(PDF) Using Genetic Programming to Identify Characteristics of Brazilian Regions in Relation to Rural Credit Allocation

agriculture Article Using Genetic Programming to Identify Characteristics of Brazilian Regions in Relation to Rural Credit Allocation Adolfo Vicente Araújo 1, *, Caroline Mota 1 and Sajid Siraj 2 1 Department of Industrial Engineering, Federal University of Pernambuco, Recife 50670-901, Brazil 2 Centre for Decision Research, Leeds University Business School, University of Leeds, Leeds LS2 9JT, UK * Correspondence:

Abstract: Rural credit policies have a strong impact on food production and food security. The attribution of credit policies to agricultural production is one of the main problems preventing the guarantee of agricultural expansion. In this work, we conduct family typology analysis applied to a set of research data to characterize different regions. Through genetic programming, a model was developed using user-defined terms to identify the importance and priority of each criterion used for each region. Access to credit results in economic growth and provides greater income for family farmers, as observed by the results obtained in the model for the Sul region. The Nordeste region indicates that the cost criterion is relevant, and according to previous studies, the Nordeste region has the highest number of family farming households and is also the region with the lowest economic growth. An important aspect discovered by this research is that the allocation of rural credit is not ideal. Another important aspect of the research is the challenge of capturing the degree of diversity across different regions, and the typology is limited in its ability to accurately represent all variations. Therefore, it was possible to characterize how credit is distributed across the country and the main factors that can influence access to credit. Keywords: rural credit; criteria analysis; family farming; genetic programming; machine learning Citation: Araújo, A.V.; Mota, C.; Siraj, S. Using Genetic Programming to 1. Introduction Identify Characteristics of Brazilian Food insecurity is a global challenge, and the Central Rural Work Conference in 2021 Regions in Relation to Rural Credit pointed out that in order to ensure food security, attention should be paid to adjusting rural Allocation. Agriculture 2023, 13, 935. credit [1]. The allocation of credit to agricultural production is one of the main problems https://doi.org/10.3390/ in ensuring agricultural expansion, since the credit is financed with lower interest rates agriculture13050935 than those adopted in the market [2]. Rural credit consists of loans provided by financial Academic Editors: Hung-Hao Chang, institutions to producers and rural cooperatives [3]. According to data from the Central Pei-An Liao and Jiun-Hao Wang Bank of Brazil [4], in 1999, the rural credit/agricultural GDP ratio was approximately 24%, and in 2018, it reached approximately 61%. The increase in rural credit and its importance Received: 1 April 2023 to Brazilian agricultural policy become even more relevant when we consider studies that Revised: 14 April 2023 show the impact of positive rural credit on agricultural variables such as production value, Accepted: 16 April 2023 agricultural products, agribusiness products, and total factor productivity [5,6]. Published: 24 April 2023 Many studies from different parts of the world have shown significant economic and social elevation for the beneficiaries of rural credit programs [7]. In addition, many specialists believe that large farmers linked to global companies are key actors, based on Copyright: © 2023 by the authors. both the size of their production and the potential for agricultural intensification. However, Licensee MDPI, Basel, Switzerland. for other specialists, diversified systems of family agriculture allow for greater potential This article is an open access article for development. Other experts analyze the impact of public policies on the well-being distributed under the terms and and economic improvement of rural areas around the world, concluding that rural credit conditions of the Creative Commons policies represent an essential factor in the development of agriculture [8,9]. Although Attribution (CC BY) license (https:// some studies have addressed rural credit, no study has sought to understand how rural creativecommons.org/licenses/by/ credit is allocated to farmers, and no specific technique or methodology has been used to 4.0/). properly assess rural credit for the actors involved. Agriculture 2023, 13, 935. https://doi.org/10.3390/agriculture13050935 https://www.mdpi.com/journal/agriculture Agriculture 2023, 13, 935 2 of 14 The difficulty in finding studies related to the conception of rural credit is due to the complexity of the rural credit system. For example, the government of Brazil has a complex set of funding sources and rural credit programs and offers a range of credit lines targeted at producers with different income levels and property sizes. However, flaws in the current design lead to substantially reduced access and distribution of rural credit. This diminishes the benefits of the policy and threatens the country’s ability to balance its agricultural productivity with environmental preservation [3]. During the 2017 agricultural year, the Brazilian rural credit system offered 18 sources of financing. Important differences existed among these funding sources in terms of beneficiary qualification criteria and funding conditions. This generated a complex system and made it difficult for creditors and debtors to define the best credit option in each case. The complex set of rules for the different credit lines was not only excessively complicated for the agents operating the system but also generated distortions in the allocation of resources [10]. It is argued that the current structure favors the three public banks: (1) Banco do Brasil, the main creditor in the sul, sudeste, and centro-oeste revisions; (2) Banco do Nordeste, the main creditor in the nordeste region; and (3) Banco da Amazônia, the main creditor in the norte region. Considering the BRL 218 billion made available during the 2017–2018 harvest, which represents approximately 7% of the balance of credit operations in the entire financial system, rural credit is restricted to a small portion of rural establishments in Brazil. According to the Brazilian Institute of Geography and Statistics (IBGE) [11] only 15.5% of rural establishments had access to the rural credit system. Among those who did not obtain it, 42.8% stated reasons that did not prevent them from taking out rural credit. Such values correspond to the existing paradigm at specialized rural credit institutions [12] and, consequently, to the hypothesis of rural credit rationing in the country [13,14]. Banco do Brasil, the public bank, provided 47% of all loans in the 2017 fiscal year. Itaú and Bradesco, two of the most important private banks in Brazil, together with Banco do Brasil, provided about 60% of all loans in the same period. Credit cooperatives were responsible for another 15% of rural credit in 2017 [10]. In this respect, guaranteeing access to rural credit for all farmers, and not just for a minority, is considered a vital requirement for sustainable economic growth and for improving the quality of life in less developed countries. In order to understand the rural credit allocation process, we used family typology analysis applied to a research dataset to characterize different regions. Previous studies used several approaches to determine rural credit but did not take into account the complexity of heterogeneous family farming systems. There is no work in the literature that characterizes how rural credit, an important public policy that has been adopted by several countries, is conceived. Therefore, it was necessary to investigate and characterize the allocation of rural credit to different Brazilian regions using an artificial intelligence technique. The technique used in this study was designed using user-defined terms to identify the importance and priority of each criterion used for each region. Thus, farmers who are interested in accessing rural credit may have a better decision-making capacity in relation to the most important criteria in a given region. This paper is organized as follows: Section 2 presents the bibliographic review, and Section 3 describes the genetic programing. In Section 4, we discuss the method, and in Section 5, we discuss the results. Finally, we provide the conclusion in Section 6. 2. Bibliographic Review The period of 1995 to 2022 was selected for this systematic review, because the National Program to Strengthen Family Farming (PRONAF) was created in 1995. PRONAF was introduced to support family farmers because there was an increase in farmer indebtedness and non-payment [15]. For the systematic review, first, the criteria for inclusion were defined, followed by the systematic implementation of defined search strings across the Web of Science, Scopus, and SciELO databases. To achieve quality and ensure relevance to the topic, only articles Agriculture 2023, 13, 935 3 of 14 that were published in respected international peer-reviewed journals were shortlisted. All other publications, including conference articles, post-graduation theses, and editorial notes, were excluded from this review. This approach allowed for a description of the techniques, methodologies, applied tools, and possible trends in the bibliography, as well as the gaps in research on rural credit. Peer-reviewed articles were included in the analysis based on the criteria listed in Table 1. Table 1. Inclusion criteria for the systematic review. Category Inclusion Details Language Non-English studies have been excluded Publication date Any studies prior to 1995 have been excluded Peer-reviewed Only peer-reviewed articles have been included Geography Only studies related to rural credit around the world Primary data Only the studies presenting primary data Subjects Only those studies that relate to family farming The studies must be related to rural credit, or to one of its practices or Treatment pseudonyms, as a financing policy Studies must be related to one or more aspects of Rural Credit: Rural credit aspect • Criteria (quantity) • Methodology • Tools • Distribution The next step was to define the keywords (search strings) to be used in the first filter to select the articles. The words defined in advance were “rural credit” and “family farming”, “rural credit distribution”, “rural credit measurement”, and “indicators of rural credit” as terms on one axis of the theoretical background. The keywords connected to rural credit and family farming were combined to form the other axis of the research. Then, the keywords were constructed, as shown in Table 2. Table 2. Keywords. Keywords TOPIC—Search Strings in the Title and Summary of the Articles P1 Topic = (“Rural Credit”) AND Topic = (“Family Farming”) P2 Topic = (“Rural credit distribution”) AND Topic = (“Family Farming”) P3 Topic = (“Rural credit measurement”) AND Topic = (“Family Farming”) P4 Topic = (“Indicators for rural credit”) AND Topic = (“Family Farming”) P5 Topic = (“Model used in rural credit”) AND Topic = (“Family Farming”) P6 Topic = (“Distribution of public resources in agriculture”) AND Topic P1 P7 Topic = (“Agriculture performance”) AND Topic P1 P8 Topic = (“Tools used in agriculture”) AND Topic P1 P9 Topic = (“Criteria for public resources”) AND Topic P1 P10 Topic = (“Methodology used in sustainable agriculture”) AND Topic P1 Then, the articles that were considered to be aligned with the theme of this research were analyzed using the Journal Citation Reports (JCR) of their respective publishers. The objective was to verify whether they possessed a JCR impact factor (IF) score different from zero. As a quality standard, only journals with a JCR IF greater than zero were included in this research. Selection of the Theoretical Framework Using the inclusion criteria for the systematic review and the defined keywords, the search of the database yielded 2699 results. The summaries of those 2699 articles were then analyzed to check whether their themes were aligned with the research. After this initial analysis, 2597 references were excluded for not being aligned with this research or for being duplicates. Then, the 102 remaining articles were analyzed using the JCR criterion. It was observed that 49 did not meet the requirements, meaning that the JCR indicator was zero. Hence, the remaining 53 articles were aligned with regard to the title and abstract and met initial analysis, 2597 references were excluded for not being aligned with this research or for being duplicates. Then, the 102 remaining articles were analyzed using the JCR criterion. It was observed that 49 did not meet the requirements, meaning that the JCR indicator was zero. Hence, the remaining 53 articles were aligned with regard to the title Agriculture 2023, 13, 935 4 of 14 and abstract and met the JCR requirement established by the researcher. Those articles were then read in full in order to evaluate whether they would contribute valuable information to thisthe study. In this established JCR requirement process, three by thearticles were researcher. excluded, Those resulting articles were then readin 50 in in full articles, as shownorder in Figure 1. to evaluate whether they would contribute valuable information to this study. In this process, three articles were excluded, resulting in 50 articles, as shown in Figure 1. Figure 1. FlowchartFigure illustrating the systematic 1. Flowchart review illustrating the process. systematic review process. Figure 2 shows the systematic process for the visualization of techniques and criteria Figure 2 shows the systematic process for the visualization of techniques and criteria from the identification of 50 papers deemed eligible for full analysis. For this research, we from the identification of 50articles divided the papers deemed into eligiblethat five techniques forwere fullused analysis. in theirFor this research, respective we work: statistical, divided the articles into five techniques computational, that multicriteria, were used exploratory in their review, respective and other. The aim work: statistical, was to find a technique computational, multicriteria, that could applyexploratory review, and to the work, considering other. The aim was to find a its limitations. A total to technique that could apply of 72% of articles the work, reported a quantitative considering approach, among which 16% used its limitations. statistical techniques to solve the problems [16–23]. Computational techniques were used in 28% [8,24–37]; multicriteria techniques were used in 22% [38–48]; literature review, a qualitative approach, was used in 28% [49–62]; and other types were used in 6% [63–65], Table 3. Agriculture Agriculture 2023, 2023, 13,13, 935x FOR PEER REVIEW 55of of 14 Figure 2. Flowchart illustrating the systematic process. Figure 2. Flowchart illustrating the systematic process. A total of 72% of articles reported a quantitative approach, among which 16% used Table 3. Percentage of technical approaches. statistical techniques to solve the problems [16–23]. Computational techniques were used in 28% [8,24–37];Totalmulticriteria techniques Percentage wereAdopted of Techniques used inin22% the [38–48]; Literatureliterature review, a qualitative approach, was used in 28% [49–62]; and other types were used in 6% [63–65], Statistical techniques 16% Table 3. Computational techniques 28% Table 3. Percentage of technical Multicriteria approaches. techniques 22% Literature Totalreview 28% Percentage of Techniques Adopted in the Literature Other typesStatistical techniques 6% 16% Computational techniques 28% Multicriteria techniques 22% 3. Genetic Programming Literature review 28% Genetic programming hasOther attracted typesattention for solving credit problems,6% both aca- demically and empirically, and is mainly implemented for problems with less information. For genetic programming, 3. Genetic Programming it fits as a machine learning method, but unlike with other learning methods, the answer is already a readable and interpretable model in the form of Genetic programming has attracted attention for solving credit problems, both a program. When we are able to define the language in which the program will be written, academically and empirically, and is mainly implemented for problems with less the obtained program will be explicitly interpretable and will not require an additional step information. For genetic programming, it fits as a machine learning method, but unlike to understand the decision-making process. For example, in [62], the authors performed an with other learning methods, the answer is already a readable and interpretable model in analysis of credit scoring models for public banks using two evaluation criteria: the average the form of a program. When we are able to define the language in which the program correct classification (ACC) rate and estimated misclassification cost (EMC). The results will be written, the obtained program will be explicitly interpretable and will not require revealed that GP had a higher ACC and lower EMC compared to other techniques [62]. an additional step to understand the decision-making process. For example, in [62], the Another example supports the recommendation to use the “genetic programming in two authors performed an analysis of credit scoring models for public banks using two stages” (2SGP) technique to deal with credit scoring problems, incorporating IF–THEN evaluation criteria: the average correct classification (ACC) rate and estimated rules and more complex discriminating functions. Based on the numeric results, the conclu- misclassification cost (EMC). The results revealed that GP had a higher ACC and lower sion is that 2SGP can offer better precision than other models, and this improvement can EMC compared to other techniques [62]. Another example supports the recommendation result in significant savings [63]. to use the “genetic programming in two stages” (2SGP) technique to deal with credit Other studies related to credit supply describe a relationship to economic growth. For scoring problems, incorporating IF–THEN rules and more complex discriminating example, in [66], the authors used the coherence test to answer the following question: (i) does the offer of bank credit lead to economic growth? Another study [67] examined functions. Based on the numeric results, the conclusion is that 2SGP can offer better precision than other models, and this improvement can result in significant savings [63]. Other studies related to credit supply describe a relationship to economic growth. For example, in [66], the authors used the coherence test to answer the following question: Agriculture 2023, 13, 935 6 of 14 (i) does the offer of bank credit lead to economic growth? Another study [67] examined the causal link of sectoral economic credit growth in Australia using a coherence test. The results for both studies determined according to dynamic time and frequency analysis the causal reveal that link of sectoral economic economic growth credit generates growth credit in Australia for the using agricultural a coherence sector test. in the long The term. results for both studies determined according to dynamic time and frequency analysis reveal 4. that economic growth generates credit for the agricultural sector in the long term. Method A structured questionnaire-based survey was conducted using the IBGE data 4. Method collection platform to collect pooled information from 264,359 agricultural households. ThroughA structured questionnaire-based multivariate survey analysis, a typology of was conducted family farmingusing typesthe wasIBGE data collection developed based platform on to collect fourteen area pooled ranges,information from 264,359 totaling seventy agricultural groups households. of agricultural Through households. multivariate analysis, Subsequently, a typology discussions of family of these farming seventy types were groups was developed conductedbased on fourteen using criteria area ranges, totaling seventy groups of agricultural households. Subsequently, discussions developed through the survey. The purpose of the discussions was to validate the of these seventy groups were conducted using criteria developed through the survey. The typology of family farming and to explore and characterize the rural credit granted to purpose of the discussions was to validate the typology of family farming and to explore agricultural households. In addition, the genetic programming technique was introduced and characterize the rural credit granted to agricultural households. In addition, the genetic through the Bitbucket website (https://bitbucket.org/ciml (accessed on 1 June 2022)), programming technique was introduced through the Bitbucket website (https://bitbuc which is public and allows for free collaboration. The implementation is in C++, and all ket.org/ciml (accessed on 1 June 2022)), which is public and allows for free collaboration. tests were performed on the Debian/Ubuntu Linux operating system to obtain conclusions The implementation is in C++, and all tests were performed on the Debian/Ubuntu Linux that could help in decision making. operating system to obtain conclusions that could help in decision making. 4.1. 4.1. Study Study Area Area For For this this research, research, the the study study area area was was divided divided into into five five regions: regions: Norte, Norte, Nordeste, Nordeste, Sudeste, Sudeste, Sul, Sul, and and Centro-Oeste Centro-Oeste (Figure (Figure 3). 3). Figure 3. Map of Brazil showing the study areas. Figure 3. Map of Brazil showing the study areas. 4.2. Survey The dataset covers the period from June 2007 to July 2017 [10]. To evaluate the criteria, first, a document is used, which is the gateway to public policies [11,68]. Considering the legal and regulatory framework in force on 30 September 2017, the information available in the 2017 Agricultural Census, the definitions used in the 2006 Agricultural Census, and the opinions of the technical management of the Agricultural Census (GTA) of IBGE, several algorithms were proposed [69]. When their credit applications were processed, all farmers were evaluated according to the following criteria: Agriculture 2023, 13, 935 7 of 14 • The total gross income of the agricultural household does not exceed BRL 500,000. • The area of the property does not exceed four fiscal modules, a unit of measurement in hectares, whose value for each municipality is determined by the National Institute of Colonization and Agrarian Reform (INCRA). • Farmers predominantly use their own family’s labor for the activities of the establish- ment or enterprise. • Farmers have a PRONAF Aptitude Declaration (DAP). In addition to these classification criteria, the proposed model was generated by four independent criteria—production cost, annual gross income, return to crop productivity, and size of the area to be produced—and a dependent criterion: number of establishments that received rural credit (Table 4). Table 4. List of variables of the model. Variables Code Description x1 Territorial Region Norte, Nordeste, Sudeste, Sul, Centro-Oeste x2 Typology Family farming x3 Area range Fourteen groups of categorized areas Production value of agricultural establishments (per thousand x4 Productivity Reais (BRL)) Value of expenses incurred by agricultural establishments x5 Cost (per thousand Reais (BRL)) Value of income or income obtained by agricultural establishments x6 Income (per thousand Reais (BRL)) Y Approved quantity Quantity of establishments that received rural credit With this set of criteria, genetic programming was used to characterize rural credit. For this work, two scenarios were developed in an attempt to find a function that would explain it analytically: • Scenario 01, using the dataset separately for each region. • Scenario 02, a generalist function using the entire dataset without separating by region. Some authors use absolute error for fitness functions [64,70], while others use linear combinations of the mean square error and mean classification error [71]. In this paper, we preferred the latter approach. The fitness function, F, for evolution was calculated as follows: n | a − ei | F (ep) = ∑ i i =1 n where F is the fitness function, ep is the evolved program, ai is the actual observation, ei is the expected (predicted) observation, and n is the sample size. 4.3. Typology Construction The typological approach has previously been used in studies to characterize farming families [72,73]. The advantage of organization and the use of aggregated data is that the data are more stable, and this approach is widely used to build typologies of farmers [74,75]. Therefore, the aggregated data for this research were organized and used for different categories of agricultural areas corresponding to each region (Table 5). Agriculture 2023, 13, 935 8 of 14 Table 5. Sample size determination. Norte Nordeste Sudeste Sul Centro-Oeste Total population of farmers 10,764 73,612 56,229 112,830 10,924 Sample size (0–0.1 ha) 38 406 89 38 4 Sample size (0.2–0.5 ha) 49 364 72 27 1 Sample size (0.5–1 ha) 68 1455 197 63 1 Sample size (1–2 ha) 144 4069 384 200 7 Sample size (2–3 ha) 148 8641 1622 585 34 Sample size (3–4 ha) 142 6501 2584 1296 65 Sample size (4–5 ha) 148 5506 2837 1993 59 Sample size (5–10 ha) 486 3915 3136 2809 253 Sample size (10–20 ha) 1023 11,837 9951 17,758 964 Sample size (20–50 ha) 3204 11,460 13,060 32,152 1844 Sample size (50–100 ha) 2621 12,536 14,788 42,114 3110 Sample size (100–200 ha) 2072 4783 5994 13,464 2777 Sample size (200–500 ha) 615 1811 1403 326 1378 Sample size (500–1000 ha) 6 328 112 5 427 4.4. Typology Validation Evaluating aggregate data involves analyzing and interpreting data that have been combined. The steps used in the research to evaluate the aggregated data, according to [76], are as follows: • Understand the purpose and context of the data. For this research, we did not want to use the machine learning technique for prediction but rather to characterize ru- ral credit. • Check the data quality. We used a reliable Brazilian census [11], which is prepared by a trustworthy technical team that carries out mapping in different areas. The aggregated data were certified as complete by eliminating missing data. • Compare the data. The literature was compared with data obtained from the census to identify similarities and differences. • Draw a conclusion. Based on the analysis, conclusions and recommendations were made. It is important to be cautious when interpreting data and consider the limitations. Therefore, evaluating aggregated data requires a systematic approach that involves understanding the purpose and context of the data, checking the data quality, analyzing the data, comparing the data, drawing conclusions, and communicating the results. For this research, the use of aggregate data was justified by the objective of the work, which was to characterize farmers from different regions regarding their willingness to receive rural credit. The interest of the research was to group agricultural households according to total area and not to infer the information of each farmer. 5. Results 5.1. First Scenario Following the methods described above, five regions were characterized using the equations generated by the genetic programming technique based on symbolic regression. The five regions presented the output of the model (evolved program). The characterization of regions was carried out according to the variables used in the model (Table 6). To verify the robustness in terms of whether the characterization generated by the model resembled reality, the model was validated through discussion based on the litera- ture [77]. Equations for each region were developed. From these equations, we identified the variables that allowed for a qualitative comparison (no, low, moderate, or high influ- ence) for the approved number of agricultural establishments in relation to rural credit among regions (Table 7). Agriculture 2023, 13, 935 9 of 14 Table 6. Characterization of regions based on their variables. Characterization of Regions Territorial Region Evolved Program Based on Their Variables x3 = area Norte 3.21507 x6 = income x3 = area Nordeste 44.57690 x5 = cost x3 = area x4 = productivity Sudeste 52.21970 x6 = income x5 = cost Sul 29.76710 x6 = income x3 = area x4 = productivity Centro-Oeste 0.92433 x5 = cost Table 7. Characterization of the type of region identified. Territorial Region Equation Area Productivity Cost Income x Norte ep = 35x33 x6 Moderate influence No influence No influence High influence Nordeste ( x5 ) Moderate influence No influence High influence No influence ep = ( x −5) 3 (81+( x3 −4))+ x1 +2 ( 3 x3 3 Sudeste x 3 ≤ 10 High influence No influence High influence High influence ep = 1027 x62 5x4 > 10 − x5 Sul ep = x693 No influence No influence Low influence High influence x4 Centro-Oeste ep = x5 3 > 5 x High influence High influence Low influence No influence x4 x3 ≤ 5 Norte: According to the GP model, the higher the income of farming families, the greater the chance their farms will obtain approved rural credit. Nordeste: According to the GP model, the higher the production cost for farming families, the greater the chance their farms will obtain approved rural credit. This implies that the Nordeste region has high production costs and needs access to rural credit to produce. This reflects reality, as this region has low agricultural production compared to other regions [77]. Sudeste: The GP model allows for inequality, with the characterization of rural credit being represented by the variables area, productivity, and income. According to the model, for farms with an area greater than 10 hectares, income positively influences the allocation of rural credit. When the area is less than or equal to 10 hectares, the function is totally dependent on the area. Sul: According to the GP model, the greater the difference between income and cost for agricultural families, the greater the chance their farms will obtain approved rural credit. Centro-Oeste: The GP model allowed for an inequality, with the characterization of rural credit being represented by the variables area, productivity, and cost. According to the model, for establishments with an area greater than 5 hectares, the ratio of productivity and area has a positive influence on the allocation of rural credit. The cost for this area range has a negative influence. When the area is less than or equal to 5 hectares, the function is represented by the variables area and productivity, and the greater this ratio, the greater the chances that establishments will have approved credit. 5.2. Second Scenario The GP model allowed for an inequality, with the characterization of rural credit being represented by the variables area, productivity, cost, and income. According to the model, for establishments with an area equal to or greater than 20 hectares, the productivity and area ratio positively influences the allocation of rural credit. Cost and income for this area range have a negative influence. When the area is in the range of 10 to 20 hectares, the function is represented by the variables area, productivity, and income, and the greater the positive relationship between the area and productivity, the greater the chances the establishments will obtain approved rural credit. When the area is less than or equal to 10 hectares, cost has a positive influence (Table 8). Agriculture 2023, 13, 935 10 of 14 Table 8. Characterization of Brazil. Territory Equation Total Area Groups Evolved Program Variables 64( x5 − x35 −3130) x3 = area ep = x3 ≤ 10 9409 x5 = cost x3 = area 2x3 + x4 − x6 10 < x3 < 20 x4 = productivity ep = 85 Brazil 646.33000 x6 = income x3 = area 3 ( x3 ) +( x3 × x4 )− x6 x4 = productivity ep = x3 ≥ 20 ( x5 )2 x5 = cost x6 = income Different regions have different degrees of need when making decisions based on the analyzed variables. Therefore, according to the characterization of the territory in relation to the allocation of rural credit, this research demonstrates that using a single rule to describe Brazil would not be ideal. 5.3. Discussion of the Findings The advent of models generated via machine learning has impacted the world in different ways, with a presence in practically all areas of knowledge [78]. In some areas, models are applied directly, while in others, they function as a decision-making tool. However, in order to make a decision, it is desirable to understand how it was taken, which is where several learning models fail. A current example is the use of deep learning to generate artificial neural networks: although they are highly accurate, there is a trade-off between accuracy and complexity, making it difficult to extract information about how they work. The need to explain these models leads to them being restricted or to the use of auxiliary tools capable of generating a more familiar representation of the model. Local In- terpretable Model-Agnostic Explanations (LIME) is a tool that can identify an interpretable model that is locally true to the original [78]. Developed by researchers at the University of Washington to achieve greater transparency in terms of what happens inside the model, LIME has become very popular in the community for explaining AI models. When it comes to developing a highly accurate model, explainability is more difficult to achieve due to increasing complexity. For problems with higher dimensions, the lack of explain- ability is even more evident. Interpretability is an advantage for symbolic regression, as developed by the GP model; in this research, productivity is seen as contributing to the description of “approved rural credit”, while the high cost of production is evidenced as “without approval”. For example, studies indicate [66,67] that access to credit provides economic growth, improving agricultural productivity and providing higher incomes for family farmers, as observed by the result of the model for the Sul region. As another example, for the Nordeste region, the cost criterion is relevant, and according to studies [62,77], the Nordeste region has the highest number of family farm households and is also the region with the lowest economic growth. Therefore, it lacks technological development, allowing for higher production costs. Therefore, the decision-making process can be based on a non-black-box model with a clear understanding of how the decision was made (Figure 4). observed by the result of the model for the Sul region. As another example, for the Nordeste region, the cost criterion is relevant, and according to studies [62,77], the Nordeste region has the highest number of family farm households and is also the region with the lowest economic growth. Therefore, it lacks technological development, allowing for higher production costs. Therefore, the decision-making process can be based on a Agriculture 2023, 13, 935 11 of 14 non-black-box model with a clear understanding of how the decision was made (Figure 4). Figure 4. A model providing an answer based on data. LIME builds possible explanations according Figure 4. A model providing an answer based on data. LIME builds possible explanations according to why that answer was given. to why that answer was given. 6. 6. Conclusions Conclusions The The improvement improvement of of state-sponsored state-sponsored agricultural agricultural policies policies plays plays aa decisive decisive role role inin maintaining the distribution of rural credit. Groups of family maintaining the distribution of rural credit. Groups of family farmers seek to introducefarmers seek to introduce credit credit instruments instruments to to help help them them become become moremore competitive competitive on on the the agricultural agricultural market. market. However, However, the budget constraints of rural credit credit make it it difficult purchase items difficult to purchase items suchsuch asas agricultural agricultural inputs. inputs. AnAn important important aspect aspect discovered discovered by by this this research research is is that that the the allocation allocation of of rural rural credit credit is not ideal. Another Another important important aspect aspect of of this this research research is is the the challenge challenge of of capturing capturing the the degree degree of of diversity diversity in in different different regions, regions, and and the the typology typology is is limited limited in in its its ability ability to to accurately accurately represent represent all variations. 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However, However, itit is is possible to characterize characterizehow howcredit creditisisdistributed distributed across acrossthethe country countryandandthe the main factors main that factors can influence that access can influence to credit; access therefore, to credit; this isthis therefore, strong and innovative is strong research, and innovative since public research, since policiespolicies public for rural forcredit ruralare worldwide, credit and many are worldwide, and countries that are in many countries theare that same in condition the same as Brazil have condition this problem. as Brazil have thisTherefore, problem.using the machine Therefore, using learning the machinetechnique learningcould provide technique a better understanding of the regions according to the needs of agricultural could provide a better understanding of the regions according to the needs of agricultural households. In addition, GPIn households. models can GP addition, helpmodels in implementing can help inpolicies for smallholder implementing policiessupport services. for smallholder The technique used in this study was designed to generate a symbolic response using user-defined terms and identify the importance and priority of each criterion used for each region. Thus, those who are interested in rural credit may have better decision-making ability in relation to the most important criteria in a given territorial group and region. Author Contributions: Conceptualization, A.V.A. and C.M.; Methodology, A.V.A. and S.S.; Val- idation, A.V.A., C.M. and S.S.; Formal analysis, C.M.; Investigation, A.V.A.; Resources, A.V.A.; Writing–original draft, A.V.A.; Writing–review & editing, A.V.A.; Supervision, C.M. and S.S. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Data Availability Statement: https://sidra.ibge.gov.br/pesquisa/censo-agropecuario/censo-agro pecuario-2017/resultados-definitivos (accessed on 31 March 2023). Acknowledgments: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and CNPq. Agriculture 2023, 13, 935 12 of 14 Conflicts of Interest: The authors declare no conflict of interest. References 1. Zhang, J.; Li, X.; Xie, S.; Xia, X. Research on the Influence Mechanism of Land Tenure Security on Farmers’ Cultivated Land Non-Grain Behavior. Agriculture 2022, 12, 1645. [CrossRef] 2. Ernst, J.A. Políticas de Crédito Rural e as Particularidades do Pronaf: Impactos Sofridos Mediante as Transformações Econômicas Recentes no Brasil. Bachelor’s Thesis, Universidade Federal de Santa Maria, Santa Maria, Brazil, 2018. 3. Bojanic, H.A. The rapid agricultural development of Brazil in the last 20 years. EuroChoices 2017, 16, 5–10. [CrossRef] 4. BACEN. Banco Central do Brasil 2019. Anuário Estatístico de Crédito Rural. 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