Financial capability is a complex and comprehensive concept that is influenced by multiple levels of factors. Therefore, discussing the factors affecting farmers' financial capability improvement requires a multiple-level layer-by-layer analysis.

At the individual level, improving farmers' financial ability is closely related to their education situation, economic status, financial behaviour and habits, financial goals and planning. The individual's educational level is directly related to farmers' understanding and mastery of financial knowledge. Farmers who have received good education are more likely to understand the operational mechanisms of financial markets, various financial products, and investment tools and thus implement financial decisions more wisely. Farmers who have received good education often have higher financial literacy. In terms of financial management, they can better plan funds, avoid risks, and create more investment opportunities. The personal economic situation directly impacts the improvement of farmers' financial ability, directly affecting their activities, choices, and decisions in the financial field. Farmers with better economic conditions may also be more susceptible to certain levels of risk and better able to cope with larger financial risks, which is closely related to risk awareness and management in improving financial capabilities. Improving farmers' financial ability is related to their financial behaviour and habits, as their financial behaviour and habits directly reflect their understanding of financial knowledge, ability to plan finances, and level of risk awareness. Improving farmers' financial capabilities is also related to their personal financial goals and plans, as clear goals help farmers make more targeted financial planning and decisions, such as saving, investing, or purchasing a house. Setting financial goals requires carefully considering individual values, life stages, and future plans, directly affecting the direction and intensity of financial capability improvement. At the social level, improving farmers' financial capabilities is closely related to community support, social digitization, and the socio-cultural environment.

Improving farmers' financial capabilities is related to community support, mainly reflected in the community's support for financial education, financial services, etc. The increase in the number of communities and the abundance of activities usually means more platforms are used to carry out financial activities, including training courses, seminars, etc. Farmers can have a more comprehensive understanding of financial knowledge through these financial activities, thereby improving their financial literacy and decision-making level. Improving farmers' financial capabilities is related to community digitization because the widespread application of digital technology in the financial field provides farmers with more convenient, efficient, and inclusive financial services, thereby promoting their better participation in financial activities. Through mobile banking, electronic payments, and other digital platforms, farmers can more easily transfer funds, make payments, and check account balances, reducing time and geographical limitations in traditional financial services and improving the accessibility of financial services. Improving farmers' financial capabilities inevitably relates to the social and cultural environment. To a certain extent, the social and cultural environment even determines an individual's values and beliefs, especially for farmers. Due to the development of urban informatization and digitization, personal values and beliefs are also influenced by the online world, and the influence of the social and cultural environment is not significant. However, in underdeveloped areas such as rural areas with information and digitization, an individual's values and beliefs are almost determined by the current social and cultural environment. Their values directly shape their attitude, behaviour, and decision-making in the financial field, thereby affecting the acquisition of financial knowledge, the setting of financial goals, and the execution of financial planning, which greatly impacts the improvement of financial capabilities.

At the government level, the improvement of farmers' financial capabilities is related to the financial regulations and policies implemented by the government, financial education and training conducted, and support from financial institutions.

The improvement of farmers' financial capabilities is related to the financial regulations and policies implemented by the government. This is because the government's regulations and policies directly shape the financial market's operating environment and profoundly impact the financial services, accessibility of financial products, and financial behaviour norms of farmers. The government has formulated relevant regulations to promote financial institutions to provide more financial products and services to rural areas, promoting the improvement of financial capabilities. By formulating incentive policies, the government can encourage financial institutions to provide preferential measures such as low-interest loans and financial subsidies to farmers, thereby reducing the cost of obtaining financial products for farmers and improving their financial capabilities. In addition, the financial regulations and policies formulated by the government also have a guiding role in regulating the financial behaviour of farmers, helping to prevent financial risks and protect the rights and interests of farmers. The financial education and training carried out by the government can also significantly enhance the financial capabilities of farmers. Farmers can gain specific financial knowledge and enhance their financial capabilities through financial education and training. The support of financial institutions can also significantly enhance the financial capabilities of farmers. The existence and services of financial institutions directly affect farmers' participation and development in the financial field. By providing services such as funding, savings, financial management, training, and insurance, farmers can better participate in and respond to various activities in the financial market.

In summary, the factors affecting farmers' financial capability improvement can be approached by individuals, society, and government. These three levels also constitute the secondary indicators that affect the improvement of farmers' financial capabilities. These three levels can be subdivided into several three-level indicators, namely education situation, economic situation, financial behaviour and habits, financial goals and planning; Community support, social digitization, and socio-cultural environment; Financial regulations and policies implemented by the government, financial education and training conducted, and support from financial institutions; Summarized in Table 1.

Drawing on Bhyan et al. [25] idea of developing a comprehensive sustainability assessment system in the whole building life cycle stage of group housing in India, this paper uses a FAHP to say so. The FAHP handles fuzzy information and uncertainty in multi-criteria decision-making. It is developed based on the traditional Analytic Hierarchy Process (AHP), and compared to AHP, FAHP aims to better deal with the fuzziness of expert judgments and the uncertainty in real-world decision-making problems. It overcomes the limitations of the traditional AHP. The most significant difference is that AHP requires experts to provide accurate ratings, clear comparisons and rankings. It assumes that all elements of the judgment matrix are definite and accurate values. At the same time, FAHP introduces the concept of fuzzy mathematics, allowing for fuzziness and uncertainty in the judgment matrix. It is more suitable for dealing with fuzzy information in decision problems. In real life, the info experts judge is often fuzzy, such as equally important, strongly important, etc. FAHP needs to convert these fuzzy evaluations into numerical values, while AHP bypasses fuzzy evaluations and directly provides specific numerical values. Therefore, FAHP is more flexible in dealing with real-life decision-making problems.

Before conducting FAHP, indicators must be divided into target, standard, substandard, and decision layers. A fuzzy judgment matrix can be constructed by converting the fuzzy evaluations given by experts on the indicators of the standard, substandard, and decision layers into numerical values. The elements in the judgment matrix represent the importance of row indicators relative to column indicators, and the elements on the diagonal are all 1. The comparison between indicators is not transitive. Therefore, a fuzzy judgment matrix can be constructed for each set of indicators. The number of fuzzy judgment matrices that need to be constructed is the sum of first-level, second-level, and third-level indicators. This article consists of 14 fuzzy judgment matrices. A fuzzy judgment matrix cannot be constructed arbitrarily and needs to meet consistency testing. Due to the subjectivity of expert fuzzy evaluation, consistency testing is precisely to ensure the objectivity of the fuzzy judgment matrix. Only through consistency testing can the expert's fuzzy evaluation have credibility. Consistency testing requires calculating the Consistency Index (CI) and ratio and determining whether they have passed the consistency test based on size. The specific operating steps are as follows: Specific mathematical formulas must be used to calculate the CI and Consistency Ratio (CR) through the judgment matrix. The specific Python code can be found in Algorithm A1. Firstly, calculate the maximum eigenvalue of the judgment matrix:

Among them is the element in the judgment matrix, is the element of the normalized judgment matrix, and n is the number of elements. Calculate the CI based on the calculated maximum eigenvalue

The consistency ratio can be calculated using the CI, which is the ratio of the CI to the average Random Consistency Index (RCI). There is a certain correspondence between the average RCI and the order of the judgment matrix, as shown in Table 3.

By consulting relevant literature, it can be seen that the consistency of the fuzzy judgment matrix can be accepted when the CI and consistency ratio are less than 0.1. After passing the consistency check, the fuzzy weight can be calculated.

To calculate fuzzy weights through a fuzzy judgment matrix, it is necessary first to normalize the judgment matrix, which is to divide the original matrix by the sum of each column, then calculate the mean of each row of the normalized matrix, and finally obtain 3×1 matrix refers to fuzzy weights, and the specific Python code can be found in Algorithm A2.

Based on the indicator selection mentioned above, construct the framework of FAHP. The target layer is to enhance the financial capabilities of farmers. The standard layer includes the individual, social, and government levels. The substandard and decision layers are the corresponding third and fourth-level indicators in indicator selection. Based on consistency testing, 14 judgment matrices are established based on the fuzzy scores given by experts. The weights of 3 secondary indicators, 10 tertiary indicators, and 32 fourth-level indicators are calculated based on the judgment matrices. Finally, the weights of each decision-making level are obtained by multiplying them. Based on this weight, effective decisions for improving the financial capacity of farmers are obtained.

To construct a fuzzy judgment matrix, it is necessary first to compare the indicators individually. Given that expert fuzzy evaluation is more objective, this study consulted experts who have conducted extensive research on farmer finance to conduct a fuzzy evaluation. The experts provided five criteria for the same, slightly important, obviously important, strongly important, and extremely important between two indicators, and then converted these fuzzy evaluations into scores corresponding to 1, 3, 5, 7, and 9, respectively. The size of the score only represents the important differences between indicators in the same category, and its scale is summarized in Table 4.

1 Indicates that two factors have the same importance compared to each other 3 Compared to two factors, the former is slightly more important than the latter 5 Compared to two factors, the former is significantly more important than the latter 7 Indicates that compared to the latter, the former is more strongly important than the latter 9 Compared to the two factors, the former is extremely important compared to the latter The reciprocal of the above scale If the ratio of importance between factor A and factor B is a, then the ratio of importance between factor B and factor A is 1/a

Based on expert fuzzy evaluation, this article uses rating scales to convert specific values and constructs 14 judgment matrices. This article only lists the fuzzy judgment matrices constructed by the standard layer to avoid excessive length. The results are shown in Table 5.

According to the meaning of fuzzy evaluation, to improve the financial capabilities of farmers, the individual level is extremely important compared to the social level. The individual level is slightly more critical. Compared to the social level, the government level is important. According to the research of Liu and Zhanmin [26] the main responsibility for improving the financial capabilities of farmers lies with individuals and the government, and it gradually shifts from the government to the individual . This is consistent with constructing the fuzzy judgment matrix, proving the credibility of expert fuzzy evaluation.

The fuzzy judgment matrix needs to pass consistency testing to have credibility. The steps of consistency testing have been mentioned earlier, and CR and CI need to be calculated. Generally, when both CR and CI are less than 0.1, constructing the fuzzy judgment matrix is considered more reasonable.

The consistency test results of the fuzzy judgment matrix constructed by the target, standard, and sub-standard layers are shown in Table 6.

Target layer Improving the financial capabilities of farmers 0.01453 0.02505 Individual level 0.05688 0.06321 Standard layer Social level 0.03244 0.05498 At the government level 0.00002 0.00001 Education situation 0.03244 0.05498 Economic situation 0.07238 0.08042 Financial behavior and habits 0.04015 0.06805 Financial goals and planning 0.03244 0.05498 Sub standard layer Community support 0.04015 0.06922 Social digitization 0.04015 0.06922 Social and cultural environment 0.00276 0.00477 Financial regulations and policies 0.03899 0.04333 Financial education and training 0.01926 0.03320 Financial institution support 0.00351 0.00605

From this, it can be seen that the construction of the 14 fuzzy judgment matrices meets the consistency test; that is, both CI and CR meet the threshold of less than 0.1. Fuzzy evaluation by experts has a certain degree of credibility.

Based on expert fuzzy evaluation, the fuzzy judgment matrix can be used to calculate the corresponding weights of each indicator in the matrix. For example, the fuzzy judgment matrix constructed by the target layer can calculate the weights of individual, social, and government levels, respectively. The calculation method of weights has been explained in the research method introduction above, and the calculated results are shown in the Tabel A1.

The sum of weights obtained for each fuzzy matrix is 1. The results indicate that to enhance the financial capacity of farmers, more attention should be paid to starting from the individual level, and the government and society levels should not be ignored. It is necessary to deepen together at the individual level. At the individual level, it is important to pay primary attention to the economic situation of farmers, as having a good economic situation is the most important foundation for enhancing financial capabilities. At the social level, more attention should be paid to the development of social digitization, and the improvement of social digitization has a strong positive effect on the financial capacity of farmers. The government should pay more attention to the support of financial institutions; in other words, it is necessary to ensure a certain number of rural banks and credit cooperatives and actively enrich the types of financial products they provide. To better start from the decision-making level and provide effective decision-making suggestions so that the weights of each decision-making level indicator are clearly visible, the weights calculated from the fuzzy judgment matrix constructed by the target layer, standard layer, and substandard layer are multiplied accordingly to obtain the final weights of the decision-making level, as shown in Table 7.

weight results for the decision-making level:

factors.

applications in improving financial literacy.

Name of Decision-Maker Indicators Weight Number of mobile phones/computers owned 0.01309 Internet user proportion 0.02882 Enterprise digital technology level 0.00252 Number of public service facilities 0.00120 Financial values 0.01412 Social traditions and customs 0.00421 Personal financial information protection 0.00285 regulations Agricultural credit disbursement policy 0.00611 Regulations on the protection of farmers' rights 0.02796 and interests Financial risk prevention measures 0.01320 Financial education program for farmers 0.03174 Professional training for rural financial 0.00532 practitioners Digital finance training 0.01306 Number of banks 0.10054 Number of credit cooperatives 0.03655

The above is the weight of all indicators for the decision-making level, and the following is an analysis of the

I. Economic factors dominate. The weight of personal income is the highest, reaching 26.45%, indicating the significant impact of personal economic status on improving the financial capacity of farmers. Personal consumption and savings are also around 10%, further emphasizing the dominant position of economic

II. The key role of personal financial training time. Financial training time accounts for 8.89% of the overall weight, emphasizing the key role of financial training in improving financial literacy. This indicates that improving the training of farmers on financial knowledge and skills is crucial.

III. The importance of financial institutions. The number of banks, the number of credit cooperatives, and the types of financial products account for 10.05%, 3.66%, and 1.33% of the overall weight, respectively, indicating the importance of financial institutions in enhancing the financial capabilities of farmers. The diversity and increase in the number of financial institutions are crucial for expanding financial service channels.

IV. Digital finance and internet applications. The proportion of internet users and digital financial training accounts for 2.88% and 1.31%, respectively, highlighting the potential value of digital technology and internet

V. Social factors are relatively low. Social traditions, customs, and social capital investment account for 0.42% and 0.40% of the overall weight, respectively, relatively low. This indicates that social and cultural factors have a relatively small impact on rural financial development.

VI. The regulatory factors, such as regulations on protecting the rights and interests of farmers and agricultural credit issuance policies, have relatively low weights. However, they still occupy a place in overall decision-making, accounting for 2.80% and 0.61%, respectively.

In summary, when formulating policies and plans, special attention should be paid to improving personal economic level, promoting practical financial training, developing diversified financial institutions, and promoting the application of digital financial technology.