wr ( 0111 ) , R wr ( 1100 ) , R wr ( 1111 ) } = { 0.2 , 0.5 , 0.8 , 0.6 , 0.4 , 0.9 , 0.3 , 1 } be a fuzzy code of the eight computers under consideration. Let E = { e 1 , e 2 , e 3 , e 4 } be the set of qualities of the given computers, where the symbols e 1 denote a super computer, e 2 a micro computer, e 3 a workstation computer,and e 4 a personal computer. Let μ : E → R wr ( a i ) × [ 0 , 1 ] = [0, 1] be a fuzzy code subset defined as follows: μ ( e 1 ) = R wr ( 0110 ) = 0.5 ; μ ( e 2 ) = R wr ( 1001 ) = 0.6 ; μ ( e 3 ) = R wr ( 1100 ) = 0.3 ; and μ ( e 4 ) = R wr ( 1011 ) = 0.8 ; And we define a function Fμ : E → P ( R wr ( a i ) ) × R wr ( a i ) , be defined as follows: F μ ( e 1 ) = ( { R wr ( 0001 ) 0.4 , R wr ( 0111 ) 0.9 , R wr ( 1110 ) 0.6 , R wr ( 1010 ) 0.4 } , 0.5 ) F μ ( e 2 ) = ( { R wr ( 1011 ) 0.8 , R wr ( 1110 ) 0.6 , R wr ( 1010 ) 0.4 , R wr ( 1111 ) 1 } , 0.6 ) F μ ( e 3 ) = ( { R wr ( 1110 ) 0.6 , R wr ( 0001 ) 0.4 , R wr ( 1011 ) 0.8 , R wr ( 0111 ) 0.9 } , 0.3 ) F μ ( e 4 ) = ( { R wr ( 0101 ) 0.6 , R wr ( 1100 ) 0.3 , R wr ( 1010 ) 0.4 , R wr ( 1111 ) 1 } , 0.8 ) A Generalised fuzzy soft code over ( R wr ( a ) , E ) is then F μ . This can be represented in matrix form as follows: F μ = [ 0.4 0.9 0.6 0.4 | 0.5 0.8 0.6 0.4 1 | 0.6 0.6 0.4 0.8 0.9 | 0.3 0.6 0.3 0.4 1 | 0.8 ] where the last column represents the values of μ ( e i ) , the row vectors i th represent F μ ( e i ) , and the column vector i th represents R wr ( a i ) for some a i ∈ F 2 4 . This will be referred to as the membership matrix of F μ . The GFSC is then can be defined as F μ ( e i ) , ( e i ) = ( F ( e i ) , μ ( e i ) ) , ∀ e ∈ E , F ( e ) ∈ P ( R wr ( a i ) ) and ∀ i . Definition 17. Given two GFSCs over ( R wr ( a ) , E ) , let F μ and G σ . Specifically, F μ is a subset of G σ that is considered a generalised fuzzy soft code if i μ ⊆ σ ii F ( e ) ⊆ G ( e ) , ∀ e ∈ E Here, we compose F μ ⊆ G σ . Example 2. The GFSC F μ over ( R wr ( a ) , E ) is the one presented in example 3.12. Let G σ be an additional GFSC defined as follows over ( R wr ( a ) , E ) . G σ ( e 1 ) = ( { R wr ( 1001 ) 0.5 , R wr ( 0111 ) 0.9 , R wr ( 1011 ) 0.8 , R wr ( 0110 ) 0.5 } , 0.6 ) G σ ( e 2 ) = ( { R wr ( 1011 ) 0.8 , R wr ( 0110 ) 0.5 , R wr ( 1110 ) 0.6 , R wr ( 1111 ) 1 } , 0.8 ) G σ ( e 3 ) = ( { R wr ( 1011 ) 0.8 , R wr ( 1010 ) 0.4 , R wr ( 0111 ) 0.9 , R wr ( 1111 ) 1 } , 0.5 ) G σ ( e 4 ) = ( { R wr ( 1011 ) 0.8 , R wr ( 1010 ) 0.4 , R wr ( 1001 ) 0.5 , R wr ( 1111 ) 1 } , 0.7 ) Here σ and R wr ( a ) are the respective mapping given by σ : E → [ 0 , 1 ] , and R wr ( a ) : C → 0 , 1 ] Then, a generalised fuzzy soft code subset of G σ is F μ . Matrix representation of G σ is given by G σ = [ 0.5 0.9 0.8 0.9 | 0.6 0.8 0.5 0.6 1 | 0.8 0.8 0.4 0.9 1 | 0.5 0.8 0.4 0.5 1 | 0.7 ] Definition 18. (Intersection of GFSC). F μ ⋂ G σ represents the GFSC intersection of two GFSCs of F μ and G σ over ( R wr ( a ) , E ) , and is defined as (14) Fμ ⋂ G σ = min { ( F μ ( e ) , μ ( e ) ) , ( G σ ( e ) , σ ( e ) ) , ∀ e ∈ E } . Definition 19. (Union of GFSC) F μ ⋃ G σ represents the GFSC union of two GFSCs of F μ and G σ over a soft universe ( R wr ( a ) , E ) , and is defined as (15) Fμ ⋃ G σ = max { ( F μ ( e ) , μ ( e ) ) , ( G σ ( e ) , σ ( e ) ) , ∀ e ∈ E } . Definition 20. (Complement of GFSC). The following notation represents the complement of the GFSC of F μ : ( F μ ) ∁ or Subtracting the GFSC of each member of ( F μ ( e ) , μ ( e ) ) from 1 yield F ∁ μ ∁ . That is, (16) F ∁ μ ∁ = ( 1 − F μ ( e ) , 1 − μ ( e ) Theorem 1. If F μ and G σ represent any GFSC over a shared soft universe ( R wr ( a ) , E ) , then the following result is hold: (i) F μ = F μ ⋂ F μ (ii) F μ = F μ ⋃ F μ (iii) ( F ∁ μ ∁ ) ∁ = F μ (i) ( F μ ⋂ G σ ) ∁ = F ∁ μ ∁ ⋃ G ∁ μ ∁ (ii) ( F μ ⋃ G σ ) ∁ = F ∁ μ ∁ ⋂ G ∁ μ ∁ Proof: The proof follows directly from the definition. Theorem 2. The following properties are hold, if ( F , A ) and ( G , B ) are two generalised fuzzy soft codes over the common universe R wr ( a ) . (i) ( ( F , A ) ⋃ ( G , B ) ) ∁ = ( F , A ) ∁ ⋂ ( G , B ) ∁ (ii) ( ( F , A ) ⋂ ( G , B ) ) ∁ = ( F , A ) ∁ ⋃ ( G , B ) ∁ Proof (i) ( ( F , A ) ⋃ ( G , B ) ) ∁ = ( F ∁ , ¬ A ) ⋂ ( G ∁ , ¬ B ) = ( H ∁ , ¬ A × ¬ B ) , where H ( ¬ e , ¬ e ′ ) = F ∁ ( e ) ⋃ G ∁ ( e ′ ) = ( H , ¬ ( A × B ) ) ) ⇒ ( F , A ) ∁ ⋃ ( G , B ) ∁ = ( H , ¬ ( A × B ) ) Assume that, ( ( F , A ) ⋂ ( G , B ) ) = ( H , A × B ) ) ⇒ ( ( F , A ) ⋂ ( G , B ) ) ∁ = ( H , A × B ) ∁ = ( Hc , ¬ ( A × B ) ) , ∀ ( e , e ′ ) ∈ A × B ) ⇒ H ∁ ( ¬ e , ¬ e ′ ) = ( H ( e , e ′ ) ) ∁ = ( F ( e ) ⋂ G ( e ′ ) ) ∁ = ( F ( e ) ) ∁ ⋃ ( G ( e ′ ) ) ∁ = F ∁ ( ¬ e ) ⋃ Gc ( ¬ e ′ ) = ( H , ¬ ( A × B ) ) ) ⇒ ( ( F , A ) ⋂ ( G , B ) ) ∁ Thus, from our discussion we get the result, ( ( F , A ) ⋃ ( G , B ) ) ∁ = ( F , A ) ∁ ⋂ ( G , B ) ∁ The proof of (ii) is similar to the above. Definition 21. A generalised null fuzzy soft code, represented by F μ , is considered to be a generalised null fuzzy soft code if F μ : E → P ( R wr ( a ) ) × R wr ( a ) and F μ ( e ) = ( F ( e ) , μ ( e ) ) , where F ( e ) = 0 ¯ and μ ( e ) = 0 , ∀ e ∈ E . Definition 22. A GFSC is said to be a generalised absolute fuzzy soft code, denoted by G σ if G σ : E → P ( R wr ( a ) ) × R wr ( a ) , where G σ ( e ) = ( G ( e ) , σ ( e ) ) is defined by G ( e ) = 1 ¯ , ∀ e ∈ E , and σ ( e ) = 1 ∀ e ∈ E . Theorem 3. Given any GFSC over ( R wr ( a ) , E ) , let’s say F μ . The generalised null fuzzy soft code and generalised absolute fuzzy soft code over ( R wr ( a ) , E ) denoted as G σ and H θ , respectively. Then, thefollowing result is hold: (i) F μ ⋂ G σ = G σ (ii) F μ ⋂ H θ = F μ (iii) F μ ⋃ G σ = F μ (iv) F μ ⋃ H θ = H θ (v) G σ ⋃ H θ = H θ (vi) G σ ⋂ H θ = G σ Proof (i) Let F μ be any GFSC over ( R wr ( a ) , E ) and let G σ be the generalised null fuzzy soft code over ( R wr ( a ) , E ) . Then F μ ⋂ G σ = F μ ( e ) ⋂ G σ ( e ) = ( F ( e ) , μ ( e ) ) ⋂ ( G ( e ) , σ ( e ) ) = ( F ( e ) , μ ( e ) ) ⋂ ( 0 ¯ , 0 ) = ( 0 ¯ , 0 ) = G σ (ii-v) Similar to the proof of (i) Definition 23. Given a universal set U = R wr ( a ) , consider two generalised fuzzy soft codes over R wr ( a ) : ( F , A ) and ( G , B ) . Then, the addition operation modulo between ( F , A ) and ( G , B ) is represented by ( F , A ) ⊕ ( G , B ) , and the multiplication operation modulo between ( F , A ) and ( G , B ) is represented by ( F , A ) ⊙ ( G , B ) . The interpretationof these notations are as follows: ( F , A ) ⊕ ( G , B ) = ( H , a × b ) , where ( H , a × b ) = F ( a ) ⋃ G ( b ) ( F , A ) ⊙ ( G , B ) = ( H , a × b ) , where ( H , a × b ) = F ( a ) ⋂ G ( b ) and a × b ∈ A × B . 4. Relation on generalised fuzzy soft code and its application Theorem 4. Consider the generalised fuzzy soft codes ( F , A ) , ( G , B ) , and ( H , C ) over the common universe R wr ( a ) . That, the following characteristics are held: (i) ( ( F , A ) ⊕ ( F , A ) ) = ( F , A ) (ii) ( ( F , A ) ⊙ ( F , A ) ) = ( F , A ) . From the definition, the argument is obvious. Definition 24. Over the parameterized universe ( R wr ( a ) , E ) . and A ⊆ E 2 , let F μ and G π be two GFSC. A fuzzy soft code relation R between F μ and G π is a function that looks like the following: (17) R : A → P ( R wr ( a ) ) × R wr ( a ) characterized as (18) R ( e , f ) = min { F μ ( e ) , G π ( e ) } , ∀ ( e , f ) ∈ A . Definition 25. Let F = { F μ i i , i ∈ I } , as any collection of GFSC over ( R wr ( a ) , E ) and A ⊆ E n , where I is the index set. The mapping R : A → P ( R wr ( a ) ) × R wr ( a ) is then a n − ary generalised fuzzy soft code relation R on F , defined by R ( e i 1 , e i 2 , e i 3 , … , e i n ) = min { F μ i 1 i 1 ( e i 1 ) , F μ i 2 i 2 ( e i 2 ) , … , F μ i n i n ( e i n ) } , where ( e i 1 , e i 2 , e i 3 , … , e i n ) ∈ A . The following illustrates how this generalized fuzzy soft code relation is used in a decision-making problem. Assume there are four computers in the universal set U = { c 1 , c 2 , c 3 , c 4 } and there are four parameters E = { e 1 , e 2 , e 3 , e 4 } which characterize their performance regarding a certain task. Assume a company wishes to purchase one of these computers based on certain criteria. Let there are two observations F μ and G σ by two experts A and B respectively Let the membership matrices that correspond to them be as follows: F μ = [ R wr ( 1010 ) 0.4 R wr ( 0111 ) 0.9 R wr ( 0101 ) 0.6 R wr ( 1010 ) 0.4 | R wr ( 0110 ) 0.5 R wr ( 1011 ) 0.8 R wr ( 1110 ) 0.6 R wr ( 1010 ) 0.4 R wr ( 1111 ) 1 | R wr ( 1110 ) 0.6 R wr ( 0101 ) 0.6 R wr ( 1010 ) 0.4 R wr ( 1011 ) 0.8 R wr ( 0111 ) 0.9 | R wr Rwr ( 1100 ) 0.3 R wr ( 1110 ) 0.6 R wr ( 1100 ) 0.3 R wr ( 1010 ) 0.4 R wr ( 1111 ) 1 | R wr ( 1011 ) 0.8 ] G σ = [ R wr ( 0110 ) 0.5 R wr ( 0111 ) 0.9 R wr ( 1011 ) 0.8 R wr ( 1010 ) 0.4 | R wr ( 1110 ) 0.6 R wr ( 1011 ) 0.8 R wr ( 0110 ) 0.5 R wr ( 0101 ) 0.6 R wr ( 1111 ) 1 | R wr ( 1011 ) 0.8 R wr ( 1110 ) 0.6 R wr ( 1010 ) 0.4 R wr ( 1011 ) 0.8 R wr ( 0111 ) 0.9 | R wr Rwr ( 1100 ) 0.3 R wr ( 1011 ) 0.8 R wr ( 1010 ) 0.4 R wr ( 0110 ) 0.5 R wr ( 1000 ) 0.1 | R wr ( 0011 ) 0.7 ] Let R : A → P ( R wr ( a ) ) × R wr ( a ) , be the generalised fuzzy soft code relation between F μ and G σ , defined as follows: Table 1. Numerical grades. R c 1 c 2 c 3 c 4 λ ( e 1 , e 1 ) 0.4 (0.9) 0.6 0.4 0.5 ( e 1 , e 2 ) 0.4 0.5 (0.6) 0.4 0.5 ( e 1 , e 3 ) 0.4 0.4 (0.6) 0.4 0.3 ( e 1 , e 4 ) 0.4 0.4 (0.5) 0.1 0.5 ( e 2 , e 1 ) 0.5 (0.6) 0.4 0.5 0.6 ( e 2 , e 2 ) 0.8 0.5 0.4 (1) 0.6 ( e 2 , e 3 ) 0.8 0.4 0.4 (1) 0.3 ( e 2 , e 4 ) (0.8) 0.4 0.4 0.1 0.6 ( e 3 , e 1 ) 0.5 0.4 (0.8) 0.5 0.3 ( e 3 , e 2 ) 0.6 0.4 0.6 (0.9) 0.3 ( e 3 , e 3 ) 0.6 0.4 0.8 (0.9) 0.3 ( e 3 , e 4 ) (0.6) 0.4 0.5 0.1 0.3 ( e 4 , e 1 ) (0.5) 0.3 0.4 0.4 0.6 ( e 4 , e 2 ) 0.6 0.3 0.4 (1) 0.8 ( e 4 , e 3 ) 0.6 0.3 0.4 (1) 0.3 ( e 4 , e 4 ) (0.6) 0.3 0.4 0.1 0.7 Table 2. Finding the grade outcome. R c i Highest numerical grade λ ( e 1 , e 1 ) c 2 ----- ----- ( e 1 , e 2 ) c 3 0.6 0.5 ( e 1 , e 3 ) c 3 0.6 0.3 ( e 1 , e 4 ) c 3 0.5 0.5 ( e 2 , e 1 ) c 2 0.6 0.6 ( e 2 , e 2 ) c 4 ----- ----- ( e 2 , e 3 ) c 4 1 0.3 ( e 2 , e 4 ) c 1 0.8 0.6 ( e 3 , e 1 ) c 3 0.8 0.3 ( e 3 , e 2 ) c 4 0.9 0.3 ( e 3 , e 3 ) c 4 ----- ---- ( e 3 , e 4 ) c 1 0.6 0.3 ( e 4 , e 1 ) c 1 0.5 0.6 ( e 4 , e 2 ) c 4 1 0.8 ( e 4 , e 3 ) c 4 1 0.3 ( e 4 , e 4 ) c 1 ----- ---- In order to identify the optimal computer, we first identify the greatest numerical grade indicated by the parenthesis in each column, with the exception of the final row, which represents the computer’s grade of belongingness in relation to each set of parameters. Now, the total of the products of these numerical grades with the associated values of λ is used to calculate each of these computers’ scores. That is the desired computer, the one with the greatest score. We do not take into account the computers’ numerical grades in relation to the pair ( e i , e i ) , i = 1 , 2 , 3 , 4 , as both the parameters are same. Hence, score ( c 1 ) = 0.8 ∗ 0.6 + 0.6 ∗ 0.3 = 0.66 , score ( c 2 ) = 0.6 ∗ 0.6 = 0.36 , score ( c 3 ) = 0.6 ∗ 0.5 + 0.6 ∗ 0.3 + 0.5 ∗ 0.5 + 0.8 ∗ 0.3 = 0.97 , score ( c 4 ) = 1 ∗ 0.3 + 0.9 ∗ 0.3 + 1 ∗ 0.8 + 1 ∗ 0.3 = 1.67 The company will then choose the computer that scored the highest, and they will purchase that computer c 4 . 5. Conclusion In this study, we have presented a Generalised fuzzy soft set and a New view of fuzzy codes and its application to introduce the new concept of Generalised fuzzy soft code and its characteristics. In fact, in this study, we introduced binary fuzzy soft code and its properties, and an application of Generalised fuzzy soft code has been presented. This study will serve as an introduction for future researchers who will work in this area. 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Publisher Full Text Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 02 Dec 2024 ADD YOUR COMMENT Comment Author details Author details 1 Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia 2 Debark University, Debark, Amhara, Ethiopia 3 Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia Masresha Wassie Woldie Roles: Conceptualization, Investigation, Methodology, Writing – Original Draft Preparation Jejaw Demamu Mebrat Roles: Methodology, Supervision, Writing – Review & Editing Mihret Alamneh Taye Roles: Conceptualization, Supervision, Writing – Review & Editing Competing interests No competing interests were disclosed. Grant information The author(s) declared that no grants were involved in supporting this work. Article Versions (2) version 2 Revised Published: 09 Apr 2025, 13:1461 https://doi.org/10.12688/f1000research.158747.2 version 1 Published: 02 Dec 2024, 13:1461 https://doi.org/10.12688/f1000research.158747.1 Copyright © 2024 Woldie MW et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Woldie MW, Mebrat JD and Taye MA. New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.12688/f1000research.158747.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS track receive updates on this article Track an article to receive email alerts on any updates to this article. TRACK THIS ARTICLE Share Open Peer Review Current Reviewer Status: ? Key to Reviewer Statuses VIEW HIDE Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Version 1 VERSION 1 PUBLISHED 02 Dec 2024 Views 0 Cite How to cite this report: Zulqarnain RM. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367664 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367664 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 11 Mar 2025 Rana Muhammad Zulqarnain , Zhejiang Normal University, Zhejiang, China Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.174381.r367664 I encourage you to improve the abstract section precisely with your core contributions. Keywords are inappropriate; please add proper keywords for readers' convenience. Considering the innovative nature of this methodology and its potential ... Continue reading READ ALL I encourage you to improve the abstract section precisely with your core contributions. Keywords are inappropriate; please add proper keywords for readers' convenience. Considering the innovative nature of this methodology and its potential influence on academic research and industrial practices, the authors should emphasize the interdisciplinary aspects of their study, particularly regarding evolutionary economics and organizational behavior. The problem statement and motivation is given. Please explain the problem in detail. There are no research questions, so please add the research question for the reader's convenience. The introduction and theoretical background are not enough. I suggest some important studies for authors to improve the introduction and background of this manuscript. Also, I strongly recommend reading these studies carefully and cite in the introduction and background sections. The literature review would not have been acceptable to me without the following studies in the introduction and references section. So, carefully revised the introduction and background. (a): Some Einstein geometric aggregation operators for Q-rung orthopair fuzzy soft set with their application in MCDM. (b): Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set with Their Application to Solve Multi-Attribute Group Decision Making Problem. (c): Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision‐Making. (d): An interaction and feedback mechanism-based group decision-making for emergency medical supplies supplier selection using T-spherical fuzzy information. (d): Optimal cloud service provider selection: An MADM framework on correlation-based TOPSIS with interval-valued q-rung orthopair fuzzy soft set. (e): Algorithms for a Generalized Multipolar Neutrosophic Soft Set with Information Measures to Solve Medical Diagnoses and Decision‐Making Problems. (f): Extension of Einstein average aggregation operators to medical diagnostic approach under Q-rung orthopair fuzzy soft set. (g): Novel multicriteria decision making approach for interactive aggregation operators of q-rung orthopair fuzzy soft set. (h): Selection of unmanned aerial vehicles for precision agriculture using interval-valued q-rung orthopair fuzzy information based TOPSIS method. (i): An integrated group decision-making technique under interval-valued probabilistic linguistic T-spherical fuzzy information and its application to the selection of cloud storage provider. (j): Einstein ordered weighted aggregation operators for Pythagorean fuzzy hypersoft set with its application to solve MCDM problem. (k): Supplier Selection in Green Supply Chain Management using Correlation-based TOPSIS in a q-rung Orthopair Fuzzy Soft Environment. (l): An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets. (m): Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques. (n): Assessment of bio-medical waste disposal techniques using interval-valued q-rung orthopair fuzzy soft set based EDAS method. (o): Einstein Hybrid Structure of q-Rung Orthopair Fuzzy Soft Set and Its Application for Diagnosis of Waterborne Infectious Disease. (p): Transportation decisions in supply chain management using interval-valued q-rung orthopair fuzzy soft information. Please clarify which of the assumptions is new in this area in the problem definition. How did you consider the data in the case study? The input section mentions constructing a group of decision-makers but doesn't clearly explain how they influence the process. Similarly, the output section could benefit from more detail on the final results, such as how the ranking is used for decision-making. The authors should discuss how their presented work is needed at the time and whether it will be helpful to the scientific community. The role of weights in the aggregation process could be explained more explicitly, particularly how they are assigned to each alternative and how they impact the final decision-making process. How are the experts’ weights determined, and how do they influence the decision-making process? Comparative analysis section in the manuscript is not enough, please add more comparative studies to prove the validity of the proposed model. Can the research's shortcomings be commented on, particularly regarding the number of participants and the range of sectors addressed in the focus groups? Please bring and focus on future research directions. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Partly Competing Interests: No competing interests were disclosed. Reviewer Expertise: Fuzzy extensions. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Zulqarnain RM. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367664 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367664 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response We incorporated all comments as the reviewer's suggestions. Competing Interests: No competing interests were disclosed. We incorporated all comments as the reviewer's suggestions. We incorporated all comments as the reviewer's suggestions. Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response We incorporated all comments as the reviewer's suggestions. Competing Interests: No competing interests were disclosed. We incorporated all comments as the reviewer's suggestions. We incorporated all comments as the reviewer's suggestions. Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Karaaslan F. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367656 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367656 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 05 Mar 2025 Faruk Karaaslan , Çankırı Karatekin University,, Çankırı, Turkey Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.174381.r367656 Review Report for “New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings” A new aspect of this paper is to introduce and develop the definition and application of generalized fuzzy ... Continue reading READ ALL Review Report for “New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings” A new aspect of this paper is to introduce and develop the definition and application of generalized fuzzy soft code by combining the concepts of fuzzy soft sets and fuzzy codes. The definition and features of relations on generalized fuzzy soft codes are proposed. But there are some problems in the paper. After the following revisions, Paper can be revaluated for indexing. In definition 4, R wr c i ∪ R wr c j = max⁡ (….) subindices should be checked and corrected. Citation of definition 6 should be corected, because soft set was defined by Molodtsov (1999). Also, in same definition, “P(U) be represents…” should be replaced by “P(U) represents”. Definition 6, line 8-9, “ e∈A. where… “ should be corrected. Also, sentences beginning with “We might consider…” I think that soft set is a special type of Zadeh’s fuzz sets. Check this sentence In definition 8, should be replaced by ” In definition 9. “The universal set of elements is ,…” should be rewritten as “The universal set of elements is ,…” In same definition, where ” should be checked and corrected. In Definition 12, “t-norm” should be replaced by “s-norm or t-conorm” In Definition 13, “ ” should be replaced by “ ” and, “*” should be “t-norm” In definition 14, 15, authors use some notations without they give an explanation, for example “ ” and . They should be explained. In example 1. I see that basic idea is that authors take the parameter set E, and define a fuzzy set on this parameter set; also, they take for any set of . In example 1, “Let …” What does it mean? According to definition of , Why you write ” is not true expression as mathematically. In example 2, “…in example 3.2 ”. Where is the example 3.2? In example 2, should be replaced by ”. In example 2, “e generalized fuzzy soft code subset of G σ is .” This is not true, it should be checked. In definition 18, minimum operation is not defined between pairs and So if author write the . Same problem is available for Definition 19. We know that is a fuzzy set. How can you maket he substruction operation between a number and fuzzy set. Actually I understand what you make, bu this writting is not true mathematical. Check and rewrite them. When I investigate the proof of theorem 2, I see that it is same with the proof for generalized fuzzy soft sets. What is the difference between generalized fuzzy soft code and generalized fuzzy soft set. I think that Theorem 2, and 3 are trivial results of the generalized fuzzy soft set. In Definition 24, “GFSC” should be replaced by “GFSCs”. The application part related to generalized fuzzy soft code relations is elementary and we can apply this to all generalized fuzzy soft sets. What is the importance of this application in terms of the codes? The results of the application are independent of codes. The importance and effect of the codes must be explained in the paper. The introduction part should be improved. The paper could benefit from refinement in terms of mathematical writing style to enhance clarity and precision. The title should be rewritten. Decision: Major Revision Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? I cannot comment. A qualified statistician is required. Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Partly Competing Interests: No competing interests were disclosed. Reviewer Expertise: Fuzzy set, soft sets, decision-making, fuzzy graphs, fuzzy algebraic. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Karaaslan F. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367656 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367656 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy ... Continue reading 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy soft set takes ''the set of fuzzy sets''. However, the generalised fuzzy soft code takes ''the set of fuzzy code sets''. 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy soft set takes ''the set of fuzzy sets''. However, the generalised fuzzy soft code takes ''the set of fuzzy code sets''. Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy ... Continue reading 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy soft set takes ''the set of fuzzy sets''. However, the generalised fuzzy soft code takes ''the set of fuzzy code sets''. 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy soft set takes ''the set of fuzzy sets''. However, the generalised fuzzy soft code takes ''the set of fuzzy code sets''. Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Mahmood T. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r346175 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-346175 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 03 Jan 2025 Tahir Mahmood , International Islamic University Islamabad, Islamabad, Pakistan Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.174381.r346175 The paper "New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings " aims to develop a decision-making approach based on generalized fuzzy soft sets. The subject of the paper fits the aims and scope ... Continue reading READ ALL The paper "New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings " aims to develop a decision-making approach based on generalized fuzzy soft sets. The subject of the paper fits the aims and scope of the Journal. More detailed comments are as follows and I recommend the following major revision. Revise the title as “New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” The abstract is not written well. It has a lot of unexplained abbreviations. The authors didn’t adequately introduce the topic they are covering in the paper. It lacks an Information Classification: General adequate background of the problem highlighting the motivation for the study, main results, and conclusions. Further it is too short. Keywords are not enough to understand the theme of the manuscript. These should be enhanced. Most of what is currently Introduction should be moved from another section or should be extended, since it is too short to be useful and it should deal with the background of the problem and literature review effectively. Within this section, the authors should highlight the research gaps that this paper is trying to cover. The authors should discuss in the introduction a short overview of the problem and highlight the purpose and the aim of the study, as well as the main results, conclusions, and scientific contributions. It also lacks the historical background and literature review of the proposed study including the framework of soft set. The paper does not have a proper discussion. The authors did not discuss how the results can be interpreted from the perspective of previous studies. Discussion should clearly and concisely explain the significance of the obtained results to demonstrate the actual contribution of the article to this field of research when compared with the existing and studied literature. In the manuscript all the references should be cited correctly. For Example, in Definition 6, the reference (Kong, Wang, and Wu 2011) is cited, which needs correction. In subsection 3.1 and hence in the whole manuscript “generalised” should be “generalized”. The authors didn’t explain the limitations and implications of the proposed approach. Applications of the proposed theory needs attention as it is not properly treated. The conclusion is scarce. The authors should address the main research questions and highlight the main results, conclusions, contributions, and future research directions in the conclusion. Future scope of research should be multidirectional like bipolar soft sets, double framed soft sets, soft algebraic structures etc. English writing should be improved, particularly regarding syntax and style errors. Information Classification: General To address the above mentioned issues regarding literature review and future scope of the proposed study authors must add and cite some recent and well related manuscripts by Ashraf ul Quran, Tahir Mahmood and Muhammad Akram. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? No source data required Are the conclusions drawn adequately supported by the results? Partly Competing Interests: No competing interests were disclosed. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Mahmood T. Reviewer Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r346175 ) The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-346175 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy ... Continue reading 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” 2. From definition 6 change by 12 from the reference Kong, Wang, and Wu 2011. 3. The manuscript "Generalised" can't change by "Generalized". For example see the motivated papers "Generalised fuzzy soft set" and " Generalised interval-valued fuzzy soft set" etc 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” 2. From definition 6 change by 12 from the reference Kong, Wang, and Wu 2011. 3. The manuscript "Generalised" can't change by "Generalized". For example see the motivated papers "Generalised fuzzy soft set" and " Generalised interval-valued fuzzy soft set" etc Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 09 Apr 2025 Masresha Wassie Woldie , Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 09 Apr 2025 Author Response 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy ... Continue reading 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” 2. From definition 6 change by 12 from the reference Kong, Wang, and Wu 2011. 3. The manuscript "Generalised" can't change by "Generalized". For example see the motivated papers "Generalised fuzzy soft set" and " Generalised interval-valued fuzzy soft set" etc 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” 2. From definition 6 change by 12 from the reference Kong, Wang, and Wu 2011. 3. The manuscript "Generalised" can't change by "Generalized". For example see the motivated papers "Generalised fuzzy soft set" and " Generalised interval-valued fuzzy soft set" etc Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 02 Dec 2024 ADD YOUR COMMENT Comment keyboard_arrow_left keyboard_arrow_right Open Peer Review Reviewer Status info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Reviewer Reports Invited Reviewers 1 2 3 4 Version 2 (revision) 09 Apr 25 read read Version 1 02 Dec 24 read read read Tahir Mahmood , International Islamic University Islamabad, Islamabad, Pakistan Faruk Karaaslan , Çankırı Karatekin University,, Çankırı, Turkey Rana Muhammad Zulqarnain , Zhejiang Normal University, Zhejiang, China Ajoy Kanti Das , Tripura University, Suryamani Nagar, India Comments on this article All Comments (0) Add a comment Sign up for content alerts Sign Up You are now signed up to receive this alert Browse by related subjects keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Zulqarnain R. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 28 Apr 2025 | for Version 2 Rana Muhammad Zulqarnain , Zhejiang Normal University, Zhejiang, China 0 Views copyright © 2025 Zulqarnain R. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions The authors revised the manuscript very well. I have no further questions for the authors. Competing Interests No competing interests were disclosed. Reviewer Expertise Fuzzy extensions. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. reply Respond to this report Responses (0) Zulqarnain RM. Peer Review Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.179056.r377009) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/13-1461/v2#referee-response-377009 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Das A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 22 Apr 2025 | for Version 2 Ajoy Kanti Das , Tripura University, Suryamani Nagar, Tripura, India 0 Views copyright © 2025 Das A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions REVIEW REPORT New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings This manuscript proposes a new concept called Generalised Fuzzy Soft Code (GFSC), integrating the ideas of generalised fuzzy soft sets with fuzzy codes. The paper attempts to formalize definitions, operations (union, intersection, complement), and matrix representations of GFSC, with illustrative examples and basic theorems. The paper is well-structured, with clear objectives and systematic development of theoretical models. However, there are several areas where the manuscript could benefit from improvement, both in terms of structure and content. Some comments are suggested to improve the quality of this paper. Suggestions for Improvement: Check and correct all typographical and grammatical errors. For example: (i) “on fuzzy Codes and Its Properties...” in the Title should be: “on Fuzzy Codes and Their Properties...” In the third paragraph of the Introduction, the phrase “formationed works” is used, which is not a valid expression. This should be replaced with an appropriate and grammatically correct alternative, such as “foundational works” or “previous studies”, depending on the intended meaning. Abbreviations should be defined before their first use. This is not consistently followed in the manuscript. For example, IFSS appears in the Introduction but is not explained. It is recommended to define all abbreviations upon first use and include a list of abbreviations in a table after the abstract or before Section 1. The citation for Definition 6 is incorrect. It is currently cited as (Molodtsov 2011), but it should be (Molodtsov, 1999), as the original soft set theory was introduced in that year. Please update this citation accordingly. In Definition 9 , the phrase “The universal set of elements is = {x₁,x₂,…,x ₙ} ” is incorrect and incomplete. It should be written as: “ The universal set of elements is U= {x₁,x₂,…,x ₙ} ” Set and function symbols are sometimes misused or introduced without adequate explanation. For example, in Definition 16, the statement “Let U = Rwr(ai) for which C is the universal element” is unclear, what and represent in this context. Please revise this definition to clearly specify the meaning and roles of all symbols and sets involved. I strongly recommend double-checking all the symbols and formulas to ensure accuracy in indices, notation, and conceptual consistency. To improve readability, consider adding a table summarizing all mathematical symbols and their definitions used in the manuscript. This addition would enhance clarity and accessibility, especially for readers who may not be familiar with the specific notation employed. While the theoretical contributions are clear, the paper would benefit from a stronger justification of why Generalised Fuzzy Soft Sets on Fuzzy Codes are useful or necessary. Specifically, the manuscript lacks discussion on real-world problems or domains where these models offer distinct advantages over classical or existing fuzzy set approaches. It is recommended to add a dedicated section that illustrates practical scenarios—such as in medical diagnosis, information coding, or decision-making under uncertainty—where Generalised Fuzzy Soft Sets on Fuzzy Codes provide improved interpretability, flexibility, or accuracy. This would significantly enhance the paper’s relevance and motivate the proposed theoretical framework. The focus is primarily theoretical; real-world applications or potential use cases are not discussed. Expand the literature review by including more recent research on fuzzy soft set and its applications in various domains. I suggest: Refer: 1,2,3,4,5,6. Ensure consistent formatting of equations, as some appear cramped or unclear. Include a future research section that outlines the next steps for further research to emphasize the study’s broader relevance. Please recheck all references to ensure they are written correctly and include complete information. Some references are incomplete. For instance, the reference to Muhammad et al. (2023) is incomplete — the journal name, volume number, and page range are missing and should be included. The paper makes a significant theoretical contribution and has strong potential for real-world applications but requires significant revision in terms of language, structure, and typesetting before it can be accepted for indexing. Recommendation : Accept with revisions. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? No source data required Are the conclusions drawn adequately supported by the results? Yes References 1. Wang X, Mostafa Khalil A: A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making. Computer Modeling in Engineering & Sciences . 2023; 136 (3): 2861-2871 Publisher Full Text 2. Lu H, Khalil A, Alharbi W, El-Gayar M: A new type of generalized picture fuzzy soft set and its application in decision making. Journal of Intelligent & Fuzzy Systems . 2021; 40 (6): 12459-12475 Publisher Full Text 3. Das A, Granados C: An Advanced Approach to Fuzzy Soft Group Decision-Making Using Weighted Average Ratings. SN Computer Science . 2021; 2 (6). Publisher Full Text 4. Mukherjee A, Das A: Einstein-operations on fuzzy soft multi sets and decision making. Boletim da Sociedade Paranaense de Matemática . 2022; 40 : 1-10 Publisher Full Text 5. Department of Mathematics, Bir Bikram Memorial College, India, Das A, Granados C, Estudiante de Doctorado en Matemáticas, Magister en Ciencias Matemáticas, Universidad de Antioquia, Colombia: FP-intuitionistic multi fuzzy N-soft set and its induced FP-Hesitant N soft set in decision-making. Decision Making: Applications in Management and Engineering . 2022; 5 (1): 67-89 Publisher Full Text 6. Al-shami T, Alcantud J, Mhemdi A: New generalization of fuzzy soft sets: $ (a, b) $-Fuzzy soft sets. AIMS Mathematics . 2023; 8 (2): 2995-3025 Publisher Full Text Competing Interests No competing interests were disclosed. Reviewer Expertise Fuzzy set theory and applications, soft set theory, Fuzzy extensions, Sequence spaces, Water quality assessment I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (0) Das AK. Peer Review Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.179056.r377656) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/13-1461/v2#referee-response-377656 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Zulqarnain R. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 11 Mar 2025 | for Version 1 Rana Muhammad Zulqarnain , Zhejiang Normal University, Zhejiang, China 0 Views copyright © 2025 Zulqarnain R. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions I encourage you to improve the abstract section precisely with your core contributions. Keywords are inappropriate; please add proper keywords for readers' convenience. Considering the innovative nature of this methodology and its potential influence on academic research and industrial practices, the authors should emphasize the interdisciplinary aspects of their study, particularly regarding evolutionary economics and organizational behavior. The problem statement and motivation is given. Please explain the problem in detail. There are no research questions, so please add the research question for the reader's convenience. The introduction and theoretical background are not enough. I suggest some important studies for authors to improve the introduction and background of this manuscript. Also, I strongly recommend reading these studies carefully and cite in the introduction and background sections. The literature review would not have been acceptable to me without the following studies in the introduction and references section. So, carefully revised the introduction and background. (a): Some Einstein geometric aggregation operators for Q-rung orthopair fuzzy soft set with their application in MCDM. (b): Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set with Their Application to Solve Multi-Attribute Group Decision Making Problem. (c): Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision‐Making. (d): An interaction and feedback mechanism-based group decision-making for emergency medical supplies supplier selection using T-spherical fuzzy information. (d): Optimal cloud service provider selection: An MADM framework on correlation-based TOPSIS with interval-valued q-rung orthopair fuzzy soft set. (e): Algorithms for a Generalized Multipolar Neutrosophic Soft Set with Information Measures to Solve Medical Diagnoses and Decision‐Making Problems. (f): Extension of Einstein average aggregation operators to medical diagnostic approach under Q-rung orthopair fuzzy soft set. (g): Novel multicriteria decision making approach for interactive aggregation operators of q-rung orthopair fuzzy soft set. (h): Selection of unmanned aerial vehicles for precision agriculture using interval-valued q-rung orthopair fuzzy information based TOPSIS method. (i): An integrated group decision-making technique under interval-valued probabilistic linguistic T-spherical fuzzy information and its application to the selection of cloud storage provider. (j): Einstein ordered weighted aggregation operators for Pythagorean fuzzy hypersoft set with its application to solve MCDM problem. (k): Supplier Selection in Green Supply Chain Management using Correlation-based TOPSIS in a q-rung Orthopair Fuzzy Soft Environment. (l): An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets. (m): Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques. (n): Assessment of bio-medical waste disposal techniques using interval-valued q-rung orthopair fuzzy soft set based EDAS method. (o): Einstein Hybrid Structure of q-Rung Orthopair Fuzzy Soft Set and Its Application for Diagnosis of Waterborne Infectious Disease. (p): Transportation decisions in supply chain management using interval-valued q-rung orthopair fuzzy soft information. Please clarify which of the assumptions is new in this area in the problem definition. How did you consider the data in the case study? The input section mentions constructing a group of decision-makers but doesn't clearly explain how they influence the process. Similarly, the output section could benefit from more detail on the final results, such as how the ranking is used for decision-making. The authors should discuss how their presented work is needed at the time and whether it will be helpful to the scientific community. The role of weights in the aggregation process could be explained more explicitly, particularly how they are assigned to each alternative and how they impact the final decision-making process. How are the experts’ weights determined, and how do they influence the decision-making process? Comparative analysis section in the manuscript is not enough, please add more comparative studies to prove the validity of the proposed model. Can the research's shortcomings be commented on, particularly regarding the number of participants and the range of sectors addressed in the focus groups? Please bring and focus on future research directions. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Partly Competing Interests No competing interests were disclosed. Reviewer Expertise Fuzzy extensions. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 09 Apr 2025 Masresha Wassie Woldie, Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia We incorporated all comments as the reviewer's suggestions. View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Zulqarnain RM. Peer Review Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367664) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367664 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Karaaslan F. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 05 Mar 2025 | for Version 1 Faruk Karaaslan , Çankırı Karatekin University,, Çankırı, Turkey 0 Views copyright © 2025 Karaaslan F. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Review Report for “New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings” A new aspect of this paper is to introduce and develop the definition and application of generalized fuzzy soft code by combining the concepts of fuzzy soft sets and fuzzy codes. The definition and features of relations on generalized fuzzy soft codes are proposed. But there are some problems in the paper. After the following revisions, Paper can be revaluated for indexing. In definition 4, R wr c i ∪ R wr c j = max⁡ (….) subindices should be checked and corrected. Citation of definition 6 should be corected, because soft set was defined by Molodtsov (1999). Also, in same definition, “P(U) be represents…” should be replaced by “P(U) represents”. Definition 6, line 8-9, “ e∈A. where… “ should be corrected. Also, sentences beginning with “We might consider…” I think that soft set is a special type of Zadeh’s fuzz sets. Check this sentence In definition 8, should be replaced by ” In definition 9. “The universal set of elements is ,…” should be rewritten as “The universal set of elements is ,…” In same definition, where ” should be checked and corrected. In Definition 12, “t-norm” should be replaced by “s-norm or t-conorm” In Definition 13, “ ” should be replaced by “ ” and, “*” should be “t-norm” In definition 14, 15, authors use some notations without they give an explanation, for example “ ” and . They should be explained. In example 1. I see that basic idea is that authors take the parameter set E, and define a fuzzy set on this parameter set; also, they take for any set of . In example 1, “Let …” What does it mean? According to definition of , Why you write ” is not true expression as mathematically. In example 2, “…in example 3.2 ”. Where is the example 3.2? In example 2, should be replaced by ”. In example 2, “e generalized fuzzy soft code subset of G σ is .” This is not true, it should be checked. In definition 18, minimum operation is not defined between pairs and So if author write the . Same problem is available for Definition 19. We know that is a fuzzy set. How can you maket he substruction operation between a number and fuzzy set. Actually I understand what you make, bu this writting is not true mathematical. Check and rewrite them. When I investigate the proof of theorem 2, I see that it is same with the proof for generalized fuzzy soft sets. What is the difference between generalized fuzzy soft code and generalized fuzzy soft set. I think that Theorem 2, and 3 are trivial results of the generalized fuzzy soft set. In Definition 24, “GFSC” should be replaced by “GFSCs”. The application part related to generalized fuzzy soft code relations is elementary and we can apply this to all generalized fuzzy soft sets. What is the importance of this application in terms of the codes? The results of the application are independent of codes. The importance and effect of the codes must be explained in the paper. The introduction part should be improved. The paper could benefit from refinement in terms of mathematical writing style to enhance clarity and precision. The title should be rewritten. Decision: Major Revision Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? I cannot comment. A qualified statistician is required. Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Partly Competing Interests No competing interests were disclosed. Reviewer Expertise Fuzzy set, soft sets, decision-making, fuzzy graphs, fuzzy algebraic. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 09 Apr 2025 Masresha Wassie Woldie, Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 1. we incorporated all suggested comments and submitted the corrected version. 2. The difference between a generalised fuzzy soft set and generalised fuzzy soft code is that the generalised fuzzy soft set takes ''the set of fuzzy sets''. However, the generalised fuzzy soft code takes ''the set of fuzzy code sets''. View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Karaaslan F. Peer Review Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r367656) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-367656 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Mahmood T. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 03 Jan 2025 | for Version 1 Tahir Mahmood , International Islamic University Islamabad, Islamabad, Pakistan 0 Views copyright © 2025 Mahmood T. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions The paper "New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings " aims to develop a decision-making approach based on generalized fuzzy soft sets. The subject of the paper fits the aims and scope of the Journal. More detailed comments are as follows and I recommend the following major revision. Revise the title as “New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” The abstract is not written well. It has a lot of unexplained abbreviations. The authors didn’t adequately introduce the topic they are covering in the paper. It lacks an Information Classification: General adequate background of the problem highlighting the motivation for the study, main results, and conclusions. Further it is too short. Keywords are not enough to understand the theme of the manuscript. These should be enhanced. Most of what is currently Introduction should be moved from another section or should be extended, since it is too short to be useful and it should deal with the background of the problem and literature review effectively. Within this section, the authors should highlight the research gaps that this paper is trying to cover. The authors should discuss in the introduction a short overview of the problem and highlight the purpose and the aim of the study, as well as the main results, conclusions, and scientific contributions. It also lacks the historical background and literature review of the proposed study including the framework of soft set. The paper does not have a proper discussion. The authors did not discuss how the results can be interpreted from the perspective of previous studies. Discussion should clearly and concisely explain the significance of the obtained results to demonstrate the actual contribution of the article to this field of research when compared with the existing and studied literature. In the manuscript all the references should be cited correctly. For Example, in Definition 6, the reference (Kong, Wang, and Wu 2011) is cited, which needs correction. In subsection 3.1 and hence in the whole manuscript “generalised” should be “generalized”. The authors didn’t explain the limitations and implications of the proposed approach. Applications of the proposed theory needs attention as it is not properly treated. The conclusion is scarce. The authors should address the main research questions and highlight the main results, conclusions, contributions, and future research directions in the conclusion. Future scope of research should be multidirectional like bipolar soft sets, double framed soft sets, soft algebraic structures etc. English writing should be improved, particularly regarding syntax and style errors. Information Classification: General To address the above mentioned issues regarding literature review and future scope of the proposed study authors must add and cite some recent and well related manuscripts by Ashraf ul Quran, Tahir Mahmood and Muhammad Akram. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? No source data required Are the conclusions drawn adequately supported by the results? Partly Competing Interests No competing interests were disclosed. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 09 Apr 2025 Masresha Wassie Woldie, Bahir Dar University Department of Mathematics, Bahir Dar, Ethiopia 1. we accept the title revision "New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications on Decision-Makings” to New Approaches of Generalized Fuzzy Soft Sets on Fuzzy Codes and Its Applications in Decision-Makings” 2. From definition 6 change by 12 from the reference Kong, Wang, and Wu 2011. 3. The manuscript "Generalised" can't change by "Generalized". For example see the motivated papers "Generalised fuzzy soft set" and " Generalised interval-valued fuzzy soft set" etc View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Mahmood T. Peer Review Report For: New Approaches of Generalised Fuzzy Soft sets on fuzzy Codes and Its Properties on Decision-Makings [version 1; peer review: 3 approved with reservations] . F1000Research 2024, 13 :1461 ( https://doi.org/10.5256/f1000research.174381.r346175) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/13-1461/v1#referee-response-346175 Alongside their report, reviewers assign a status to the article: Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions Adjust parameters to alter display View on desktop for interactive features Includes Interactive Elements View on desktop for interactive features Competing Interests Policy Provide sufficient details of any financial or non-financial competing interests to enable users to assess whether your comments might lead a reasonable person to question your impartiality. 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