A Feasibility study on using electric heating in cold rural areas of China

A Feasibility study on using electric heating in cold rural areas of China | 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 Research Article A Feasibility study on using electric heating in cold rural areas of China Wei Yu, Haixia Zhou, Jiaying Huang, Zixian Yu, Shen Wei, Xiaochun Wu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2280851/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 In response to China’s “double carbon” policy, cold, rural areas of the nation are currently upgrading their heating methods. Since rural areas are more dispersed than urban areas, centralized heating is not easy to use. Therefore, electric heating has become one of the major solutions. However, few studies have investigated the performance, suitability, and user impressions of electric heating in rural areas in China. Here, therefore, we used a literature review, questionnaires, and expert consultations to determine the relevant indicators that best reflect the suitability of electric heating usage in cold rural areas in northern China. Then, by using both expert questionnaires and the analytic hierarchy process (AHP) to determine the weights of these indicators, we developed a hybrid model established based on the gray whitening weight clustering method. We then applied this model to two case studies in different provinces, namely 20 households from a village in northern China where electric heating was being uses. Our major findings were 1) the primary indicators were technology, economy, comfort, safety, aesthetic portability, and environmental protection; 2) the weights of these indicators were 16.17%, 31.58%, 23.37%, 18.46%, 5.16%, and 5.25%, respectively, with all indicators passing the consistency test; 3) results of two case studies were consistent with the villagers' actual subjective evaluation results; 4) evaluation software has been developed. Our evaluation method developed can effectively reflect the actual needs of people living in rural areas of China. The government can use evaluation software to get the feasibility of adopting electric heating in villages to achieve reasonable low-carbon promotion in rural areas. electric heating indicator system questionnaire research analytic hierarchy process gray whitening weight clustering Figures Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Highlights Evaluation index system of suitability on using electric heating in cold rural areas of China based on hierarchical analysis and grey whitening weight clustering method. Based on field research, comprehensive consideration of user and expert opinions to establish an evaluation index system of electric heating, mainly including economy, comfort, safety, beauty and portability, and environmental protection. This evaluation index system can avoid the unbalanced impact of indicators. This evaluation method is validated by cases with practical application, guiding the government to help improve electric heating in cold rural areas of China. 1. Introduction Under China’s “dual carbon” target, all industries are undergoing energy upgrades and transformations. In the rural areas of northern China, the most popular heating sources in winter are Kang and a simple stove, accounting for more than 75% (Zhu et al. 2020 ). Traditional heating methods mainly transfer heat to a room through the burning of scattered coal, straw, or firewood (Gong et al. 2020 ), which is both environmentally detrimental and harmful to air quality (Tao et al. 2018 ). Cities in China are dominated by central heating (Chen et al. 2014 ); as rural buildings are more scattered, however, central heating systems are not suitable in rural areas(Ma et al. 2017 ). Therefore, it is crucial to find a heating method that is suitable for the rural areas of northern China. Electricity became one of the leading energy sources for households (ranked as the second dominant source after biomass) (Wang et al. 2022 ). During the 12th Five-Year Plan period (2010–2015), China’s rural areas achieved full grid coverage (China Government Network 2016 ) By the end of 2020, the rural grid reliability reached 99.8% (China Government Network 2016 ). China’s electricity sources can mainly be divided into coal, hydro, nuclear, wind, and solar power. According to the National Bureau of Statistics, China’s non-fossil energy supply increased from 20.8% in 2010 to 30.46% in 2019, while the nation’s coal-fired power supply has been decreasing year on year. By 2030, China will have drastically reduced the use of coal, with plans to stop using coal power completely by 2050 (Jewell et al. 2019 ). Thus, electricity will represent a relatively clean energy source. Since 2015, China has introduced a series of preferential subsidies to promote electricity as an alternative to domestic combustion for heating in rural areas (Soltero et al. 2018 ; Wang et al. 2020a ). Coal-to-electricity policies do change residential indoor air quality (Wu et al. 2020 ) and reduce pollution of the outdoor environment(Chen et al. 2020 ). In many rural northern areas, where solar energy is abundant, villagers are already using solar power to meet their heating needs (Wang et al. 2015 ; Li and Xu 2019 ; Zhao et al. 2019 ). Air source heat pumps also use electricity to transfer energy for heating. However, these approaches require significant investment, and suffer from frost and low energy efficiency in winter (Guo et al. 2008 ). Therefore, electric heating has become widely used in rural areas. Electric heating sources include thermal storage heater, electric heaters, heating cables, electric heating films, carbon crystals, heat rails, and carbon fibers (Zhang et al. 2021 ). These forms of heating convert electrical energy into heat through electrical resistance; they are very simple to use, and have become widespread (Zhang et al. 2021 ). The flexibility and convenience of electric heating makes it easy for villagers to accept (Zhang et al. 2021 ). Electric heating has been used in Northern Europe, Korea, and Japan for more than 50 years (Liu and Ran 2016 ) Due to the abundance of water, electricity, oil, and other resources, Norway in Northern Europe, France in Western Europe, Central America, and Canada all mainly use electric heating (Liu and Ran 2016 ); it is also widely used in northern China (Zhang et al. 2020 ). Zhang (Zhang 2017 ) and Wang (Wang et al. 2020b ) analyzed the advantages of electric heating in the rural areas of cold regions in northern China; they concluded that electric heating could meet the comfort requirements of rural residents, while also being economical. Time-sharing tariffs have been adopted in many places in China. Zhao et al. (Zhang 2017 ) and Li et al. (Li and Zhao 2013 ) analyzed electric heating usage under rural and urban time-sharing tariffs, respectively, showing that it is more flexible and economical than fixed price, and that it can help to facilitate the consumption of large amounts of domestic abandoned wind and electricity capacity. Regarding the performance of electric heating technology, Jin (Jin and Davis 2020 ) proposed an energy-saving control method to zero energy consumption in buildings using electric heating films; this method can achieve a low energy consumption while maintaining a stable temperature output. Ali et al. (Ali et al. 2014 ) proposed that electric heating and thermal storage, when sued in series, can achieve an optimal demand response in smart grid scenarios by simulating and analyzing heat demand and power. Campos et al. (Campos et al. 2020 ) conducted energy analysis and prediction for rural heating in Hungary; they suggested that a combination of electric energy retrofitting and efficient heating technologies can be used to meet rural heating. What types of villages are suitable for electric heating? Most previous studies into electric heating have focused on the performance of the heating equipment in question. However, the factors affect people’s acceptance of electric heating, such as investment, operating costs, and feeling of use have not been considered regarding its actual adoption. Therefore, this study proposes the concept of electric heating suitability in cold rural areas. In addition, it established an indicator system and model to evaluate the feasibility of electric heating in cold rural areas. 2. Method 2.1 Research Framework This study comprised three main sections wherein the first part addressed the selection of suitability indicators for electric heating in cold rural areas. In this section, the basic information of the research questionnaire was determined through a literature review. Subsequently, several rural areas in the cold regions were visited to conduct questionnaires, with initial primary indicators being obtained from these questionnaire data. The research for this study consisted of both field and web-based questionnaires and was conducted with the consent of each villager before filling in the questionnaire. Each primary indicator was then refined into several secondary indicators, following which all indicators were improved through expert consultation. The second section entailed the determination of weights. The weights of the secondary and primary indicators were calculated using an expert questionnaire and an Analysis Hierarchical Process (AHP). The section comprised the establishment and verification of the model. A hybrid model was established for evaluating the suitability of electric heating in cold rural areas; it aimed to divide electric heating suitability into several gray classes while setting the whitening weight function. Each secondary indicator was then quantified according to the gray grade. Finally, cases from two different provinces using electric heating were selected to validate the model. In the validation process, villagers in each village were asked to rate according to the indicators and evaluate the suitability according to the established model. Then visit the users who use electric heating for comprehensive satisfaction. The evaluation model and index system are reliable if both of them get the same conclusion; the research process is illustrated in Fig. 1 . 2.2 Research Contents 2.2.1 Selection of Indicators In this study, indicators were mainly selected based on three methods: a literature review, questionnaire surveys, and expert consultation. These three methods were used to screen and improve indicators obtained from scholars, users, and experts in related fields, to ensure a degree of credibility. Finally, the complete criterion (primary indicators) and indicator (secondary indicators) layers of the suitability indicator system for electric heating in cold rural areas were obtained. As little research has been conducted to date regarding the comprehensive evaluation, of index systems for electric heating, here relevant index research on clean heating was reviewed as a reference; suitable indexes for electric heating were screened out. When analyzing evaluation indicators for promoting the application of clean heating, two main perspectives were identified. One was framed from a macro perspective; it entailed the determination of whether a certain clean heating method was suitable for adoption in a certain place. This perspective was generally related to economic (Wei et al. 2010 ; Wang et al. 2019 ; Zhang et al. 2020 ; Huo et al. 2020 ; He et al. 2021 ), technical (Wei et al. 2010 ; Wang et al. 2019 ; Zhang et al. 2020 ), environmental protection(Wei et al. 2010 ; Wang et al. 2019 ; Zhang et al. 2020 ; He et al. 2021 ), and to the social factors (He et al. 2021 ) that are necessary to ensure a comprehensive evaluation. The other entailed the user’s perspective; it was related to the analysis of whether users were willing to adopt a certain type of clean heating. Reviewing the studies of Karytsas and Theodoropoulou revealed that when addressing the utilization of renewable energy, scholars from various countries have mainly considered factors such as socioeconomic, residential, and spatial characteristics, as well as consumers’ behavior, preferences, and attitudes toward the attributes of specific heating systems (Karytsas and Theodoropoulou 2014 ). Not all of the influencing factors for clean and renewable energy heating are suitable for electric heating, however. Table 1 shows the influencing factors that were screened for electric heating in this study Table 1 Factors influencing the choice of electric heating Socioeconomic characteristics Income, age, educational level, household size (number of residents), children in the household, number of children, gender, occupation Residence characteristics Residence size (or number of bedrooms), type of residence, year of construction, ownership, years living in the residence, infrastructure Characteristics related to the behavior of consumers, attitudes, and system attributes preferences Economic aspects, environmental considerations, energy saving, security, comfort considerations and aesthetics, general attitude, social reasons, information/knowledge aspects, supplier issues Policy requirements environmental protection, economic, technical A questionnaire was designed based on this literature review. The questionnaire comprised 27 questions covering three main areas: basic information about households, basic information about buildings’ heating conditions, and villagers’ expectations. Cold areas are widely distributed in northern China. Here, the stratified sampling method (Parsons 2017 ) was applied to divide spaces into seven parts according to administrative subdivisions (five provinces and two municipalities: Henan, Hebei, Shandong, Shanxi, Shaanxi, Beijing, and Tianjin). Then, the number of studies was distributed according to the total number of villages. The distribution of the field questionnaire survey is shown in Fig. 2 . Totally, 203 field surveys and 470 online questionnaires were obtained. The factors that villagers care about were extracted from the questionnaire data as initial primary indicators. Finally, these initial primary indicators were refined into several secondary indicators, according to a literature review and a market survey. Expert consultation was mainly conducted through a questionnaire, which was used to distribute the initial primary and secondary indicators to experts for their consultation. Their opinions on each indicator were collected, and they were asked to suggest any additions to the selected indicators. Forty-four valid expert questionnaires were collected. The invited experts were active in heating fields, aged 23 to 60 years old having a bachelor’s level degree or higher. To ensure the questionnaire quality, all experts were from universities, design units, construction units, equipment manufacturers, operation management teams, government departments, or scientific research institutes, or were user representatives 2.2.2 Indicator Weights The AHP has a particular application in group decision-making (Harker and Vargas 1990 ). It is one of the most widely used multi-standard decision-making techniques for analyzing energy and environmental issues (Zhou et al. 2006 ). The AHP can use qualitative and quantitative relationships to establish a judgment matrix and determine indicator weights. Therefore, here the AHP was selected to calculate the indicator weights. First, the relationships between indicators for the suitability of electric heating in cold rural areas were analyzed. Analysis was divided into three layers: the goal layer (suitability of electric heating in cold rural areas), the criterion layer (primary indicators), and the indicator layer (secondary indicators). The expert survey method was then used to judge the screened primary and secondary indicators. The experts involved in the consultation worked in scientific research institutions, construction units, equipment manufacturers, operation management teams, government departments, user representatives, or other departments closely related to rural heating. These experts had more than three years of heating work experience, and each possessed an engineer’s or associate professor’s title, or higher. The sample size for an AHP should be in the range of 10–50 (Du and Pang 2021 ), within which a reasonable accuracy of 10% can be achieved for general engineering evaluations. To establish a sound evaluation system, 30 copies of this survey were distributed, from which 24 valid documents were recovered. Two-by-two comparison judgments of each indicator were made according to the nine-point method recommended by Saaty (Saaty 1980 ). When the stochastic conformance ratio (CR) < 0.10, the judgment matrix was considered to have passed the consistency test. The indicator weights of the indicator layer are established in the same way as the criterion layer. Finally, the weights of each secondary and primary indicator were calculated. 2.2.3 Establishment of Suitability Evaluation Model In previous rating systems, the scores and weights of each indicator have often been used to determine the grade by summing them. (Kim et al. 2005 ). However, this approach may induce an “imbalanced performance” effect (Yu et al. 2015 ), which can lead to some rural areas with high scores not meeting villagers’ requirements regarding some of the indicators. Gray clustering was first proposed by Professor Deng in 1982 to deal with uncertainty problems (Deng 1987 ). The gray whitening power function-clustering model categorizes the values of evaluation indicators according to a set of categories. The final evaluation grade results are then determined according to the categories to which each evaluation value belongs (Deng 1987 ). Such clustering methods can avoid this “imbalanced performance” effect. Therefore, here the gray whitening power function clustering method was used to establish a model for evaluating the suitability of electric heating in cold rural areas. A scoring system with four or five levels is generally used in gray clustering evaluations (Min et al. 2018 ; Zhang et al. 2018 ). Here, five levels were used to define each level: “very suitable,” “suitable,” “more suitable,” “less suitable,” and “very unsuitable.” The highest rating was allotted ten points (Zhang and Shuang 2017 ), with the full score ranges of this study being [9–10], [7–9], [3–7], [1–3], and [0–1], respectively (Zhang and Shuang 2017 ). Each secondary index was quantified according to the gray classification and the performance of the said index. The suitability evaluation model for electric heating in cold rural areas is shown in Fig. 3 . The components of this indicator system for evaluating the suitability of electric heating in cold rural areas were divided into the goal (A), criterion (A i ), and indicator (A ij ) layers. The whitening weight function of each gray class was then determined according to the requirements of the gray class division. The critical values were taken as the boundary and midpoint values. The essential values of the five evaluated gray classes were 9, 7, 5, 3, and 1, and their whitening weight functions were respectively, as shown in Table 2 (Zhang and Shuang 2017 ). P representative households were invited to score each indicator layer, with the scoring value of each participating household being called the gray number. All secondary indicator scores (gray numbers) were constructed as a sample matrix and then substituted for the calculation model. Table 2 Distribution of Whitening Weight Functions 2.3 Empirical cases We chose two different types of villages as case studies, Zhujiayao village and Fanbao village. Zhujiayao Village in Shanxi Province was selected as a case study to evaluate the suitability of using electric heating films in cold northern regions. In the winter of 2019, the entire village of Zhujiayao transitioned to electric heating; electric heating films were used to replace coal-fired stoves and traditional heating sources. The Government funded the free installation of electric heating films for the entire village, with annual electricity costs now being as low as 0.286 RMB·kWh − 1 ·y − 1 , over a four-month heating period. Fanbao Village is located in the northeast of Qingfeng County, Puyang City, Henan Province, and was renovated in the winter of 2019. The government installed air source heat pumps for those who voluntarily chose electric heating, and the electricity price was charged according to the "coal-to-electricity" peak and valley time tariff (0.44 RMB/kw·h at peak time and 0.29 RMB/kw·h at valley time). Through the visit, although 70% of the households installed air source heat pumps, they were still dissatisfied with the high cost of electricity, resulting in 80% of the users not turning on the heat pump or turning it on less. And some of the villagers adopted the storage type electric heating, they said the electric heating effect is good, so Fanbao village was chosen as the study case. The same approach to evaluation was used in both villages. At the suggestion of the village leader, here six permanent household representatives were randomly selected within the village to rate each indicator, according to the scoring criteria specified by the quantitative rating of said indicator. Then, the suitability of electric heating was evaluated in Zhujiayao and Fanbao villages according to the above suitability evaluation method and scores. The evaluation results were compared with the subjective rating data of households and the satisfaction results of visiting villagers regarding the adoption of electric heating. If the two results are similar, the model built is proven to be reliable. An on-the-spot investigation is shown in Fig. 4 . 3. Results and Discussion 3.1 Screening Indicators 3.1.1 Initial Indicator Screening According to the questionnaire information, the present heating methods in cold rural areas in northern China during winter mainly comprised air conditioners, electric stoves, electric heating films, wall-hung stoves, and gas stoves, among others (Fig. 5). Although electric heating accounted for a large proportion of heating methods (22.31 and 14.58% for air conditioners and electric stoves, respectively), 29.32% of the households were still using unclean energy sources such as coal-fired stoves and traditional heaters. This may have mainly been due to influences such as local resources, and the economy, among others. Liu et al. studied rural houses in cold areas in 2013, finding that the main winter heating methods used by village residents were coal-fired stoves and traditional heating (49.6%) (Yang and Zhao 2013 ), so the findings presented here represent a significant improvement. This shows that the Government’s recent series of “coal to electricity” and “coal to gas” policies have had a significant effect. The specific factors that influenced village residents’ selection of their heating method were analyzed (Fig. 6), showing that 73.73% of the households gave primary consideration to heating costs. This emphasizes that the economy was the primary consideration for village residents when choosing a heating method. Indoor comfort was the next crucial factor (56.68%), showing that, assuming that their economic needs were met, residents preferred to select heating equipment that met their comfort requirements. Safety and reliability were both identified by residents as necessary considerations when choosing heating equipment (50.69%). Moreover, 31.34% of the households also considered environmental protection. Aesthetics and portability were also a consideration for 18.89% of residents, showing that certain attention was also directed to decorative beauty, along with functionality. As shown in Fig. 7, villagers with lower annual incomes were less likely to adopt air conditioning, electric heaters, and floor heating for household heating. Residents with higher incomes, however, were more likely to use quality heating. Similar findings were also obtained in Wang’s indoor study in Hebi, Henan Province, which found that as incomes rose, more residents chose cleaner heating sources (Yang and Zhao 2013 ; Yan et al. 2020 ). However, regardless of the annual income levels of households, coal-burning stoves and traditional heating sources were still used to some extent. High heating costs were only considered acceptable for a minority of residents. The residents of the surveyed rural areas were asked whether they agreed with electric heating. Approximately 69.12% of the households agreed, while 30.88% disagreed (primarily because of the high electricity costs). Analysis of the heating factors identified by residential customers who either accepted or did not accept electric heating is shown in Fig. 8. The main factor was the cost of heating, followed by the indoor safety and energy efficiency of electric heating. If a more beneficial electricity price subsidy policy were to be introduced, more households may agree with electric heating. A further examination of the performance expectations of residents who adopted electric heating is shown in Fig. 9, revealing that 73.27 and 71.43% of households expected high-energy efficiencies and safety ratings, respectively. However, more than half of the households expected that electric heating was adjustable, had a long life, and had a large heating area; a minor proportion of households identified requirements regarding appearance. According to the field research data, the issues that were most concerning to villagers were divided into the following six categories: technical (fast heating and large heating area), comfort, economy (heating costs, energy efficiency, and service life), safety (high safety level), aesthetics (beautiful appearance) and portability, and environmental protection. Therefore, these six items were considered primary indicators. Each primary indicator was decomposed into several secondary indicators, combined with relevant studies and market surveys. Finally, 25 secondary indicators were selected, as listed in Table 3 . Table 3 indicator Statistics Table Goal layer Primary indicators (criterion layer) Secondary indicators (indicator layer) Study on the suitability indicator of electric heating in northern rural areas A 1 Technical 1. A 11 heating method/electric heat conversion rate 2. A 12 gear adjustment 3. A 13 end type 4. A 14 heating up time 5. A 15 temperature control accuracy 6. A 16 heat storage time 7. A 17 heat storage efficiency A 2 Economy 1. A 21 Initial investment 2. A 22 O&M costs 3. A 23 Useful life A 3 Comfort 1. A 31 heat sensation 2. A 32 heat comfort 3. A 33 blowing sensation 4. A 34 humidity sensation A 4 Security 1. A 41 whether it has tipping cutoff 2. A 42 whether it has anti-touch protection 3. A 43 whether it is waterproof 4. A 44 whether it is partially overheated 5. A 45 surface temperature A 5 Aesthetic Portability 1. A 51 Color profile 2. A 52 Control method 3. A 53 Easy to place 4. A 54 Easy to move and install A 6 Environmental friendliness 1. A 61 Sensable air quality 2. A 62 Does it make noise 3.1.2 Indicator Optimization The experts did not add any additional indicators to the primary and secondary indicators. All ratings exceeded 50%, as shown in Figs. 10 and 11. Therefore, the six primary and 25 secondary indicators screened using the above method were considered valid. 3.2 Indicator weights Data processing was performed on the expert questionnaires. After eliminating expert no. 2, the judgment matrix of the criterion level group was built with \({\lambda }_{max}\) (The maximum eigenroot of the matrix) = 6.0848. A consistency test was then performed on the expert group judgment matrix, revealing that CR = 0.0137 (< 0.10). Therefore, its normalized feature vector was used as the weight vector; the corresponding weights of each indicator are listed in Table 4 . Table 4 Criterion-layer weight indicator The eigenvector corresponding to the largest eigenvalue Normalized weights Technicality 0.3448 0.1617 Economic Activity 0.6733 0.3158 Comfortableness 0.4983 0.2337 Security 0.3935 0.1846 Aesthetic Portability 0.1100 0.0516 Environmental 0.1120 0.0525 The normalized weights of the criterion layer in Table 4 show that the economy was allotted the heaviest weight (31.58%). From the experts’ point of view; the economic aspect was also the primary reason for villagers to choose electric heating. If the state and Government can provide better support in this area, this would help villagers to choose electric heating. Comfort was also relatively important, with a 23.37% weightage. This indicates that, following the economy, villagers were most focused on whether the comfort of the environment created by electric heating could meet their needs. The safety and technical aspects of electric heating were also identified as important factors, with weights of 18.46 and 16.17%, respectively. Finally, beauty, portability, and environmental protection had relatively small weights. This weighted ranking matches the results of the villager-focused research, highlighting the practical significance of the criterion layer weights. The weights of the primary and secondary indicators are aggregated to get a summary of the indicator weights, as shown in Table 5 . Table 5 Summary of indicator weights Criterion layer Criterion layer weights indicator layer indicator layer weights Aggregate weights Weighting order A 1 0.1617 A 11 0.2642 0.0427 9 A 12 0.1129 0.0183 17 A 13 0.1581 0.0256 14 A 14 0.2880 0.0465 10 A 15 0.1000 0.0162 19 A 16 0.0429 0.0069 23 A 17 0.0339 0.0055 25 A 2 0.3159 A 21 0.4206 0.1329 1 A 22 0.3287 0.1038 2 A 23 0.2507 0.0792 5 A 3 0.2337 A 31 0.3904 0.0912 3 A 32 0.3854 0.0901 4 A 33 0.1215 0.0284 13 A 34 0.1027 0.0240 15 A 4 0.1846 A 41 0.2743 0.0506 6 A 42 0.1737 0.0321 11 A 43 0.2243 0.0414 9 A 44 0.2552 0.0471 7 A 45 0.0726 0.0134 21 A 5 0.0516 A 51 0.1122 0.0058 24 A 52 0.2948 0.0152 20 A 53 0.3345 0.0173 18 A 54 0.2584 0.0133 22 A 6 0.0525 A 61 0.5725 0.0301 12 A 62 0.4275 0.0224 16 As shown in Table 5 , the proportion of initial investment (A 21 ), which was a secondary indicator under the most important primary indicator (the economy, A 2 ), had the heaviest weight (13.32%). O&M costs (A 22 ) were allotted the next heaviest weight (10.38%). This shows that, when promoting electric heating in rural areas, the initial investment and operating costs are the primary problems that need to be solved. The second most important factor was comfort (A 3 ). Among the three secondary indicators for comfort, thermal sensation (A 31 ) and thermal comfort (A 32 ) were relatively significant. Village residents reported that they often opened doors and windows. Winters are generally cold and dry in cold rural areas, so the sensations of blowing wind and humidity occur relatively rarely. For safety (A 4 ) and technical (A 1 ) indicators, the heating time (A 14 ) and electric heating conversion rate (A 11 ) both had relatively high weights. Other than surface temperature (A 45 ), the weights of the other secondary indicators under safety were fairly balanced. When selecting electric heating equipment, experts concluded that relatively few residents considered factors related to aesthetics, portability, or environmental protection. After reviewing the evaluation rules and standards of green buildings, healthy buildings, and clean energy heating indicator systems in the literature; searching for information and consulting experts in related industries; and combining standards related to electric heating appliances, here quantitative indicator valuation standards for electric heating in cold rural areas were finally determined, as shown in Appendix Table A.1. 3.3 Evaluation Software and Model validation 3.3.1 Evaluation Software To more conveniently evaluate the suitability of electric heating using the gray whitening power clustering evaluation model, this paper uses the MATLAB programming language to construct the model calculation process and create a user interface, input the scoring results of 25 indicators by representatives of six permanent residents into the interface at the indicated locations, click on the calculated results, and get the comprehensive score. 3.3.2 Evaluation of Electric Heating Film Demonstration Village The scoring sample matrix was aggregated for Zhujiayao Village in Shanxi Province, and the results are shown in Table 6 . Table 6 Household score sheet Indicator Scoring households Average 1 2 3 4 5 6 A 11 9 9 9 9 9 9 9.00 A 12 9 9 9 9 9 9 9.00 A 13 9 9 9 9 9 9 9.00 A 14 7 9 8 7 9 7 7.83 A 15 9 9 9 9 9 9 9.00 A 16 10 10 10 10 10 10 10.00 A 17 10 10 10 10 10 10 10.00 A 21 7 9 7 9 7 9 8.00 A 22 7 9 7 9 7 9 8.00 A 23 9 9 7 9 5 9 8.00 A 31 7 9 9 9 8 9 8.50 A 32 9 9 8 9 8 9 8.67 A 33 7 9 9 9 7 7 8.00 A 34 9 8 7 6 7 9 7.67 A 41 7 7 7 7 7 7 7.00 A 42 9 9 9 9 9 9 9.00 A 43 10 10 10 10 10 10 10.00 A 44 9 9 9 9 9 9 9.00 A 45 9 9 9 9 9 9 9.00 A 51 9 9 9 5 9 7 8.00 A 52 9 9 8 7 9 9 8.50 A 53 9 9 9 9 9 9 9.00 A 54 9 7 7 9 9 9 8.33 A 61 9 9 9 9 9 9 9.00 A 62 9 9 9 9 9 9 9.00 Table 6 shows the scores of the villagers' experts in Zhujiayao village. The electric heating suitability evaluation model was used to calculate the suitability of the Zhujiayao village. The evaluation weights of the 25 secondary indicators and 6 primary indicators were calculated. The comprehensive evaluation C (Gray Number) = 6.7993 was obtained. According to the principle of maximum whitening weight, its value was calculated as follows: Therefore, Zhujiayao village belongs to the second gray category, which means that the suitability of Zhujiayao village for electric heating is “suitable.” 3.3.3 Evaluation of Electric storage heaters Village Fanbao Village (Electric storage heaters Village) used the software developed in section 3.3.1 to evaluate the suitability with a comprehensive score of 5.4826, and the comprehensive comment is: The suitability of your village for electric heating is rated as "more suitable". 3.3.4 Validation of Results Visiting 20 households in Zhujiayao village (electric heating film demonstration village) revealed that the initial investment and the O&M costs of the electric heating films achieved 98% satisfaction among the residents. In the Fanjiabao Village, 18 households using heat-storage electric heaters were visited. They said that the cost of heat storage electric heater is acceptable, and the heating effect can meet the basic needs. The results of both visits are consistent with their evaluation results. The villagers’ subjective rating data and the personal approval ratings of the visited villagers were both very consistent with the objective evaluation results of the model, indicating that the evaluation results accurately reflected the current situation that the villagers were experiencing after using electric heating films. Therefore, this evaluation method can help the government to evaluate the suitability of villages for electric heating projects in cold rural areas. 4. Conclusions and Policy Implications To improve the current situation of heating in cold rural areas. We have established an electric heating suitability evaluation index system as a reference for clean heating evaluation. This study was mainly carried out in the rural areas of cold regions in China. The evaluation indicators were obtained by a combination of literature search, questionnaire, and expert consultation. The weighting of primary indicators was established using the analytic hierarchy process, and the evaluation model was built through the gray whitening weights, validated against real cases. From this study, the following main findings could be obtained: An evaluation method for the feasibility of using electric heating in cold rural areas in China has been developed, and it has six primary indicators and 25 secondary indicators. The weight of each primary indicator was found to be 0.1617, 0.3158, 0.2337, 0.1846, 0.0516, and 0.0525, respectively. From the AHP, the economy accounts for the highest proportion (up to 31.59%). This is consistent with the findings of the questionnaire results of indicators. The three secondary indicators under the economy (A 2 ) accounted for a relatively high proportion, of which initial investment (A 21 ) accounted for the highest proportion, amounting to 13.32%. Therefore, the economy is an essential concern of using electric heating in rural areas in China. This study constructed an evaluation method for electric heating usage in cold rural areas in China. The model was validated with 2 different villages and the evaluation results of villages are consistent with the actual villagers' subjective demands. So, the evaluation model can be used as a theoretical and applied reference for the government in the promotion of clean heating in cold rural areas. This study can determine the feasibility of using electric heating for users in a rural area when the government carries out the policy of "coal-to-electricity". But, this paper is based on the study of Government subsidies for electric heating. In future studies, more attention should be paid to the size of the impact of increasing or decreasing subsidies on electric heating or even clean heating options, which will further help Villagers using clean heating sustainable. Abbreviation list Nomenclature A Overall goal W i The weight vector corresponding to the i-th criterion layer indicator Ai A i The i-th criterion level under the Overall goal R i Grey composite evaluation matrix of criteria level indicators A ij The j-th indicator in the i-th criterion level under A B Grey composite evaluation vector of target layer A d ijh Scoring of A ij by the h-th expert W The weight vector of the indicator layer k K-th gray category C Gray Number r ij Grey evaluation weight vector of A ij Critical values for each evaluation gray category: 1, 3, 5, 7, 9 CI Consistency indicators A e Judgment matrix of the e-th expert Declarations CRediT authorship contribution statement Wei Yu: Supervision, Writing-Review & Editing, Resources, Project administration, Methodology. Haixia Zhou: Conceptualization, Writing-Original Draft, Visualization, Formal analysis. Jiaying Huang: Validation, Investigation. Zixian Yu: Validation, Investigation. Shen Wei: Supervision, Writing - Review & Editing. Xiaochun Wu: Validation, Investigation. Xiao Ma: Investigation. All authors read and approved the final manuscript. Funding This work was supported by the National Natural Science Foundation of China (Grant Number 52078076), and the National Key R&D Project (Grant Number 2018YFD1100703-01). Data availability Corresponding authors can provide data used in the study on appropriate request. Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Consent for publication Not applicable Ethics approval and consent to participate Not applicable. References Ali M, Jokisalo J, Siren K, Lehtonen M (2014) Combining the Demand Response of direct electric space heating and partial thermal storage using LP optimization. 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Energy 31:2604–2622. https://doi.org/10.1016/j.energy.2005.10.023 Zhu L, Liao H, Hou B, et al (2020) The status of household heating in northern China: a field survey in towns and villages. Environ Sci Pollut Res 27:16145–16158. https://doi.org/10.1007/s11356-020-08077-9 Supplementary Files Appendices.docx 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-2280851","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":204869095,"identity":"31fb9947-36d5-4fa8-8e8b-e1494da56908","order_by":0,"name":"Wei 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Investigation\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/cb5b7239372f9488311d74b9.jpeg"},{"id":37769739,"identity":"0ef37a6c-1cba-46c2-bc67-e5a01ab79101","added_by":"auto","created_at":"2023-05-31 14:13:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":58266,"visible":true,"origin":"","legend":"\u003cp\u003eHeating method statistics chart\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/c19267493f48d12d2fae9e9b.png"},{"id":37769752,"identity":"c83a4d8f-5ec6-494c-b7e3-93c9bbfc183b","added_by":"auto","created_at":"2023-05-31 14:13:47","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":50724,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of heating selection factors\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/77b2d5354b76319067a0f468.png"},{"id":37771562,"identity":"dbb47cf3-9374-4fbb-9cab-d463d8c13c2f","added_by":"auto","created_at":"2023-05-31 14:21:46","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":83698,"visible":true,"origin":"","legend":"\u003cp\u003eChoice of heating methods for different household incomes\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/1f91240c9d36b62772ec24fb.png"},{"id":37771569,"identity":"0ec0dea3-0883-40f8-b86a-1d8b16d94659","added_by":"auto","created_at":"2023-05-31 14:21:46","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":83106,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of the selection factors of electric heating\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/827f4793e562d1bf57e9e77c.png"},{"id":37769741,"identity":"eb122f83-1306-4eea-a8bf-3bc9ca4eb52e","added_by":"auto","created_at":"2023-05-31 14:13:46","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":48302,"visible":true,"origin":"","legend":"\u003cp\u003eStatistical graph of electric heating performance expectations\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/8658742bf3389f49d8b7d408.png"},{"id":37774641,"identity":"98e3d413-eb1c-4169-ad45-8ace4a4c7727","added_by":"auto","created_at":"2023-05-31 14:45:46","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":73074,"visible":true,"origin":"","legend":"\u003cp\u003eA statistical chart of primary indicators\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/78bc67b2f50753fd10ddba46.png"},{"id":37769747,"identity":"a9c5705f-fe43-4042-a27d-72061ee1126b","added_by":"auto","created_at":"2023-05-31 14:13:46","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":65014,"visible":true,"origin":"","legend":"\u003cp\u003eA statistics chart of level II indicator under each secondary indicator\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/b32f8b9c4ef01ca858c1aa8d.png"},{"id":37772507,"identity":"bd5bfdae-a671-4e87-af07-8d1c9e6bfc8e","added_by":"auto","created_at":"2023-05-31 14:29:47","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":37525,"visible":true,"origin":"","legend":"\u003cp\u003eMATLAB program interface\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/fcd06db040ddc507183ce32e.png"},{"id":52848233,"identity":"0c0f0fdf-a718-4c8c-bb1e-f78ea0f6df95","added_by":"auto","created_at":"2024-03-17 20:01:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1372480,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/ed3f3968-64e4-4400-83c8-9229d8365391.pdf"},{"id":52848232,"identity":"8b35ee53-c2e6-4658-84a2-a7af19377775","added_by":"auto","created_at":"2024-03-17 20:01:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1372480,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/a26541be-00d3-411c-bd02-fafab761a2da.pdf"},{"id":37771561,"identity":"a067fd4a-ca20-42b7-8fec-3ccdcbcc26e3","added_by":"auto","created_at":"2023-05-31 14:21:46","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":36186,"visible":true,"origin":"","legend":"","description":"","filename":"Appendices.docx","url":"https://assets-eu.researchsquare.com/files/rs-2280851/v1/e96747fe758911f6a20f65b3.docx"}],"financialInterests":"","formattedTitle":"A Feasibility study on using electric heating in cold rural areas of China","fulltext":[{"header":"Highlights","content":"\u003cp\u003eEvaluation index system of suitability on using electric heating in cold rural areas of China based on hierarchical analysis and grey whitening weight clustering method.\u003c/p\u003e\n\u003cp\u003eBased on field research, comprehensive consideration of user and expert opinions to establish an evaluation index system of electric heating, mainly including economy, comfort, safety, beauty and portability, and environmental protection.\u003c/p\u003e\n\u003cp\u003eThis evaluation index system can avoid the unbalanced impact of indicators.\u003c/p\u003e\n\u003cp\u003eThis evaluation method is validated by cases with practical application, guiding the government to help improve electric heating in cold rural areas of China.\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eUnder China\u0026rsquo;s \u0026ldquo;dual carbon\u0026rdquo; target, all industries are undergoing energy upgrades and transformations. In the rural areas of northern China, the most popular heating sources in winter are Kang and a simple stove, accounting for more than 75% (Zhu et al. \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Traditional heating methods mainly transfer heat to a room through the burning of scattered coal, straw, or firewood (Gong et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), which is both environmentally detrimental and harmful to air quality (Tao et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Cities in China are dominated by central heating (Chen et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e); as rural buildings are more scattered, however, central heating systems are not suitable in rural areas(Ma et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Therefore, it is crucial to find a heating method that is suitable for the rural areas of northern China.\u003c/p\u003e \u003cp\u003eElectricity became one of the leading energy sources for households (ranked as the second dominant source after biomass) (Wang et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). During the 12th Five-Year Plan period (2010\u0026ndash;2015), China\u0026rsquo;s rural areas achieved full grid coverage (China Government Network \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) By the end of 2020, the rural grid reliability reached 99.8% (China Government Network \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). China\u0026rsquo;s electricity sources can mainly be divided into coal, hydro, nuclear, wind, and solar power. According to the National Bureau of Statistics, China\u0026rsquo;s non-fossil energy supply increased from 20.8% in 2010 to 30.46% in 2019, while the nation\u0026rsquo;s coal-fired power supply has been decreasing year on year. By 2030, China will have drastically reduced the use of coal, with plans to stop using coal power completely by 2050 (Jewell et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Thus, electricity will represent a relatively clean energy source. Since 2015, China has introduced a series of preferential subsidies to promote electricity as an alternative to domestic combustion for heating in rural areas (Soltero et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020a\u003c/span\u003e). Coal-to-electricity policies do change residential indoor air quality (Wu et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and reduce pollution of the outdoor environment(Chen et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In many rural northern areas, where solar energy is abundant, villagers are already using solar power to meet their heating needs (Wang et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Li and Xu \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhao et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Air source heat pumps also use electricity to transfer energy for heating. However, these approaches require significant investment, and suffer from frost and low energy efficiency in winter (Guo et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Therefore, electric heating has become widely used in rural areas.\u003c/p\u003e \u003cp\u003eElectric heating sources include thermal storage heater, electric heaters, heating cables, electric heating films, carbon crystals, heat rails, and carbon fibers (Zhang et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These forms of heating convert electrical energy into heat through electrical resistance; they are very simple to use, and have become widespread (Zhang et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The flexibility and convenience of electric heating makes it easy for villagers to accept (Zhang et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Electric heating has been used in Northern Europe, Korea, and Japan for more than 50 years (Liu and Ran \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) Due to the abundance of water, electricity, oil, and other resources, Norway in Northern Europe, France in Western Europe, Central America, and Canada all mainly use electric heating (Liu and Ran \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2016\u003c/span\u003e); it is also widely used in northern China (Zhang et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Zhang (Zhang \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Wang (Wang et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020b\u003c/span\u003e) analyzed the advantages of electric heating in the rural areas of cold regions in northern China; they concluded that electric heating could meet the comfort requirements of rural residents, while also being economical. Time-sharing tariffs have been adopted in many places in China. Zhao et al. (Zhang \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Li et al. (Li and Zhao \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) analyzed electric heating usage under rural and urban time-sharing tariffs, respectively, showing that it is more flexible and economical than fixed price, and that it can help to facilitate the consumption of large amounts of domestic abandoned wind and electricity capacity. Regarding the performance of electric heating technology, Jin (Jin and Davis \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) proposed an energy-saving control method to zero energy consumption in buildings using electric heating films; this method can achieve a low energy consumption while maintaining a stable temperature output. Ali et al. (Ali et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) proposed that electric heating and thermal storage, when sued in series, can achieve an optimal demand response in smart grid scenarios by simulating and analyzing heat demand and power. Campos et al. (Campos et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) conducted energy analysis and prediction for rural heating in Hungary; they suggested that a combination of electric energy retrofitting and efficient heating technologies can be used to meet rural heating.\u003c/p\u003e \u003cp\u003eWhat types of villages are suitable for electric heating? Most previous studies into electric heating have focused on the performance of the heating equipment in question. However, the factors affect people\u0026rsquo;s acceptance of electric heating, such as investment, operating costs, and feeling of use have not been considered regarding its actual adoption. Therefore, this study proposes the concept of electric heating suitability in cold rural areas. In addition, it established an indicator system and model to evaluate the feasibility of electric heating in cold rural areas.\u003c/p\u003e"},{"header":"2. Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Research Framework\u003c/h2\u003e\n \u003cp\u003eThis study comprised three main sections wherein the first part addressed the selection of suitability indicators for electric heating in cold rural areas. In this section, the basic information of the research questionnaire was determined through a literature review. Subsequently, several rural areas in the cold regions were visited to conduct questionnaires, with initial primary indicators being obtained from these questionnaire data. The research for this study consisted of both field and web-based questionnaires and was conducted with the consent of each villager before filling in the questionnaire. Each primary indicator was then refined into several secondary indicators, following which all indicators were improved through expert consultation. The second section entailed the determination of weights. The weights of the secondary and primary indicators were calculated using an expert questionnaire and an Analysis Hierarchical Process (AHP). The section comprised the establishment and verification of the model. A hybrid model was established for evaluating the suitability of electric heating in cold rural areas; it aimed to divide electric heating suitability into several gray classes while setting the whitening weight function. Each secondary indicator was then quantified according to the gray grade. Finally, cases from two different provinces using electric heating were selected to validate the model. In the validation process, villagers in each village were asked to rate according to the indicators and evaluate the suitability according to the established model. Then visit the users who use electric heating for comprehensive satisfaction. The evaluation model and index system are reliable if both of them get the same conclusion; the research process is illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Research Contents\u003c/h2\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1 Selection of Indicators\u003c/h2\u003e\n \u003cp\u003eIn this study, indicators were mainly selected based on three methods: a literature review, questionnaire surveys, and expert consultation. These three methods were used to screen and improve indicators obtained from scholars, users, and experts in related fields, to ensure a degree of credibility. Finally, the complete criterion (primary indicators) and indicator (secondary indicators) layers of the suitability indicator system for electric heating in cold rural areas were obtained.\u003c/p\u003e\n \u003cp\u003eAs little research has been conducted to date regarding the comprehensive evaluation, of index systems for electric heating, here relevant index research on clean heating was reviewed as a reference; suitable indexes for electric heating were screened out. When analyzing evaluation indicators for promoting the application of clean heating, two main perspectives were identified. One was framed from a macro perspective; it entailed the determination of whether a certain clean heating method was suitable for adoption in a certain place. This perspective was generally related to economic (Wei et al. \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wang et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhang et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Huo et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; He et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e), technical (Wei et al. \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wang et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhang et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e), environmental protection(Wei et al. \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wang et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhang et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; He et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e), and to the social factors (He et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) that are necessary to ensure a comprehensive evaluation. The other entailed the user\u0026rsquo;s perspective; it was related to the analysis of whether users were willing to adopt a certain type of clean heating. Reviewing the studies of Karytsas and Theodoropoulou revealed that when addressing the utilization of renewable energy, scholars from various countries have mainly considered factors such as socioeconomic, residential, and spatial characteristics, as well as consumers\u0026rsquo; behavior, preferences, and attitudes toward the attributes of specific heating systems (Karytsas and Theodoropoulou \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e). Not all of the influencing factors for clean and renewable energy heating are suitable for electric heating, however. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the influencing factors that were screened for electric heating in this study\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFactors influencing the choice of electric heating\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSocioeconomic characteristics\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIncome, age, educational level, household size (number of residents), children in the household, number of children, gender, occupation\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eResidence characteristics\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eResidence size (or number of bedrooms), type of residence, year of construction, ownership, years living in the residence, infrastructure\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCharacteristics related to the behavior of consumers, attitudes, and system attributes preferences\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEconomic aspects, environmental considerations, energy saving, security, comfort considerations and aesthetics, general attitude, social reasons, information/knowledge aspects, supplier issues\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePolicy requirements\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eenvironmental protection, economic, technical\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003eA questionnaire was designed based on this literature review. The questionnaire comprised 27 questions covering three main areas: basic information about households, basic information about buildings\u0026rsquo; heating conditions, and villagers\u0026rsquo; expectations.\u003c/p\u003e\n \u003cp\u003eCold areas are widely distributed in northern China. Here, the stratified sampling method (Parsons \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e) was applied to divide spaces into seven parts according to administrative subdivisions (five provinces and two municipalities: Henan, Hebei, Shandong, Shanxi, Shaanxi, Beijing, and Tianjin). Then, the number of studies was distributed according to the total number of villages. The distribution of the field questionnaire survey is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. Totally, 203 field surveys and 470 online questionnaires were obtained. The factors that villagers care about were extracted from the questionnaire data as initial primary indicators. Finally, these initial primary indicators were refined into several secondary indicators, according to a literature review and a market survey.\u003c/p\u003e\n \u003cp\u003eExpert consultation was mainly conducted through a questionnaire, which was used to distribute the initial primary and secondary indicators to experts for their consultation. Their opinions on each indicator were collected, and they were asked to suggest any additions to the selected indicators. Forty-four valid expert questionnaires were collected. The invited experts were active in heating fields, aged 23 to 60 years old having a bachelor\u0026rsquo;s level degree or higher. To ensure the questionnaire quality, all experts were from universities, design units, construction units, equipment manufacturers, operation management teams, government departments, or scientific research institutes, or were user representatives\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.2 Indicator Weights\u003c/h2\u003e\n \u003cp\u003eThe AHP has a particular application in group decision-making (Harker and Vargas \u003cspan class=\"CitationRef\"\u003e1990\u003c/span\u003e). It is one of the most widely used multi-standard decision-making techniques for analyzing energy and environmental issues (Zhou et al. \u003cspan class=\"CitationRef\"\u003e2006\u003c/span\u003e). The AHP can use qualitative and quantitative relationships to establish a judgment matrix and determine indicator weights. Therefore, here the AHP was selected to calculate the indicator weights.\u003c/p\u003e\n \u003cp\u003eFirst, the relationships between indicators for the suitability of electric heating in cold rural areas were analyzed. Analysis was divided into three layers: the goal layer (suitability of electric heating in cold rural areas), the criterion layer (primary indicators), and the indicator layer (secondary indicators). The expert survey method was then used to judge the screened primary and secondary indicators. The experts involved in the consultation worked in scientific research institutions, construction units, equipment manufacturers, operation management teams, government departments, user representatives, or other departments closely related to rural heating. These experts had more than three years of heating work experience, and each possessed an engineer\u0026rsquo;s or associate professor\u0026rsquo;s title, or higher. The sample size for an AHP should be in the range of 10\u0026ndash;50 (Du and Pang \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e), within which a reasonable accuracy of 10% can be achieved for general engineering evaluations. To establish a sound evaluation system, 30 copies of this survey were distributed, from which 24 valid documents were recovered. Two-by-two comparison judgments of each indicator were made according to the nine-point method recommended by Saaty (Saaty \u003cspan class=\"CitationRef\"\u003e1980\u003c/span\u003e). When the stochastic conformance ratio (CR)\u0026thinsp;\u0026lt;\u0026thinsp;0.10, the judgment matrix was considered to have passed the consistency test. The indicator weights of the indicator layer are established in the same way as the criterion layer. Finally, the weights of each secondary and primary indicator were calculated.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.3 Establishment of Suitability Evaluation Model\u003c/h2\u003e\n \u003cp\u003eIn previous rating systems, the scores and weights of each indicator have often been used to determine the grade by summing them. (Kim et al. \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e). However, this approach may induce an \u0026ldquo;imbalanced performance\u0026rdquo; effect (Yu et al. \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e), which can lead to some rural areas with high scores not meeting villagers\u0026rsquo; requirements regarding some of the indicators. Gray clustering was first proposed by Professor Deng in 1982 to deal with uncertainty problems (Deng \u003cspan class=\"CitationRef\"\u003e1987\u003c/span\u003e). The gray whitening power function-clustering model categorizes the values of evaluation indicators according to a set of categories. The final evaluation grade results are then determined according to the categories to which each evaluation value belongs (Deng \u003cspan class=\"CitationRef\"\u003e1987\u003c/span\u003e). Such clustering methods can avoid this \u0026ldquo;imbalanced performance\u0026rdquo; effect. Therefore, here the gray whitening power function clustering method was used to establish a model for evaluating the suitability of electric heating in cold rural areas.\u003c/p\u003e\n \u003cp\u003eA scoring system with four or five levels is generally used in gray clustering evaluations (Min et al. \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zhang et al. \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). Here, five levels were used to define each level: \u0026ldquo;very suitable,\u0026rdquo; \u0026ldquo;suitable,\u0026rdquo; \u0026ldquo;more suitable,\u0026rdquo; \u0026ldquo;less suitable,\u0026rdquo; and \u0026ldquo;very unsuitable.\u0026rdquo; The highest rating was allotted ten points (Zhang and Shuang \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e), with the full score ranges of this study being [9\u0026ndash;10], [7\u0026ndash;9], [3\u0026ndash;7], [1\u0026ndash;3], and [0\u0026ndash;1], respectively (Zhang and Shuang \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e). Each secondary index was quantified according to the gray classification and the performance of the said index. The suitability evaluation model for electric heating in cold rural areas is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eThe components of this indicator system for evaluating the suitability of electric heating in cold rural areas were divided into the goal (A), criterion (A\u003csub\u003ei\u003c/sub\u003e), and indicator (A\u003csub\u003eij\u003c/sub\u003e) layers. The whitening weight function of each gray class was then determined according to the requirements of the gray class division. The critical values were taken as the boundary and midpoint values. The essential values of the five evaluated gray classes were 9, 7, 5, 3, and 1, and their whitening weight functions were \u003cimg src=\"data:image/png;base64,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\" width=\"274\" height=\"32\"\u003e respectively, as shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e (Zhang and Shuang \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e). P representative households were invited to score each indicator layer, with the scoring value of each participating household being called the gray number. All secondary indicator scores (gray numbers) were constructed as a sample matrix and then substituted for the calculation model.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e Distribution of Whitening Weight Functions\u003c/p\u003e\n \u003cp\u003e\u003cimg 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\" width=\"664\" height=\"408\"\u003e\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Empirical cases\u003c/h2\u003e\n \u003cp\u003eWe chose two different types of villages as case studies, Zhujiayao village and Fanbao village.\u003c/p\u003e\n \u003cp\u003eZhujiayao Village in Shanxi Province was selected as a case study to evaluate the suitability of using electric heating films in cold northern regions. In the winter of 2019, the entire village of Zhujiayao transitioned to electric heating; electric heating films were used to replace coal-fired stoves and traditional heating sources. The Government funded the free installation of electric heating films for the entire village, with annual electricity costs now being as low as 0.286 RMB\u0026middot;kWh\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u0026middot;y\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, over a four-month heating period.\u003c/p\u003e\n \u003cp\u003eFanbao Village is located in the northeast of Qingfeng County, Puyang City, Henan Province, and was renovated in the winter of 2019. The government installed air source heat pumps for those who voluntarily chose electric heating, and the electricity price was charged according to the \u0026quot;coal-to-electricity\u0026quot; peak and valley time tariff (0.44 RMB/kw\u0026middot;h at peak time and 0.29 RMB/kw\u0026middot;h at valley time). Through the visit, although 70% of the households installed air source heat pumps, they were still dissatisfied with the high cost of electricity, resulting in 80% of the users not turning on the heat pump or turning it on less. And some of the villagers adopted the storage type electric heating, they said the electric heating effect is good, so Fanbao village was chosen as the study case.\u003c/p\u003e\n \u003cp\u003eThe same approach to evaluation was used in both villages. At the suggestion of the village leader, here six permanent household representatives were randomly selected within the village to rate each indicator, according to the scoring criteria specified by the quantitative rating of said indicator. Then, the suitability of electric heating was evaluated in Zhujiayao and Fanbao villages according to the above suitability evaluation method and scores. The evaluation results were compared with the subjective rating data of households and the satisfaction results of visiting villagers regarding the adoption of electric heating. If the two results are similar, the model built is proven to be reliable. An on-the-spot investigation is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Screening Indicators\u003c/h2\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.1 Initial Indicator Screening\u003c/h2\u003e\n \u003cp\u003eAccording to the questionnaire information, the present heating methods in cold rural areas in northern China during winter mainly comprised air conditioners, electric stoves, electric heating films, wall-hung stoves, and gas stoves, among others (Fig.\u0026nbsp;5). Although electric heating accounted for a large proportion of heating methods (22.31 and 14.58% for air conditioners and electric stoves, respectively), 29.32% of the households were still using unclean energy sources such as coal-fired stoves and traditional heaters. This may have mainly been due to influences such as local resources, and the economy, among others. Liu et al. studied rural houses in cold areas in 2013, finding that the main winter heating methods used by village residents were coal-fired stoves and traditional heating (49.6%) (Yang and Zhao \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e), so the findings presented here represent a significant improvement. This shows that the Government\u0026rsquo;s recent series of \u0026ldquo;coal to electricity\u0026rdquo; and \u0026ldquo;coal to gas\u0026rdquo; policies have had a significant effect.\u003c/p\u003e\n \u003cp\u003eThe specific factors that influenced village residents\u0026rsquo; selection of their heating method were analyzed (Fig.\u0026nbsp;6), showing that 73.73% of the households gave primary consideration to heating costs. This emphasizes that the economy was the primary consideration for village residents when choosing a heating method. Indoor comfort was the next crucial factor (56.68%), showing that, assuming that their economic needs were met, residents preferred to select heating equipment that met their comfort requirements. Safety and reliability were both identified by residents as necessary considerations when choosing heating equipment (50.69%). Moreover, 31.34% of the households also considered environmental protection. Aesthetics and portability were also a consideration for 18.89% of residents, showing that certain attention was also directed to decorative beauty, along with functionality.\u003c/p\u003e\n \u003cp\u003eAs shown in Fig.\u0026nbsp;7, villagers with lower annual incomes were less likely to adopt air conditioning, electric heaters, and floor heating for household heating. Residents with higher incomes, however, were more likely to use quality heating. Similar findings were also obtained in Wang\u0026rsquo;s indoor study in Hebi, Henan Province, which found that as incomes rose, more residents chose cleaner heating sources (Yang and Zhao \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Yan et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, regardless of the annual income levels of households, coal-burning stoves and traditional heating sources were still used to some extent. High heating costs were only considered acceptable for a minority of residents.\u003c/p\u003e\n \u003cp\u003eThe residents of the surveyed rural areas were asked whether they agreed with electric heating. Approximately 69.12% of the households agreed, while 30.88% disagreed (primarily because of the high electricity costs). Analysis of the heating factors identified by residential customers who either accepted or did not accept electric heating is shown in Fig.\u0026nbsp;8. The main factor was the cost of heating, followed by the indoor safety and energy efficiency of electric heating. If a more beneficial electricity price subsidy policy were to be introduced, more households may agree with electric heating. A further examination of the performance expectations of residents who adopted electric heating is shown in Fig.\u0026nbsp;9, revealing that 73.27 and 71.43% of households expected high-energy efficiencies and safety ratings, respectively. However, more than half of the households expected that electric heating was adjustable, had a long life, and had a large heating area; a minor proportion of households identified requirements regarding appearance.\u003c/p\u003e\n \u003cp\u003eAccording to the field research data, the issues that were most concerning to villagers were divided into the following six categories: technical (fast heating and large heating area), comfort, economy (heating costs, energy efficiency, and service life), safety (high safety level), aesthetics (beautiful appearance) and portability, and environmental protection. Therefore, these six items were considered primary indicators. Each primary indicator was decomposed into several secondary indicators, combined with relevant studies and market surveys. Finally, 25 secondary indicators were selected, as listed in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eindicator Statistics Table\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eGoal layer\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePrimary indicators (criterion layer)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSecondary indicators\u003c/p\u003e\n \u003cp\u003e(indicator layer)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"6\" align=\"left\"\u003e\n \u003cp\u003eStudy on the suitability indicator of electric heating in northern rural areas\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e1\u003c/sub\u003e Technical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e11\u003c/sub\u003e heating method/electric heat conversion rate 2. A\u003csub\u003e12\u003c/sub\u003e gear adjustment 3. A\u003csub\u003e13\u003c/sub\u003e end type 4. A\u003csub\u003e14\u003c/sub\u003e heating up time 5. A\u003csub\u003e15\u003c/sub\u003e temperature control accuracy 6. A\u003csub\u003e16\u003c/sub\u003e heat storage time 7. A\u003csub\u003e17\u003c/sub\u003e heat storage efficiency\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e2\u003c/sub\u003e Economy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e21\u003c/sub\u003e Initial investment 2. A\u003csub\u003e22\u003c/sub\u003e O\u0026amp;M costs 3. A\u003csub\u003e23\u003c/sub\u003e Useful life\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e3\u003c/sub\u003e Comfort\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e31\u003c/sub\u003e heat sensation 2. A\u003csub\u003e32\u003c/sub\u003e heat comfort 3. A\u003csub\u003e33\u003c/sub\u003e blowing sensation\u003c/p\u003e\n \u003cp\u003e4. A\u003csub\u003e34\u003c/sub\u003e humidity sensation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e4\u003c/sub\u003e Security\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e41\u003c/sub\u003e whether it has tipping cutoff 2. A\u003csub\u003e42\u003c/sub\u003e whether it has anti-touch protection 3. A\u003csub\u003e43\u003c/sub\u003e whether it is waterproof 4. A\u003csub\u003e44\u003c/sub\u003e whether it is partially overheated 5. A\u003csub\u003e45\u003c/sub\u003e surface temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e5\u003c/sub\u003e Aesthetic Portability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e51\u003c/sub\u003e Color profile 2. A\u003csub\u003e52\u003c/sub\u003e Control method 3. A\u003csub\u003e53\u003c/sub\u003e Easy to place\u003c/p\u003e\n \u003cp\u003e4. A\u003csub\u003e54\u003c/sub\u003e Easy to move and install\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e6\u003c/sub\u003e Environmental friendliness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1. A\u003csub\u003e61\u003c/sub\u003e Sensable air quality 2. A\u003csub\u003e62\u003c/sub\u003e Does it make noise\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.2 Indicator Optimization\u003c/h2\u003e\n \u003cp\u003eThe experts did not add any additional indicators to the primary and secondary indicators. All ratings exceeded 50%, as shown in Figs.\u0026nbsp;10 and 11. Therefore, the six primary and 25 secondary indicators screened using the above method were considered valid.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Indicator weights\u003c/h2\u003e\n \u003cp\u003eData processing was performed on the expert questionnaires. After eliminating expert no. 2, the judgment matrix of the criterion level group was built with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda }_{max}\\)\u003c/span\u003e\u003c/span\u003e (The maximum eigenroot of the matrix) = 6.0848. A consistency test was then performed on the expert group judgment matrix, revealing that CR\u0026thinsp;=\u0026thinsp;0.0137 (\u0026lt;\u0026thinsp;0.10). Therefore, its normalized feature vector was used as the weight vector; the corresponding weights of each indicator are listed in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eCriterion-layer weight\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eindicator\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThe eigenvector corresponding to the largest eigenvalue\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNormalized weights\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTechnicality\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3448\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1617\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEconomic Activity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.6733\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3158\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eComfortableness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4983\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2337\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSecurity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3935\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1846\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAesthetic Portability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0516\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEnvironmental\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0525\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003eThe normalized weights of the criterion layer in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e show that the economy was allotted the heaviest weight (31.58%). From the experts\u0026rsquo; point of view; the economic aspect was also the primary reason for villagers to choose electric heating. If the state and Government can provide better support in this area, this would help villagers to choose electric heating. Comfort was also relatively important, with a 23.37% weightage. This indicates that, following the economy, villagers were most focused on whether the comfort of the environment created by electric heating could meet their needs. The safety and technical aspects of electric heating were also identified as important factors, with weights of 18.46 and 16.17%, respectively. Finally, beauty, portability, and environmental protection had relatively small weights. This weighted ranking matches the results of the villager-focused research, highlighting the practical significance of the criterion layer weights.\u003c/p\u003e\n \u003cp\u003eThe weights of the primary and secondary indicators are aggregated to get a summary of the indicator weights, as shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSummary of indicator weights\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCriterion layer\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCriterion layer weights\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eindicator layer\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eindicator layer weights\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAggregate weights\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWeighting order\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"7\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"7\" align=\"char\"\u003e\n \u003cp\u003e0.1617\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e11\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2642\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0427\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e13\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1581\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0256\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e14\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2880\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e15\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0162\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e16\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0429\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e17\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0055\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"3\" align=\"char\"\u003e\n \u003cp\u003e0.3159\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e21\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4206\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1329\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e22\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3287\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1038\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e23\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2507\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0792\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"4\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"4\" align=\"char\"\u003e\n \u003cp\u003e0.2337\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e31\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3904\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0912\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e32\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3854\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0901\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e33\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1215\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0284\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e34\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1027\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0240\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"5\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"5\" align=\"char\"\u003e\n \u003cp\u003e0.1846\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e41\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2743\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0506\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e42\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1737\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0321\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e43\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2243\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0414\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e44\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2552\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0471\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e45\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0726\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"4\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"4\" align=\"char\"\u003e\n \u003cp\u003e0.0516\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e51\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1122\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e52\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e53\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0173\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e54\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2584\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" align=\"char\"\u003e\n \u003cp\u003e0.0525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e61\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5725\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0301\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e62\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4275\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, the proportion of initial investment (A\u003csub\u003e21\u003c/sub\u003e), which was a secondary indicator under the most important primary indicator (the economy, A\u003csub\u003e2\u003c/sub\u003e), had the heaviest weight (13.32%). O\u0026amp;M costs (A\u003csub\u003e22\u003c/sub\u003e) were allotted the next heaviest weight (10.38%). This shows that, when promoting electric heating in rural areas, the initial investment and operating costs are the primary problems that need to be solved. The second most important factor was comfort (A\u003csub\u003e3\u003c/sub\u003e). Among the three secondary indicators for comfort, thermal sensation (A\u003csub\u003e31\u003c/sub\u003e) and thermal comfort (A\u003csub\u003e32\u003c/sub\u003e) were relatively significant. Village residents reported that they often opened doors and windows. Winters are generally cold and dry in cold rural areas, so the sensations of blowing wind and humidity occur relatively rarely. For safety (A\u003csub\u003e4\u003c/sub\u003e) and technical (A\u003csub\u003e1\u003c/sub\u003e) indicators, the heating time (A\u003csub\u003e14\u003c/sub\u003e) and electric heating conversion rate (A\u003csub\u003e11\u003c/sub\u003e) both had relatively high weights. Other than surface temperature (A\u003csub\u003e45\u003c/sub\u003e), the weights of the other secondary indicators under safety were fairly balanced. When selecting electric heating equipment, experts concluded that relatively few residents considered factors related to aesthetics, portability, or environmental protection.\u003c/p\u003e\n \u003cp\u003eAfter reviewing the evaluation rules and standards of green buildings, healthy buildings, and clean energy heating indicator systems in the literature; searching for information and consulting experts in related industries; and combining standards related to electric heating appliances, here quantitative indicator valuation standards for electric heating in cold rural areas were finally determined, as shown in Appendix Table A.1.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Evaluation Software and Model validation\u003c/h2\u003e\n \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.1 Evaluation Software\u003c/h2\u003e\n \u003cp\u003eTo more conveniently evaluate the suitability of electric heating using the gray whitening power clustering evaluation model, this paper uses the MATLAB programming language to construct the model calculation process and create a user interface, input the scoring results of 25 indicators by representatives of six permanent residents into the interface at the indicated locations, click on the calculated results, and get the comprehensive score.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.2 Evaluation of Electric Heating Film Demonstration Village\u003c/h2\u003e\n \u003cp\u003eThe scoring sample matrix was aggregated for Zhujiayao Village in Shanxi Province, and the results are shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eHousehold score sheet\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth rowspan=\"2\" align=\"left\"\u003e\n \u003cp\u003eIndicator\u003c/p\u003e\n \u003c/th\u003e\n \u003cth colspan=\"6\" align=\"left\"\u003e\n \u003cp\u003eScoring households\u003c/p\u003e\n \u003c/th\u003e\n \u003cth rowspan=\"2\" align=\"left\"\u003e\n \u003cp\u003eAverage\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e11\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e13\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e14\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.83\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e15\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e16\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e17\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e21\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e22\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e23\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e31\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e32\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e33\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e34\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e41\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e42\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e43\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e44\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e45\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e51\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e52\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e53\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e54\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.33\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e61\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA\u003csub\u003e62\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the scores of the villagers\u0026apos; experts in Zhujiayao village. The electric heating suitability evaluation model was used to calculate the suitability of the Zhujiayao village. The evaluation weights of the 25 secondary indicators and 6 primary indicators were calculated. The comprehensive evaluation C (Gray Number)\u0026thinsp;=\u0026thinsp;6.7993 was obtained. According to the principle of maximum whitening weight, its value was calculated as follows:\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"402\" height=\"42\"\u003e\u003c/p\u003e\n \u003cp\u003eTherefore, Zhujiayao village belongs to the second gray category, which means that the suitability of Zhujiayao village for electric heating is \u0026ldquo;suitable.\u0026rdquo;\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.3 Evaluation of Electric storage heaters Village\u003c/h2\u003e\n \u003cp\u003eFanbao Village (Electric storage heaters Village) used the software developed in section \u003cspan class=\"InternalRef\"\u003e3.3.1\u003c/span\u003e to evaluate the suitability with a comprehensive score of 5.4826, and the comprehensive comment is: The suitability of your village for electric heating is rated as \u0026quot;more suitable\u0026quot;.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.4 Validation of Results\u003c/h2\u003e\n \u003cp\u003eVisiting 20 households in Zhujiayao village (electric heating film demonstration village) revealed that the initial investment and the O\u0026amp;M costs of the electric heating films achieved 98% satisfaction among the residents. In the Fanjiabao Village, 18 households using heat-storage electric heaters were visited. They said that the cost of heat storage electric heater is acceptable, and the heating effect can meet the basic needs. The results of both visits are consistent with their evaluation results. The villagers\u0026rsquo; subjective rating data and the personal approval ratings of the visited villagers were both very consistent with the objective evaluation results of the model, indicating that the evaluation results accurately reflected the current situation that the villagers were experiencing after using electric heating films. Therefore, this evaluation method can help the government to evaluate the suitability of villages for electric heating projects in cold rural areas.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4. Conclusions and Policy Implications","content":"\u003cp\u003eTo improve the current situation of heating in cold rural areas. We have established an electric heating suitability evaluation index system as a reference for clean heating evaluation. This study was mainly carried out in the rural areas of cold regions in China. The evaluation indicators were obtained by a combination of literature search, questionnaire, and expert consultation. The weighting of primary indicators was established using the analytic hierarchy process, and the evaluation model was built through the gray whitening weights, validated against real cases. From this study, the following main findings could be obtained:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eAn evaluation method for the feasibility of using electric heating in cold rural areas in China has been developed, and it has six primary indicators and 25 secondary indicators. The weight of each primary indicator was found to be 0.1617, 0.3158, 0.2337, 0.1846, 0.0516, and 0.0525, respectively.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eFrom the AHP, the economy accounts for the highest proportion (up to 31.59%). This is consistent with the findings of the questionnaire results of indicators. The three secondary indicators under the economy (A\u003csub\u003e2\u003c/sub\u003e) accounted for a relatively high proportion, of which initial investment (A\u003csub\u003e21\u003c/sub\u003e) accounted for the highest proportion, amounting to 13.32%. Therefore, the economy is an essential concern of using electric heating in rural areas in China.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThis study constructed an evaluation method for electric heating usage in cold rural areas in China. The model was validated with 2 different villages and the evaluation results of villages are consistent with the actual villagers' subjective demands. So, the evaluation model can be used as a theoretical and applied reference for the government in the promotion of clean heating in cold rural areas.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThis study can determine the feasibility of using electric heating for users in a rural area when the government carries out the policy of \"coal-to-electricity\". But, this paper is based on the study of Government subsidies for electric heating. In future studies, more attention should be paid to the size of the impact of increasing or decreasing subsidies on electric heating or even clean heating options, which will further help Villagers using clean heating sustainable.\u003c/p\u003e"},{"header":"Abbreviation list","content":"\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"100%\" colspan=\"4\"\u003e\n \u003cp\u003e\u003cstrong\u003eNomenclature\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003eA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eOverall goal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eW\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eThe weight vector corresponding to the i-th criterion layer indicator Ai\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003eA\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eThe i-th criterion level under the Overall goal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eR\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eGrey composite evaluation matrix of criteria level indicators\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003eA\u003csub\u003eij\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eThe j-th indicator in the i-th criterion level under A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eGrey composite evaluation vector of target layer A\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003ed\u003csub\u003eijh\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eScoring of A\u003csub\u003eij\u003c/sub\u003e by the h-th expert\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eW\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eThe weight vector of the indicator layer\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003ek\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eK-th gray category\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eGray Number\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003er\u003csub\u003eij\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eGrey evaluation weight vector of A\u003csub\u003eij\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eCritical values for each evaluation gray category: 1, 3, 5, 7, 9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.954616588419405%\"\u003e\n \u003cp\u003eCI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.577464788732396%\"\u003e\n \u003cp\u003eConsistency indicators\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.668231611893583%\"\u003e\n \u003cp\u003eA\u003csub\u003ee\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.799687010954614%\"\u003e\n \u003cp\u003eJudgment matrix of the e-th expert\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Declarations","content":"\u003ch2\u003eCRediT authorship contribution statement\u003c/h2\u003e\n\u003cp\u003eWei Yu: Supervision, Writing-Review \u0026amp; Editing, Resources, Project administration, Methodology.\u003c/p\u003e\n\u003cp\u003eHaixia Zhou: Conceptualization, Writing-Original Draft, Visualization, Formal analysis.\u003c/p\u003e\n\u003cp\u003eJiaying Huang: Validation, Investigation.\u003c/p\u003e\n\u003cp\u003eZixian Yu: Validation, Investigation.\u003c/p\u003e\n\u003cp\u003eShen Wei: Supervision, Writing - Review \u0026amp; Editing.\u003c/p\u003e\n\u003cp\u003eXiaochun Wu: Validation, Investigation.\u003c/p\u003e\n\u003cp\u003eXiao Ma: Investigation.\u003c/p\u003e\n\u003cp\u003eAll authors read and approved the final manuscript.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (Grant Number 52078076), and the National Key R\u0026amp;D Project (Grant Number 2018YFD1100703-01).\u003c/p\u003e\n\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eCorresponding authors can provide data used in the study on appropriate request.\u003c/p\u003e\n\u003ch2\u003eConflict of interest\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003ch2\u003eConsent for publication\u003c/h2\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003ch2\u003eEthics approval and consent to participate\u003c/h2\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAli M, Jokisalo J, Siren K, Lehtonen M (2014) Combining the Demand Response of direct electric space heating and partial thermal storage using LP optimization. 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Renew Sustain Energy Rev 149:111339. https://doi.org/10.1016/j.rser.2021.111339\u003c/li\u003e\n \u003cli\u003eZhao D, Ji J, Yu H, Zhao X (2019) A study on thermal characteristic and sleeping comfort of a hybrid solar heating system applied in cold rural areas. Energy Build 182:242\u0026ndash;250. https://doi.org/10.1016/j.enbuild.2018.10.027\u003c/li\u003e\n \u003cli\u003eZhou P, Ang BW, Poh KL (2006) Decision analysis in energy and environmental modeling: An update. Energy 31:2604\u0026ndash;2622. https://doi.org/10.1016/j.energy.2005.10.023\u003c/li\u003e\n \u003cli\u003eZhu L, Liao H, Hou B, et al (2020) The status of household heating in northern China: a field survey in towns and villages. Environ Sci Pollut Res 27:16145\u0026ndash;16158. https://doi.org/10.1007/s11356-020-08077-9\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"electric heating, indicator system, questionnaire research, analytic hierarchy process, gray whitening weight clustering","lastPublishedDoi":"10.21203/rs.3.rs-2280851/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2280851/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn response to China’s “double carbon” policy, cold, rural areas of the nation are currently upgrading their heating methods. Since rural areas are more dispersed than urban areas, centralized heating is not easy to use. Therefore, electric heating has become one of the major solutions. However, few studies have investigated the performance, suitability, and user impressions of electric heating in rural areas in China. Here, therefore, we used a literature review, questionnaires, and expert consultations to determine the relevant indicators that best reflect the suitability of electric heating usage in cold rural areas in northern China. Then, by using both expert questionnaires and the analytic hierarchy process (AHP) to determine the weights of these indicators, we developed a hybrid model established based on the gray whitening weight clustering method. We then applied this model to two case studies in different provinces, namely 20 households from a village in northern China where electric heating was being uses. Our major findings were 1) the primary indicators were technology, economy, comfort, safety, aesthetic portability, and environmental protection; 2) the weights of these indicators were 16.17%, 31.58%, 23.37%, 18.46%, 5.16%, and 5.25%, respectively, with all indicators passing the consistency test; 3) results of two case studies were consistent with the villagers' actual subjective evaluation results; 4) evaluation software has been developed. Our evaluation method developed can effectively reflect the actual needs of people living in rural areas of China. The government can use evaluation software to get the feasibility of adopting electric heating in villages to achieve reasonable low-carbon promotion in rural areas.\u003c/p\u003e","manuscriptTitle":"A Feasibility study on using electric heating in cold rural areas of China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-31 14:13:41","doi":"10.21203/rs.3.rs-2280851/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":"4c804d60-c6e7-488b-b4c3-8760893edc75","owner":[],"postedDate":"May 31st, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-03-17T20:00:53+00:00","versionOfRecord":[],"versionCreatedAt":"2023-05-31 14:13:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2280851","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2280851","identity":"rs-2280851","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}