# Sustainable Supplier Evaluation and Selection of Fresh Agricultural Products Based on IFAHP-TODIM Model

Authors: Yupei Du; Di Zhang; Yue Zou
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

In recent years, increasing pollution of the ecological environment, excessive use of pesticides, and lack of effective management of agricultural product supply chains have made the problem of having a green and safe supply of fresh food increasingly prominent. The sustainability of the fresh agricultural products supply has become an inevitable focus in the development of agricultural enterprises. There are some problems in the supply chain of fresh agricultural products, such as scattered production sites and difficult logistics transportation, which makes it difficult for enterprises to choose reliable suppliers. Supplier selection is a key component of sustainable supply chain management, and the criteria for evaluating the quality of sustainable suppliers are often affected by economic, social, and environmental factors. Therefore, from the perspective of sustainability, based on triple bottom line theory and comprehensively considering the three aspects of society, environment, and economy, this paper proposes a novel evaluation index system for the selection of sustainable suppliers of fresh agricultural products. This paper innovatively integrates the intuition fuzzy analytic hierarchy process and TODIM (an acronym in Portuguese of interactive and multiple attribute decision-making), and these are applied to select sustainable suppliers. Finally, the integration method is applied to the example, and a sensitivity analysis is carried out to verify the validity of the evaluation model.


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## Body

## 1. Introduction

Selection of fresh agricultural product suppliers is one of the most critical links in the agricultural product supply chain. Green and sustainable agricultural product supply is not only related to the development of food enterprises, but it also has a greater impact on people's livelihood. In recent years, with the problems of ecological environment pollution, excessive use of pesticides and fertilizers, and excessive use of additives in food processing in farmland, ensuring the sustainability of agricultural products has become increasingly problematic. For example, “Sudan red,” “poisonous cowpea,” and other vicious events have aroused widespread public concern about the safety of agricultural product supply. Taking China as an example, due to the lagging development of logistics transportation in the agricultural product supply chain, agricultural product production is relatively fragmented, and intersubject information cannot be circulated quickly and effectively. This makes it difficult to choose safe and sustainable suppliers in the agricultural product supply chain. Therefore, sustainable supplier selection of fresh agricultural products has become a key link in the management of green agricultural product supply chains. Selection of fresh agricultural product suppliers must not only consider the cost and technology but also environmental pollution, resource consumption, and social responsibility. In summary, how to effectively assess the sustainability of fresh agricultural product suppliers is an important issue for companies to implement sustainable supply chain management.


## 2. Literature Review

At present, domestic and foreign studies on the food supply chain and supplier selection methods are relatively numerous, while there are relatively few studies on the selection of sustainable suppliers of fresh agricultural products. A characteristic of the food supply chain is that food is perishable [1], and the freshness of food will directly affect the quality and safety [2]. Fresh food is a critical part in the food supply chain, which greatly affects the safety of consumers’ diets. However, in this supply chain, there are a large number of intermediaries between farmers and retailers [3]. Under the trend of continuous development of food safety and quality standards, supermarkets and other suppliers have to pay a huge cost to purchase from many small-scale agricultural producers [4]. Therefore, the selection of sustainable suppliers in the fresh food supply chain has become a key issue that needs to be studied.Supplier selection is a key component of sustainable supply chain management [5]. The focus of sustainable supply chain development is the type of supply chain and the social and environmental responsibilities of products [6], while the sustainability of agricultural food supply chains obviously involves significant environmental and social impacts [7]. The sustainability of food includes environmental issues, social issues, and expected returns [8]. Therefore, previous research has attempted to establish a sustainable agricultural food supply chain evaluation index system from the three dimensions of social responsibility, economic benefits, and environmental protection. As the material basis for agricultural product production, the ecological environment has always been the main consideration in constructing a sustainable evaluation index system. Gerbens-Leenes et al. [9] applied environmental indicators to their evaluation of the environmental sustainability of food production. Solér et al. [10] explored the use of environmental information at different stages in the food supply chain. Cellura et al. [11] evaluated the sustainability of crop production and consumption from the perspectives of energy consumption and environmental burden.Corporate social responsibility is considered to be one of the major factors impacting the food supply chain [12]. Spence et al. [13] discussed the evolution from corporate social responsibility to food supply chain responsibility. Chkanikova and Mont [14] systematically elaborated the reasons and obstacles for food retailers to fulfill their supply chain responsibilities. Krejci et al. [15] studied the influence of social factors on the long-term sustainability of food supply centers. Chen et al. [16] determined optimal suppliers in the sustainable food supply chain from the perspective of social responsibility. Stranieri et al. [17] discussed the effect of implementing corporate social responsibility activities on the vertical restructuring of the food supply chain.Economic benefit is the basic indicator of sustainable supply assessment. It is generally combined with environmental performance or social performance to evaluate the sustainability of the supply chain [18–20]. In addition, some researchers have combed the existing literature on agricultural fresh food supply chain quality (AFSCQ). They found that sustainable management is one of the key issues in AFSCQ research, and performance evaluations of the agricultural fresh food supply chain are still in the development stage [21]. However, most of the previous research has focused on sustainability assessment of the food supply chain and agricultural product supply chain. Sustainability assessments of fresh agricultural product suppliers are basically nonexistent and lack a systematic measurement framework.Selection of sustainable suppliers requires evaluation of supplier performance based on multiple criteria [22], which includes two stages: determination of indicator weights and supplier ranking. The two-stage evaluation part involves two types of uncertainty: individual uncertainty and group uncertainty [23]. Individual uncertainty refers to the ambiguity of an individual’s thinking and expression [24], and group uncertainty refers to the ambiguity of different people’s preferences for something [23]. Since the decision process involves uncertain information, various methods based on fuzzy set theory are often used in the field of supplier selection to capture fuzzy or ambiguous information [25]. Among the commonly used multiattribute decision-making methods for determining weights, there are, for example, AHP [26], ANP [27], and DEMATEL [28]. These traditional weighting methods cannot deal well with the uncertainty and inaccuracy of decision information. In the supplier ranking method, compared with DEA [29], PROMETHEE [30], and TOPSIS [31] methods, the TODIM multiattribute decision-making method considers the psychological behavior of decision-makers [32] and can deal with uncertainties The problem is in the environment [33], but the TODIM method directly measures the distance between the fuzzy numbers and decomposes the fuzzy information into clear values at the beginning, which may lead to the loss of important information in decision-making problems [34]. Considering the ambiguity of decision information, applying the IF intuitionistic fuzzy set theory to the AHP method (i.e., IFAHP) can better deal with the hesitation in decision-making [35]. Thus, this article chose the IFAHP-TODIM integration method and applied it to the selection of sustainable suppliers of fresh agricultural products. Existing research on the selection of sustainable suppliers of fresh agricultural products has not yet used this integrated method, so we also expand on new ideas for subsequent scholars to study.


## 3. The Evaluation Index System of Fresh Agricultural Product Sustainable Suppliers Based on Triple Bottom Line

Sustainable supply chain management has become the focus of supply chain field. One of the most basic means of sustainable supply chain management is supplier selection [36]. Sustainable supplier selection is a key factor in sustainable supply chain management [37], because the supplier is at the beginning of the supply chain, and its economic, environmental, and social performance will have a significant impact on the downstream enterprises of the supply chain [25]. Traditional supplier selection only focuses on economic factors, but in the changing market, sustainable supply chain management should be adopted, that is, environmental and social standards [38, 39] should be considered. Choosing the right supplier based on sustainability criteria (economy, environment, and society) can help enterprises achieve sustainable development [40]. Sustainable supply chain management in the field of fresh agricultural products is facing economic, social, and ecological challenges. This sustainability is influenced by many factors, including economic, social, and environmental aspects, namely, the triple bottom line (TBL) principle (Figure 1). In the organization of production activities, enterprises not only focus on economic development but also consider their own social responsibilities and possible environmental pollution. If you simply pursue profitability and ignore social and environmental responsibilities, companies may move to oppose consumers and society and will face the dilemma of rootless trees. Unification of economic development, social responsibility, and environmental responsibility is the foundation for sustainable development of an enterprise and its longevity.Figure 1
Triple bottom line.


### 3.1. “Economic Bottom Line” Evaluation Index

Economic development is the lifeblood of an enterprise, and economic benefits (gross output value/production cost) are an important part of measuring enterprise performance. This article selects three indicators of energy consumption, logistics cost, and net product price from the cost dimension to construct an economic bottom line indicator system.


### 3.2. “Social Bottom Line” Evaluation Index

The social bottom line measures the ability of business organizations to fulfill their social responsibilities. Social responsibility includes protection of consumer rights, social welfare, green safety, and other components. This article selects six specific indicators from the dimensions of food safety and packaging materials—to reduce food additives, green R & D and innovation, reusability, biodegradable products, use of recycled materials, and use of hazardous substances—to build a social bottom line indicator system.


### 3.3. “Environmental Bottom Line” Evaluation Index

Sustainable development focuses on the coordinated development of social, economic, and environmental aspects. Changes in the vectors of indicators in these areas are expected to increase incrementally. Among them, ecological environmental protection is the prerequisite for sustainable economic development. Based on the theory of sustainable development, this article refers to the indicators recommended by the “Guide to Sustainability Reporting.” The article selects seven indicators—ISO14000 certification, environmental policies and plans, environmental remediation, environmental governance, air pollutant production, wastewater production, and solid waste production—from three dimensions—environmental management system, environmental protection, and pollution generation—and builds an environmental baseline indicator system. The established evaluation index system for the suppliers of fresh agricultural products is shown in Table1.Table 1
Evaluation index system of fresh agricultural product sustainable suppliers based on triple bottom line.
Target layerStandard layerIndicator layerExplanation layerEnvironmental controlEnvironmental management systemA1ISO 14000 certificationB11Environmental certification held by the supplierEnvironmental policy and planB12Supplier environmental protection policy planning, implementation, and reviewEnvironmental protectionA2Environmental restorationB21Supplier efforts to eliminate contamination in the mediaEnvironmental governanceB22Suppliers efforts to harmlessly dispose of wasteEconomic developmentCostA3Energy consumptionB31Energy consumption per unit of agricultural productLogistics costsB32Total cost of agricultural productsProduct net priceB33Average net price per unit of agricultural productPollutionA4Air pollutant productionB41The average amount of air pollutants emitted per dayWastewater productionB42Daily average volume of wastewaterSolid waste generationB43Average daily solid waste volumeSocial responsibilityUse of packaging materialsA5ReusabilityB51Reusable product percentageBiodegradable productsB52Percentage of biodegradable productsUse recycled materialsB53Percentage of products using recycled materialsUse of hazardous substancesB54Daily use of harmful substancesFood safetyA6Reduce food additivesB61Ability to ensure green food safetyGreen R & D and innovationB62Ability to innovate new clean technologies, processes, and practices


## 3.1. “Economic Bottom Line” Evaluation Index

Economic development is the lifeblood of an enterprise, and economic benefits (gross output value/production cost) are an important part of measuring enterprise performance. This article selects three indicators of energy consumption, logistics cost, and net product price from the cost dimension to construct an economic bottom line indicator system.


## 3.2. “Social Bottom Line” Evaluation Index

The social bottom line measures the ability of business organizations to fulfill their social responsibilities. Social responsibility includes protection of consumer rights, social welfare, green safety, and other components. This article selects six specific indicators from the dimensions of food safety and packaging materials—to reduce food additives, green R & D and innovation, reusability, biodegradable products, use of recycled materials, and use of hazardous substances—to build a social bottom line indicator system.


## 3.3. “Environmental Bottom Line” Evaluation Index

Sustainable development focuses on the coordinated development of social, economic, and environmental aspects. Changes in the vectors of indicators in these areas are expected to increase incrementally. Among them, ecological environmental protection is the prerequisite for sustainable economic development. Based on the theory of sustainable development, this article refers to the indicators recommended by the “Guide to Sustainability Reporting.” The article selects seven indicators—ISO14000 certification, environmental policies and plans, environmental remediation, environmental governance, air pollutant production, wastewater production, and solid waste production—from three dimensions—environmental management system, environmental protection, and pollution generation—and builds an environmental baseline indicator system. The established evaluation index system for the suppliers of fresh agricultural products is shown in Table1.Table 1
Evaluation index system of fresh agricultural product sustainable suppliers based on triple bottom line.
Target layerStandard layerIndicator layerExplanation layerEnvironmental controlEnvironmental management systemA1ISO 14000 certificationB11Environmental certification held by the supplierEnvironmental policy and planB12Supplier environmental protection policy planning, implementation, and reviewEnvironmental protectionA2Environmental restorationB21Supplier efforts to eliminate contamination in the mediaEnvironmental governanceB22Suppliers efforts to harmlessly dispose of wasteEconomic developmentCostA3Energy consumptionB31Energy consumption per unit of agricultural productLogistics costsB32Total cost of agricultural productsProduct net priceB33Average net price per unit of agricultural productPollutionA4Air pollutant productionB41The average amount of air pollutants emitted per dayWastewater productionB42Daily average volume of wastewaterSolid waste generationB43Average daily solid waste volumeSocial responsibilityUse of packaging materialsA5ReusabilityB51Reusable product percentageBiodegradable productsB52Percentage of biodegradable productsUse recycled materialsB53Percentage of products using recycled materialsUse of hazardous substancesB54Daily use of harmful substancesFood safetyA6Reduce food additivesB61Ability to ensure green food safetyGreen R & D and innovationB62Ability to innovate new clean technologies, processes, and practices


## 4. Methodology

The intuitionistic fuzzy analytic hierarchy process decomposes complex decision-making problems into an orderly hierarchical structure in the order of general goals, subgoals at various levels, and evaluation criteria, and then relevant experts score the indicators in the structural model. With the help of expert scores and an intuitionistic fuzzy number correspondence table (Table2), an intuitionistic fuzzy judgment matrix is established. Then, after a consistency test, the index weights at all levels are finally obtained to assist decision-making. This method can accurately reflect the uncertainty of the decision-making subject to the evaluated object to a certain extent, and it can unify the quantitative and qualitative indicators. In addition, when the judgment matrix is not consistent, an intuitionistic fuzzy judgment matrix that meets the requirements can be obtained by adjusting the parameters, and distortion of the original data is avoided as much as possible. The TODIM multiattribute decision-making method has been widely used in multiattribute decision-making problems such as intuitionistic fuzzy numbers, hesitant fuzzy numbers, and hesitant fuzzy language because it can fully consider the psychological behavior of decision-makers and obtain decision results that meet the preferences of decision-makers. In this study, the intuitionistic fuzzy analytic hierarchy process combined with the TODIM multiattribute decision-making method was used to select suppliers of fresh agricultural products. This process is specified in Figure 2.Table 2
Scale table corresponding to fuzzy numbers and ratings.
Preference evaluationIntuitionistic fuzzy numberExtremely important(0.90, 0.10, 0.00)Very important(0.80, 0.15, 0.05)Important(0.70, 0.20, 0.10)More important(0.60, 0.25, 0.15)Equally important(0.50, 0.30, 0.20)Less important(0.40, 0.45, 0.15)Unimportant(0.30, 0.60, 0.10)Very unimportant(0.20, 0.75, 0.05)Extremely unimportant(0.10, 0.90, 0.00)Figure 2
Supplier selection flowchart.


### 4.1. Construction of the Intuitionistic Fuzzy Judgment Matrix

The first step was to collect the opinions of relevant experts on the importance of each indicator. For the 6 first-level indicators and 16 second-level indicators in the indicator system, we established seven intuitive fuzzy judgment matrices according to the criteria corresponding to the scores in Table2 and the fuzzy numbers. Then, we made a pairwise comparison of the indicators of each layer to construct a R=rijn×n square matrix, where i and j represent the rows and columns in the judgment matrix, respectively. rij=uij,viji,j=1,2,…,n, where rij=uij,vij, in which uij indicates the degree that the ith index is better than the jth index; vij indicates the ith index is inferior to the jth index; πij represents the degree of hesitation, πij=1−uij−vij.The basis for constructing the intuitionistic fuzzy judgment matrix is to grade the opinions of experts in the field of fresh agricultural product suppliers. For the comparison between qualitative indicators, see Table2. The scale corresponds to expert score and intuitionistic fuzzy number. The last digit of the intuitionistic fuzzy number represents uncertainty (i.e., ambiguity). An intuitionistic fuzzy judgment matrix was constructed according to the corresponding fuzzy numbers obtained in Table 2, so as to visually check the relative importance of the indicators, and then a data consistency test was constructed.


### 4.2. Inspection Consistency Calculation

The second step was to conduct a consistency test on the collected expert evaluation opinions. If the requirements are not met, it means that the experts’ evaluations of the relative importance of the indicators are not uniform. Unlike traditional analytic hierarchy processes, intuitionistic fuzzy analytic hierarchy processes can iterate through formulas and set parameters to avoid rescoring experts. The consistency test formula for distance measurements [41] based on intuitionistic fuzzy information is given as follows [42]:(1)dR¯,R=12n−1n−2∑i=1n∑j=1nuij¯−uij+vij¯−vij+πij¯−πij,where R is the intuitionistic fuzzy judgment matrix obtained by comparing pairs of indicators at all levels and R¯ is the intuitionistic fuzzy consistency judgment matrix R¯=rij¯n×n obtained according to the following calculation formula [42]:(1)
Whenj>i+1, let R¯=u¯ij,v¯ij, where(2)u¯ij=∏t=i+1j−1uitutjj−i−1∏t=i+1j−1uitutjj−i−1+∏t=i+1j−11−uit1−utjj−i−1,(3)v¯ij=∏t=i+1j−1vitvtjj−i−1∏t=i+1j−1vitvtjj−i−1+∏t=i+1j−11−vit1−vtjj−i−1.(2)
Whenj=i+1, rij¯=rij.(3)
Whenj<i+1, rij¯=v¯ij,u¯ij.The intuitionistic fuzzy consistency judgment matrixR¯=rij¯n×n is calculated according to the above formula and substituted into equation (1) for a consistency check. If dR¯,R<0.1, it passes the consistency test, and otherwise, it fails the consistency test. When the consistency test fails, the parameter σ is introduced into the iteration, that is, the intuitionistic fuzzy consistency judgment matrix is transformed by adjusting the parameter σ until the consistency test is passed. Let the parameter σ∈0,1, then the consistency check formula is as follows [42]:(4)uij˜=uij1−σuij¯σuij1−σuij¯σ+1−uij1−σ1−uij¯σ,i,j=1,2,…,n,vij˜=vij1−σvij¯σvij1−σvij¯σ+1−vij1−σ1−vij¯σ,i,j=1,2,…,n.Through calculations of the above formula, the transformed consistency judgment matrixR˜=rij˜n×n is obtained, where rij˜=uij˜,vij˜. Then, according to formula (5), the consistency test is performed on the new consistency judgment matrix, and the above process is continued until the consistency test is passed. This is calculated as follows:(5)dR¯,R=12n−1n−2∑i=1n∑j=1nuij˜−uij+vij˜−vij+πij˜−πij.


### 4.3. Weight Calculation

Based on the intuitionistic fuzzy judgment matrix that passed the consistency test, the weight of each index is calculated, and the calculation formula is as follows [42]:(6)ωi=∑j=1nuij∑i=1n∑j=1n1−vij,1−∑j=1n1−uij∑i=1n∑j=1nvij,i=1,2,…,n.


### 4.4. Information Gathering

It can be seen from Table1 that this evaluation system has 6 first-level indicators and 16 second-level indicators. Let the weight of the first-level indicator be ωkk=1,2,…,6, and the weight of the second-level indicator relative to the first-level indicator be ωklk=1,2,…,6;l=1,2,…,4. The comprehensive weight of the secondary indicators relative to the total score of the plan is Wkl, and the number of secondary indicators under the primary indicator Ai is between two and four. Since both ωk and ωkl are intuitionistic fuzzy numbers, their calculation should be performed using the algorithm of intuitionistic fuzzy numbers [43]:(7)α1⊕α2=uα1+uα2−uα1∗uα2,vα1∗vα2,(8)α1⊗α2=uα1∗uα2,vα1+vα2−vα1∗vα2.Integration of qualitative index information uses the above formula, while the quantitative index uses the simulated value of the actual statistics.The qualitative indicators should be deblurred so that they can form an initial decision matrix with the quantitative indicators. The deblurring algorithms of intuitionistic fuzzy sets mainly include the maximum truth value method, weighted average method, and centroid method [44]. This article uses the maximum truth method, and the formula is as follows:(9)Tvu=μvu+1+μvu−πvu2πvu.Here,μvu represents the degree of membership, πvu represents the degree of hesitation, and Tvu is the true value of the intuitionistic fuzzy number.


### 4.5. Normalized Processing

The actual value of the quantitative index obtained from statistics and the real value of the qualitative index after deblurring constitute the initial decision-making matrix for the selection of fresh agricultural product suppliers, which are standardized to obtain a standardized decision matrix. The attributes of the indicator are divided into the benefit type and the cost type. The greater the value of the benefit-type index, the better, and the smaller the value of the cost-type index, the better. Therefore, the standardized formulas for different attribute indicators are as follows:Benefit index:(10)cij=cijM−mincijMmaxcijM−mincijM.Cost index:(11)cij=maxcijM−cijMmaxcijM−mincijM.


### 4.6. TODIM Method to Calculate Dominance

This method is based on the description provided by expert experience, and it judges the merits of each evaluation object by calculating the overall superiority of the evaluation object relative to other evaluation objects. The main steps are as follows [45]:(1)
The predominance matrixV=δai,akn×n of the evaluation objects is calculated, and δai,ak represents the predominance of the evaluation object ai relative to the evaluation object ak. The calculation formula is given by(12)δai,ak=∑j=1nφjai,ak.Here,φjai,ak represents the dominance of the evaluation object ai relative to the evaluation object ak with respect to the index cj. The calculation formula of φjai,ak is as follows:(13)aφjai,ak=xij−xkjwrj∑j=1nwrj,xij−xkj>0,bφjai,ak=0,xij−xkj=0,cφjai,ak=−1θxkj−xij∑j=1nwrjwrj,xij−xkj<0,wherexij,xkj are real numbers; wrj is the relative weight of the index relative to the reference index cj, wrj=wcj/w∗, where w∗=maxwcj,j=1,2,…,n; θ is the attenuation coefficient in the face of loss, and its value range is 0<θ<∑j=1nwrj/wrj, which is generally 2.25, indicating the ability of the decision-maker to avoid mistakes.(2)
The formula for calculating the overall advantageTd of the evaluation object ai relative to all other evaluation objects is as follows:(14)Td=∑k=1mδai,ak.(3)
A comprehensive score of the evaluation object is calculated.The comprehensive scoreεai of the evaluation object ai is obtained by normalizing the overall advantage Td of the evaluation object. Then, all evaluation objects are sorted according to the size of εai. The larger the εai, the better the evaluation object ai. The calculation formula of εai is as follows:(15)εai=Td−minTdmaxTd−minTd.


## 4.1. Construction of the Intuitionistic Fuzzy Judgment Matrix

The first step was to collect the opinions of relevant experts on the importance of each indicator. For the 6 first-level indicators and 16 second-level indicators in the indicator system, we established seven intuitive fuzzy judgment matrices according to the criteria corresponding to the scores in Table2 and the fuzzy numbers. Then, we made a pairwise comparison of the indicators of each layer to construct a R=rijn×n square matrix, where i and j represent the rows and columns in the judgment matrix, respectively. rij=uij,viji,j=1,2,…,n, where rij=uij,vij, in which uij indicates the degree that the ith index is better than the jth index; vij indicates the ith index is inferior to the jth index; πij represents the degree of hesitation, πij=1−uij−vij.The basis for constructing the intuitionistic fuzzy judgment matrix is to grade the opinions of experts in the field of fresh agricultural product suppliers. For the comparison between qualitative indicators, see Table2. The scale corresponds to expert score and intuitionistic fuzzy number. The last digit of the intuitionistic fuzzy number represents uncertainty (i.e., ambiguity). An intuitionistic fuzzy judgment matrix was constructed according to the corresponding fuzzy numbers obtained in Table 2, so as to visually check the relative importance of the indicators, and then a data consistency test was constructed.


## 4.2. Inspection Consistency Calculation

The second step was to conduct a consistency test on the collected expert evaluation opinions. If the requirements are not met, it means that the experts’ evaluations of the relative importance of the indicators are not uniform. Unlike traditional analytic hierarchy processes, intuitionistic fuzzy analytic hierarchy processes can iterate through formulas and set parameters to avoid rescoring experts. The consistency test formula for distance measurements [41] based on intuitionistic fuzzy information is given as follows [42]:(1)dR¯,R=12n−1n−2∑i=1n∑j=1nuij¯−uij+vij¯−vij+πij¯−πij,where R is the intuitionistic fuzzy judgment matrix obtained by comparing pairs of indicators at all levels and R¯ is the intuitionistic fuzzy consistency judgment matrix R¯=rij¯n×n obtained according to the following calculation formula [42]:(1)
Whenj>i+1, let R¯=u¯ij,v¯ij, where(2)u¯ij=∏t=i+1j−1uitutjj−i−1∏t=i+1j−1uitutjj−i−1+∏t=i+1j−11−uit1−utjj−i−1,(3)v¯ij=∏t=i+1j−1vitvtjj−i−1∏t=i+1j−1vitvtjj−i−1+∏t=i+1j−11−vit1−vtjj−i−1.(2)
Whenj=i+1, rij¯=rij.(3)
Whenj<i+1, rij¯=v¯ij,u¯ij.The intuitionistic fuzzy consistency judgment matrixR¯=rij¯n×n is calculated according to the above formula and substituted into equation (1) for a consistency check. If dR¯,R<0.1, it passes the consistency test, and otherwise, it fails the consistency test. When the consistency test fails, the parameter σ is introduced into the iteration, that is, the intuitionistic fuzzy consistency judgment matrix is transformed by adjusting the parameter σ until the consistency test is passed. Let the parameter σ∈0,1, then the consistency check formula is as follows [42]:(4)uij˜=uij1−σuij¯σuij1−σuij¯σ+1−uij1−σ1−uij¯σ,i,j=1,2,…,n,vij˜=vij1−σvij¯σvij1−σvij¯σ+1−vij1−σ1−vij¯σ,i,j=1,2,…,n.Through calculations of the above formula, the transformed consistency judgment matrixR˜=rij˜n×n is obtained, where rij˜=uij˜,vij˜. Then, according to formula (5), the consistency test is performed on the new consistency judgment matrix, and the above process is continued until the consistency test is passed. This is calculated as follows:(5)dR¯,R=12n−1n−2∑i=1n∑j=1nuij˜−uij+vij˜−vij+πij˜−πij.


## 4.3. Weight Calculation

Based on the intuitionistic fuzzy judgment matrix that passed the consistency test, the weight of each index is calculated, and the calculation formula is as follows [42]:(6)ωi=∑j=1nuij∑i=1n∑j=1n1−vij,1−∑j=1n1−uij∑i=1n∑j=1nvij,i=1,2,…,n.


## 4.4. Information Gathering

It can be seen from Table1 that this evaluation system has 6 first-level indicators and 16 second-level indicators. Let the weight of the first-level indicator be ωkk=1,2,…,6, and the weight of the second-level indicator relative to the first-level indicator be ωklk=1,2,…,6;l=1,2,…,4. The comprehensive weight of the secondary indicators relative to the total score of the plan is Wkl, and the number of secondary indicators under the primary indicator Ai is between two and four. Since both ωk and ωkl are intuitionistic fuzzy numbers, their calculation should be performed using the algorithm of intuitionistic fuzzy numbers [43]:(7)α1⊕α2=uα1+uα2−uα1∗uα2,vα1∗vα2,(8)α1⊗α2=uα1∗uα2,vα1+vα2−vα1∗vα2.Integration of qualitative index information uses the above formula, while the quantitative index uses the simulated value of the actual statistics.The qualitative indicators should be deblurred so that they can form an initial decision matrix with the quantitative indicators. The deblurring algorithms of intuitionistic fuzzy sets mainly include the maximum truth value method, weighted average method, and centroid method [44]. This article uses the maximum truth method, and the formula is as follows:(9)Tvu=μvu+1+μvu−πvu2πvu.Here,μvu represents the degree of membership, πvu represents the degree of hesitation, and Tvu is the true value of the intuitionistic fuzzy number.


## 4.5. Normalized Processing

The actual value of the quantitative index obtained from statistics and the real value of the qualitative index after deblurring constitute the initial decision-making matrix for the selection of fresh agricultural product suppliers, which are standardized to obtain a standardized decision matrix. The attributes of the indicator are divided into the benefit type and the cost type. The greater the value of the benefit-type index, the better, and the smaller the value of the cost-type index, the better. Therefore, the standardized formulas for different attribute indicators are as follows:Benefit index:(10)cij=cijM−mincijMmaxcijM−mincijM.Cost index:(11)cij=maxcijM−cijMmaxcijM−mincijM.


## 4.6. TODIM Method to Calculate Dominance

This method is based on the description provided by expert experience, and it judges the merits of each evaluation object by calculating the overall superiority of the evaluation object relative to other evaluation objects. The main steps are as follows [45]:(1)
The predominance matrixV=δai,akn×n of the evaluation objects is calculated, and δai,ak represents the predominance of the evaluation object ai relative to the evaluation object ak. The calculation formula is given by(12)δai,ak=∑j=1nφjai,ak.Here,φjai,ak represents the dominance of the evaluation object ai relative to the evaluation object ak with respect to the index cj. The calculation formula of φjai,ak is as follows:(13)aφjai,ak=xij−xkjwrj∑j=1nwrj,xij−xkj>0,bφjai,ak=0,xij−xkj=0,cφjai,ak=−1θxkj−xij∑j=1nwrjwrj,xij−xkj<0,wherexij,xkj are real numbers; wrj is the relative weight of the index relative to the reference index cj, wrj=wcj/w∗, where w∗=maxwcj,j=1,2,…,n; θ is the attenuation coefficient in the face of loss, and its value range is 0<θ<∑j=1nwrj/wrj, which is generally 2.25, indicating the ability of the decision-maker to avoid mistakes.(2)
The formula for calculating the overall advantageTd of the evaluation object ai relative to all other evaluation objects is as follows:(14)Td=∑k=1mδai,ak.(3)
A comprehensive score of the evaluation object is calculated.The comprehensive scoreεai of the evaluation object ai is obtained by normalizing the overall advantage Td of the evaluation object. Then, all evaluation objects are sorted according to the size of εai. The larger the εai, the better the evaluation object ai. The calculation formula of εai is as follows:(15)εai=Td−minTdmaxTd−minTd.


## 5. Case Study

### 5.1. Consistency Check

The intuitionistic fuzzy data in the intuitionistic fuzzy judgment matrix in this paper were obtained by experts. Based on the established index system for supplier selection criteria (Table1), this paper established seven intuitionistic fuzzy judgment matrices as shown in Table 3.Table 3
Intuitionistic fuzzy judgment matrix of first-level indicators.
First-level indicatorsEnvironmental management systemA1Environmental protectionA2CostA3PollutionA4Use of packaging materialsA5Food safetyA6Environmental management systemA1(0.5, 0.5)(0.35, 0.6)(0.4, 0.5)(0.45, 0.35)(0.65, 0.25)(0.5, 0.3)Environmental protectionA2(0.6, 0.35)(0.5, 0.5)(0.6, 0.4)(0.65, 0.25)(0.75, 0.2)(0.7, 0.2)CostA3(0.5, 0.4)(0.4, 0.6)(0.5, 0.5)(0.5, 0.35)(0.7, 0.25)(0.65, 0.2)PollutionA4(0.35, 0.45)(0.25，0.65)(0.35, 0.5)(0.5, 0.5)(0.6, 0.2)(0.6, 0.4)Use of packaging materialsA5(0.25, 0.65)(0.2, 0.75)(0.25, 0.7)(0.2, 0.6)(0.5, 0.5)(0.35, 0.6)Food safetyA6(0.3, 0.5)(0.2, 0.7)(0.2, 0.65)(0.4, 0.6)(0.6, 0.35)(0.5, 0.5)According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 4.Table 4
Intuitionistic fuzzy consistency test matrix of first-level indicators.
First-level indicatorsEnvironmental management systemA1Environmental protectionA2CostA3PollutionA4Use of packaging materialsA5Food safetyA6Environmental management systemA1(0.5, 0.5)(0.35, 0.6)(0.4468, 0.5)(0.4495, 0.3416)(0.5927, 0.2061)(0.5403, 0.2648)Environmental protectionA2(0.6, 0.35)(0.5, 0.5)(0.6, 0.4)(0.6, 0.2642)(0.7574, 0.1198)(0.6991, 0.1937)CostA3(0.5, 0.4468)(0.4, 0.6)(0.5, 0.5)(0.5, 0.35)(0.6, 0.1186)(0.5785, 0.2975)PollutionA4(0.3416, 0.4495)(0.2642, 0.6)(0.35, 0.5)(0.5, 0.5)(0.6, 0.2)(0.4468, 0.2727)Use of packaging materialsA5(0.2061, 0.5927)(0.1198, 0.7574)(0.1186, 0.6)(0.2, 0.6)(0.5, 0.5)(0.35, 0.6)Food safetyA6(0.2648, 0.5403)(0.1937, 0.6991)(0.2975, 0.5785)(0.2727, 0.4468)(0.6, 0.35)(0.5, 0.5)The next step was to calculate the consistency according to equation (1) and get dR¯,R=0.0940<0.1. This shows that the consistency test passed.Table5 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 6.Table 5
Intuitionistic fuzzy judgment matrix of secondary indicators of the environmental management system.
A1 second-level indicatorISO 14000 certificationB11Environmental policy and planB12ISO 14000 certificationB11(0.5, 0.5)(0.5, 0.45)Environmental policy and planB12(0.45, 0.5)(0.5, 0.5)Table 6
Intuitionistic fuzzy consistency test matrix of secondary indicators of environmental management system.
A1 second-level indicatorISO 14000 certificationB11Environmental policy and planB12ISO 14000 certificationB11(0.5, 0.5)(0.5, 0.45)Environmental policy and planB12(0.45, 0.5)(0.5, 0.5)It can be seen thatR¯=R, that is, the consistency check matrix was the same as the original matrix (Table 5). In the next step, the consistency was calculated according to equation (1) as dR¯,R=0<0.1, which shows that the consistency test passed. All the following 2×2 matrices (Tables 7 and 8) have the same reasoning.Table 7
Intuitionistic fuzzy judgment matrix of secondary indicators of environmental protection.
A2 second-level indicatorEnvironmental restorationB21Environmental governanceB22Environmental restorationB21(0.5, 0.5)(0.5, 0.5)Environmental governanceB22(0.5, 0.5)(0.5, 0.5)Table 8
Intuitionistic fuzzy judgment matrix of the second-level food safety index.
A6 second-level indicatorReduce food additivesB61Green R & D and innovationB62Reduce food additivesB61(0.5, 0.5)(0.45, 0.5)Green R & D and innovationB62(0.5, 0.45)(0.5, 0.5)Table9 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 10.Table 9
Intuitionistic fuzzy judgment matrix of secondary cost indicators.
A3 second-level indicatorEnergy consumptionB31Logistics costsB32Product net priceB33Energy consumptionB31(0.5, 0.5)(0.65, 0.15)(0.45, 0.35)Logistics costsB32(0.15, 0.65)(0.5, 0.5)(0.3, 0.7)Product net priceB33(0.35, 0.45)(0.7, 0.3)(0.5, 0.5)Table 10
Intuitionistic fuzzy consistency test matrix of the second-level cost index.
A3 second-level indicatorEnergy consumptionB31Logistics costsB32Product net priceB33Energy consumptionB31(0.5, 0.5)(0.65, 0.15)(0.4432, 0.2916)Logistics costsB32(0.15, 0.65)(0.5, 0.5)(0.3, 0.7)Product net priceB33(0.2916, 0.4432)(0.7, 0.3)(0.5, 0.5)In the same way, according to formula (1), the consistency was calculated as dR¯,R=0.0702<0.1, which shows the consistency test passed.Table11 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 12.Table 11
Intuitionistic fuzzy judgment matrix for secondary indicators of pollution.
A4 second-level indicatorAir pollutant productionB41Wastewater productionB42Solid waste generationB43Air pollutant productionB41(0.5, 0.5)(0.45, 0.6)(0.6, 0.35)Wastewater productionB42(0.6, 0.45)(0.5, 0.5)(0.5, 0.45)Solid waste generationB43(0.35, 0.6)(0.45, 0.5)(0.5, 0.5)Table 12
Intuitionistic fuzzy consistency test matrix for secondary indicators of pollution.
A4 second-level indicatorAir pollutant productionB41Wastewater productionB42Solid waste generationB43Air pollutant productionB41(0.5, 0.5)(0.45, 0.6)(0.45, 0.3058)Wastewater productionB42(0.6, 0.45)(0.5, 0.5)(0.5, 0.45)Solid waste generationB43(0.3058, 0.45)(0.45, 0.5)(0.5, 0.5)According to formula (1), the consistency was calculated as dR¯,R=0.0976<0.1, which shows the consistency test passed.Table13 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 14.Table 13
Intuitionistic fuzzy judgment matrix for the use of secondary indicators for packaging materials.
A5 second-level indicatorReusabilityB51Biodegradable productsB52Use recycled materialsB53Use of hazardous substancesB54ReusabilityB51(0.5, 0.5)(0.55, 0.4)(0.45, 0.55)(0.4, 0.5)Biodegradable productsB52(0.4, 0.55)(0.5, 0.5)(0.5, 0.45)(0.5, 0.3)Use recycled materialsB53(0.55, 0.45)(0.45, 0.5)(0.5, 0.5)(0.55, 0.45)Use of hazardous substancesB54(0.5, 0.4)(0.3, 0.5)(0.45, 0.55)(0.5, 0.5)Table 14
Intuitionistic fuzzy consistency test matrix for the use of secondary indicators for packaging materials.
A5 second-level indicatorReusabilityB51Biodegradable productsB52Use recycled materialsB53Use of hazardous substancesB54ReusabilityB51(0.5, 0.5)(0.55, 0.4)(0.55, 0.3529)(0.525, 0.3483)Biodegradable productsB52(0.4, 0.55)(0.5, 0.5)(0.5, 0.45)(0.55, 0.401)Use recycled materialsB53(0.3529, 0.55)(0.45, 0.5)(0.5, 0.5)(0.55, 0.45)Use of hazardous substancesB54(0.3483, 0.525)(0.401, 0.55)(0.45, 0.55)(0.5, 0.5)According to formula (1), the consistency was calculated as dR¯,R=0.0791<0.1, which shows the consistency test passed.


### 5.2. Weight Calculation

After calculations in the previous step, all intuitionistic fuzzy judgment matrices passed the consistency test. Substituting all the matricesR¯ that passed the test into equation (6), the weights in the first-level index are as follows:(16)ω1=0.1428,0.7735,ω2=0.1863,0.7366,ω3=0.1527,0.7672,ω4=0.1241,0.7804,ω5=0.0741,0.8516,ω6=0.1056,0.8178.The weights of the secondary indicators are as follows:(17)ω11=0.4878,0.4615,ω12=0.4634,0.4872,ω21=0.5,0.5,ω22=0.5,0.5,ω31=0.3209,0.4898,ω32=0.1913,0.7150,ω33=0.3004,0.5646,ω41=0.2951,0.6254,ω42=0.3373,0.6240,ω43=0.2647,0.6358,ω51=0.2538,0.6855,ω52=0.2329,0.7248,ω53=0.2213,0.7378,ω54=0.2030,0.7542,ω61=0.4634,0.4872,ω62=0.4878,0.4615.


### 5.3. Information Aggregation

#### 5.3.1. Calculating the Total Weight

After calculating the weights of the first-level indicators and the second-level indicators, they are used in equation (8) for information integration to obtain the total weight. The results are shown in Table 15.Table 15
Total weight table.
First-level indicatorsSecondary indicatorsTotal weight0.1428,0.77350.4878,0.4615(0.0697, 0.8780)0.4634,0.4872(0.0662, 0.8839)0.1863,0.73660.5,0.5(0.0932, 0.8683)0.5,0.5(0.0932, 0.8683)0.1527,0.76720.3209,0.4898(0.0490, 0.8812)0.1913,0.7150(0.0292, 0.9337)0.3004,0.5646(0.0459, 0.8986)0.1241,0.78040.2951,0.6254(0.0366, 0.9177)0.3373,0.6240(0.0419, 0.9174)0.2647,0.6358(0.0328, 0.9200)0.0741,0.85160.2538,0.6855(0.0188, 0.9533)0.2329,0.7248(0.0173, 0.9592)0.2213,0.7378(0.0164, 0.9611)0.2030,0.7542(0.0150, 0.9635)0.1056,0.81780.4634,0.4872(0.0489, 0.9066)0.4878,0.4615(0.0515, 0.9019)


#### 5.3.2. Deblurring

The total weight of the information aggregation in the previous step is a fuzzy number, which is then used in equation (9) to calculate the true value of the total weight as follows: [0.0963, 0.0916, 0.1135, 0.1135, 0.0832, 0.0476, 0.0734, 0.0592, 0.0623, 0.0561, 0.0326, 0.0290, 0.0276, 0.0257, 0.0712, 0.0749]. Then, it is normalized to get [0.0911, 0.0866, 0.1073, 0.1073, 0.0786, 0.0450, 0.0694, 0.0560, 0.0589, 0.0530, 0.0308, 0.0274, 0.0261, 0.0243, 0.0674, 0.0708].


#### 5.3.3. Weight Ratio Analysis

It can be seen from Figure3 that the highest proportions of index weights were B11, B12, B21, B22, B31, and B62, followed by B33 and B61. The sum of the two accounted for 67.6%, which can be regarded as the most influential indicator. From the perspective of the meaning of the indicators, environmental policies and certification, environmental restoration, and governance reflect the suppliers’ ability to harmlessly deal with pollution and their efforts to protect the ecological environment. The second is the cost of energy consumed by agricultural products and the ability to develop new clean technologies, which shows the economic profitability of the organization and the level of waste disposal. From the perspective of sustainability combined with the weight of indicators, the two were in line with objective cognition and scientific laws. The results show that suppliers should first consider possible ecological damage and pollution control, and then they should pay attention to controlling product cost and technological innovation for disposal.Figure 3
Proportion of total weight.


### 5.4. Decision Matrix Normalization

Experts scored the qualitative indicators of the four suppliers, and then the maximum value method was used to decompose the fuzzy numbers to obtain the true values of the qualitative indicators of each supplier. The quantitative values obtained approximately accurate values through statistical data and simulation. Finally, the initial decision matrix composed of qualitative indicators and quantitative indicators is shown in Table16.Table 16
Initial decision matrix.
Index/supplierC1C2C3C4maxcjmincjb1 ISO 14000 certification0.77160.780.66750.75130.780.6675b2 environmental policy and plan0.43380.64560.360.6750.6750.36b3 environmental restoration0.64640.71950.36480.86130.86130.3648b4 environmental governance0.65630.60.4080.62250.65630.408b5 energy consumption518532568504568504b6 logistics costs132016321893110018931100b7 product net price253027152900230029002300b8 air pollutant production545558525852b9 wastewater production130015201890110018901100b10 solid waste generation433046504882421048824210b11 reusability505532606032b12 biodegradable products625043757543b13 use recycled materials303228383828b14 use of hazardous substances120130150105150105b15 reduce food additives0.38630.40770.24090.41250.41250.2409b16 green R & D and innovation0.22880.23340.17130.21760.23340.1713Among them, the yellow part indicates that the indicator is a cost-based indicator, and the rest are benefit-based indicators. Then, the above indicators were divided into cost-type indicators and benefit-type indicators, and they were substituted into formulas (10) and (11), respectively. The standardized decision matrix is shown in Table 17.Table 17
Normalized decision matrix.
Index/supplierC1C2C3C4b1 ISO 14000 certification0.9259100.7456b2 environmental policy and plan0.23430.906701b3 environmental restoration0.56720.714401b4 environmental governance10.773300.8639b5 energy consumption0.78130.562501b6 logistics costs0.72260.329101b7 product net price0.61670.308301b8 air pollutant production0.66670.501b9 wastewater production0.74680.468401b10 solid waste generation0.82140.345201b11 reusability0.64290.821401b12 biodegradable products0.59380.218801b13 use recycled materials0.20.401b14 use of hazardous substances0.66670.444401b15 reduce food additives0.84730.972001b16 green R & D and innovation0.9259100.7456


### 5.5. Computing Dominance

After obtaining the normalized decision matrix and the weight of each indicator, the predominanceδai,ak of supplier ai relative to supplier ak with respect to indicator cj was calculated according to equation (13), where θ takes 2.25 [34]. Then, according to equation (12), the matrix of comparative advantages between suppliers was obtained as shown in Table 18.Table 18
Dominant comparison matrix.
C1C2C3C4TdεaiC10−4.39453.2165−15.5640−16.74200.7476C2−8.933203.0584−17.6883−23.56310.6643C3−24.7402−22.84350−30.3814−77.96510C4−0.05380.39253.587903.92661The advantage comparison matrix was standardized according to equations (14) and (15) to obtain the comprehensive score εai of each supplier: εa1=0.7476, εa2=0.6643, εa3=0, and εa4=1. Sorting by size shows that a4 was the best supplier, and the enterprise should choose supplier a4 to supply fresh agricultural products.As shown in Figure4, the overall advantage of each supplier and the trend of the final comprehensive score were the same. Compared with other suppliers, supplier C4 had a maximum advantage of 3.9266 and the highest overall score of 1, followed by suppliers C1, C2, and C3. The figure shows that the overall advantage of supplier C3 was far lower than that of other manufacturers. From the above calculations, it can be seen that the largest of the cost-based indicators came from C3. This means that, in terms of environmental pollution and product costs, supplier C3 had the highest proportion compared with other manufacturers, so it had the lowest sustainability and the lowest ranking. Supplier C4 was mostly in the bottom position regarding cost-based indicators, and mostly in the first place in efficiency-based indicators. This shows that supplier C4 achieved a better balance between economic development, social responsibility, and environmental protection than other manufacturers, which ultimately makes it the most sustainable and gives it the highest comprehensive score.Figure 4
Dominance and comprehensive score table.


### 5.6. Sensitivity Analysis

The purpose of the sensitivity analysis is to verify whether there are differences in the results of the selection of sustainable suppliers of fresh agricultural products under differentθ values (representing the different ability of decision-makers to avoid risks). In this paper, two values of θ = 3, 4 [34] were used for sensitivity analysis. Table 19 shows the comprehensive scores of various suppliers under different attenuation coefficients. According to Table 19, as the attenuation coefficient increased, the scores of suppliers C1 and C2 declined. This is because the ability of decision-makers to avoid risks became weaker and weaker, resulting in more errors in the judgment of suppliers. Figure 5 reflects the comprehensive score trend of various suppliers under different attenuation coefficient θ values. It can be seen that under the four different θ values, no matter how the decision-makers’ circumvention ability changed, the final supplier selection results tended to be consistent.Table 19
Comprehensive supplier scores under different attenuation coefficients.
Attenuation coefficient/supplierC1C2C3C42.250.74760.66430130.74450.66120140.74060.657401Figure 5
Comprehensive scores under different attenuation coefficients.


## 5.1. Consistency Check

The intuitionistic fuzzy data in the intuitionistic fuzzy judgment matrix in this paper were obtained by experts. Based on the established index system for supplier selection criteria (Table1), this paper established seven intuitionistic fuzzy judgment matrices as shown in Table 3.Table 3
Intuitionistic fuzzy judgment matrix of first-level indicators.
First-level indicatorsEnvironmental management systemA1Environmental protectionA2CostA3PollutionA4Use of packaging materialsA5Food safetyA6Environmental management systemA1(0.5, 0.5)(0.35, 0.6)(0.4, 0.5)(0.45, 0.35)(0.65, 0.25)(0.5, 0.3)Environmental protectionA2(0.6, 0.35)(0.5, 0.5)(0.6, 0.4)(0.65, 0.25)(0.75, 0.2)(0.7, 0.2)CostA3(0.5, 0.4)(0.4, 0.6)(0.5, 0.5)(0.5, 0.35)(0.7, 0.25)(0.65, 0.2)PollutionA4(0.35, 0.45)(0.25，0.65)(0.35, 0.5)(0.5, 0.5)(0.6, 0.2)(0.6, 0.4)Use of packaging materialsA5(0.25, 0.65)(0.2, 0.75)(0.25, 0.7)(0.2, 0.6)(0.5, 0.5)(0.35, 0.6)Food safetyA6(0.3, 0.5)(0.2, 0.7)(0.2, 0.65)(0.4, 0.6)(0.6, 0.35)(0.5, 0.5)According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 4.Table 4
Intuitionistic fuzzy consistency test matrix of first-level indicators.
First-level indicatorsEnvironmental management systemA1Environmental protectionA2CostA3PollutionA4Use of packaging materialsA5Food safetyA6Environmental management systemA1(0.5, 0.5)(0.35, 0.6)(0.4468, 0.5)(0.4495, 0.3416)(0.5927, 0.2061)(0.5403, 0.2648)Environmental protectionA2(0.6, 0.35)(0.5, 0.5)(0.6, 0.4)(0.6, 0.2642)(0.7574, 0.1198)(0.6991, 0.1937)CostA3(0.5, 0.4468)(0.4, 0.6)(0.5, 0.5)(0.5, 0.35)(0.6, 0.1186)(0.5785, 0.2975)PollutionA4(0.3416, 0.4495)(0.2642, 0.6)(0.35, 0.5)(0.5, 0.5)(0.6, 0.2)(0.4468, 0.2727)Use of packaging materialsA5(0.2061, 0.5927)(0.1198, 0.7574)(0.1186, 0.6)(0.2, 0.6)(0.5, 0.5)(0.35, 0.6)Food safetyA6(0.2648, 0.5403)(0.1937, 0.6991)(0.2975, 0.5785)(0.2727, 0.4468)(0.6, 0.35)(0.5, 0.5)The next step was to calculate the consistency according to equation (1) and get dR¯,R=0.0940<0.1. This shows that the consistency test passed.Table5 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 6.Table 5
Intuitionistic fuzzy judgment matrix of secondary indicators of the environmental management system.
A1 second-level indicatorISO 14000 certificationB11Environmental policy and planB12ISO 14000 certificationB11(0.5, 0.5)(0.5, 0.45)Environmental policy and planB12(0.45, 0.5)(0.5, 0.5)Table 6
Intuitionistic fuzzy consistency test matrix of secondary indicators of environmental management system.
A1 second-level indicatorISO 14000 certificationB11Environmental policy and planB12ISO 14000 certificationB11(0.5, 0.5)(0.5, 0.45)Environmental policy and planB12(0.45, 0.5)(0.5, 0.5)It can be seen thatR¯=R, that is, the consistency check matrix was the same as the original matrix (Table 5). In the next step, the consistency was calculated according to equation (1) as dR¯,R=0<0.1, which shows that the consistency test passed. All the following 2×2 matrices (Tables 7 and 8) have the same reasoning.Table 7
Intuitionistic fuzzy judgment matrix of secondary indicators of environmental protection.
A2 second-level indicatorEnvironmental restorationB21Environmental governanceB22Environmental restorationB21(0.5, 0.5)(0.5, 0.5)Environmental governanceB22(0.5, 0.5)(0.5, 0.5)Table 8
Intuitionistic fuzzy judgment matrix of the second-level food safety index.
A6 second-level indicatorReduce food additivesB61Green R & D and innovationB62Reduce food additivesB61(0.5, 0.5)(0.45, 0.5)Green R & D and innovationB62(0.5, 0.45)(0.5, 0.5)Table9 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 10.Table 9
Intuitionistic fuzzy judgment matrix of secondary cost indicators.
A3 second-level indicatorEnergy consumptionB31Logistics costsB32Product net priceB33Energy consumptionB31(0.5, 0.5)(0.65, 0.15)(0.45, 0.35)Logistics costsB32(0.15, 0.65)(0.5, 0.5)(0.3, 0.7)Product net priceB33(0.35, 0.45)(0.7, 0.3)(0.5, 0.5)Table 10
Intuitionistic fuzzy consistency test matrix of the second-level cost index.
A3 second-level indicatorEnergy consumptionB31Logistics costsB32Product net priceB33Energy consumptionB31(0.5, 0.5)(0.65, 0.15)(0.4432, 0.2916)Logistics costsB32(0.15, 0.65)(0.5, 0.5)(0.3, 0.7)Product net priceB33(0.2916, 0.4432)(0.7, 0.3)(0.5, 0.5)In the same way, according to formula (1), the consistency was calculated as dR¯,R=0.0702<0.1, which shows the consistency test passed.Table11 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 12.Table 11
Intuitionistic fuzzy judgment matrix for secondary indicators of pollution.
A4 second-level indicatorAir pollutant productionB41Wastewater productionB42Solid waste generationB43Air pollutant productionB41(0.5, 0.5)(0.45, 0.6)(0.6, 0.35)Wastewater productionB42(0.6, 0.45)(0.5, 0.5)(0.5, 0.45)Solid waste generationB43(0.35, 0.6)(0.45, 0.5)(0.5, 0.5)Table 12
Intuitionistic fuzzy consistency test matrix for secondary indicators of pollution.
A4 second-level indicatorAir pollutant productionB41Wastewater productionB42Solid waste generationB43Air pollutant productionB41(0.5, 0.5)(0.45, 0.6)(0.45, 0.3058)Wastewater productionB42(0.6, 0.45)(0.5, 0.5)(0.5, 0.45)Solid waste generationB43(0.3058, 0.45)(0.45, 0.5)(0.5, 0.5)According to formula (1), the consistency was calculated as dR¯,R=0.0976<0.1, which shows the consistency test passed.Table13 shows the original matrix. According to equations (2) and (3), the intuitionistic fuzzy consistency test matrix R¯ was calculated and transformed as shown in Table 14.Table 13
Intuitionistic fuzzy judgment matrix for the use of secondary indicators for packaging materials.
A5 second-level indicatorReusabilityB51Biodegradable productsB52Use recycled materialsB53Use of hazardous substancesB54ReusabilityB51(0.5, 0.5)(0.55, 0.4)(0.45, 0.55)(0.4, 0.5)Biodegradable productsB52(0.4, 0.55)(0.5, 0.5)(0.5, 0.45)(0.5, 0.3)Use recycled materialsB53(0.55, 0.45)(0.45, 0.5)(0.5, 0.5)(0.55, 0.45)Use of hazardous substancesB54(0.5, 0.4)(0.3, 0.5)(0.45, 0.55)(0.5, 0.5)Table 14
Intuitionistic fuzzy consistency test matrix for the use of secondary indicators for packaging materials.
A5 second-level indicatorReusabilityB51Biodegradable productsB52Use recycled materialsB53Use of hazardous substancesB54ReusabilityB51(0.5, 0.5)(0.55, 0.4)(0.55, 0.3529)(0.525, 0.3483)Biodegradable productsB52(0.4, 0.55)(0.5, 0.5)(0.5, 0.45)(0.55, 0.401)Use recycled materialsB53(0.3529, 0.55)(0.45, 0.5)(0.5, 0.5)(0.55, 0.45)Use of hazardous substancesB54(0.3483, 0.525)(0.401, 0.55)(0.45, 0.55)(0.5, 0.5)According to formula (1), the consistency was calculated as dR¯,R=0.0791<0.1, which shows the consistency test passed.


## 5.2. Weight Calculation

After calculations in the previous step, all intuitionistic fuzzy judgment matrices passed the consistency test. Substituting all the matricesR¯ that passed the test into equation (6), the weights in the first-level index are as follows:(16)ω1=0.1428,0.7735,ω2=0.1863,0.7366,ω3=0.1527,0.7672,ω4=0.1241,0.7804,ω5=0.0741,0.8516,ω6=0.1056,0.8178.The weights of the secondary indicators are as follows:(17)ω11=0.4878,0.4615,ω12=0.4634,0.4872,ω21=0.5,0.5,ω22=0.5,0.5,ω31=0.3209,0.4898,ω32=0.1913,0.7150,ω33=0.3004,0.5646,ω41=0.2951,0.6254,ω42=0.3373,0.6240,ω43=0.2647,0.6358,ω51=0.2538,0.6855,ω52=0.2329,0.7248,ω53=0.2213,0.7378,ω54=0.2030,0.7542,ω61=0.4634,0.4872,ω62=0.4878,0.4615.


## 5.3. Information Aggregation

### 5.3.1. Calculating the Total Weight

After calculating the weights of the first-level indicators and the second-level indicators, they are used in equation (8) for information integration to obtain the total weight. The results are shown in Table 15.Table 15
Total weight table.
First-level indicatorsSecondary indicatorsTotal weight0.1428,0.77350.4878,0.4615(0.0697, 0.8780)0.4634,0.4872(0.0662, 0.8839)0.1863,0.73660.5,0.5(0.0932, 0.8683)0.5,0.5(0.0932, 0.8683)0.1527,0.76720.3209,0.4898(0.0490, 0.8812)0.1913,0.7150(0.0292, 0.9337)0.3004,0.5646(0.0459, 0.8986)0.1241,0.78040.2951,0.6254(0.0366, 0.9177)0.3373,0.6240(0.0419, 0.9174)0.2647,0.6358(0.0328, 0.9200)0.0741,0.85160.2538,0.6855(0.0188, 0.9533)0.2329,0.7248(0.0173, 0.9592)0.2213,0.7378(0.0164, 0.9611)0.2030,0.7542(0.0150, 0.9635)0.1056,0.81780.4634,0.4872(0.0489, 0.9066)0.4878,0.4615(0.0515, 0.9019)


### 5.3.2. Deblurring

The total weight of the information aggregation in the previous step is a fuzzy number, which is then used in equation (9) to calculate the true value of the total weight as follows: [0.0963, 0.0916, 0.1135, 0.1135, 0.0832, 0.0476, 0.0734, 0.0592, 0.0623, 0.0561, 0.0326, 0.0290, 0.0276, 0.0257, 0.0712, 0.0749]. Then, it is normalized to get [0.0911, 0.0866, 0.1073, 0.1073, 0.0786, 0.0450, 0.0694, 0.0560, 0.0589, 0.0530, 0.0308, 0.0274, 0.0261, 0.0243, 0.0674, 0.0708].


### 5.3.3. Weight Ratio Analysis

It can be seen from Figure3 that the highest proportions of index weights were B11, B12, B21, B22, B31, and B62, followed by B33 and B61. The sum of the two accounted for 67.6%, which can be regarded as the most influential indicator. From the perspective of the meaning of the indicators, environmental policies and certification, environmental restoration, and governance reflect the suppliers’ ability to harmlessly deal with pollution and their efforts to protect the ecological environment. The second is the cost of energy consumed by agricultural products and the ability to develop new clean technologies, which shows the economic profitability of the organization and the level of waste disposal. From the perspective of sustainability combined with the weight of indicators, the two were in line with objective cognition and scientific laws. The results show that suppliers should first consider possible ecological damage and pollution control, and then they should pay attention to controlling product cost and technological innovation for disposal.Figure 3
Proportion of total weight.


## 5.3.1. Calculating the Total Weight

After calculating the weights of the first-level indicators and the second-level indicators, they are used in equation (8) for information integration to obtain the total weight. The results are shown in Table 15.Table 15
Total weight table.
First-level indicatorsSecondary indicatorsTotal weight0.1428,0.77350.4878,0.4615(0.0697, 0.8780)0.4634,0.4872(0.0662, 0.8839)0.1863,0.73660.5,0.5(0.0932, 0.8683)0.5,0.5(0.0932, 0.8683)0.1527,0.76720.3209,0.4898(0.0490, 0.8812)0.1913,0.7150(0.0292, 0.9337)0.3004,0.5646(0.0459, 0.8986)0.1241,0.78040.2951,0.6254(0.0366, 0.9177)0.3373,0.6240(0.0419, 0.9174)0.2647,0.6358(0.0328, 0.9200)0.0741,0.85160.2538,0.6855(0.0188, 0.9533)0.2329,0.7248(0.0173, 0.9592)0.2213,0.7378(0.0164, 0.9611)0.2030,0.7542(0.0150, 0.9635)0.1056,0.81780.4634,0.4872(0.0489, 0.9066)0.4878,0.4615(0.0515, 0.9019)


## 5.3.2. Deblurring

The total weight of the information aggregation in the previous step is a fuzzy number, which is then used in equation (9) to calculate the true value of the total weight as follows: [0.0963, 0.0916, 0.1135, 0.1135, 0.0832, 0.0476, 0.0734, 0.0592, 0.0623, 0.0561, 0.0326, 0.0290, 0.0276, 0.0257, 0.0712, 0.0749]. Then, it is normalized to get [0.0911, 0.0866, 0.1073, 0.1073, 0.0786, 0.0450, 0.0694, 0.0560, 0.0589, 0.0530, 0.0308, 0.0274, 0.0261, 0.0243, 0.0674, 0.0708].


## 5.3.3. Weight Ratio Analysis

It can be seen from Figure3 that the highest proportions of index weights were B11, B12, B21, B22, B31, and B62, followed by B33 and B61. The sum of the two accounted for 67.6%, which can be regarded as the most influential indicator. From the perspective of the meaning of the indicators, environmental policies and certification, environmental restoration, and governance reflect the suppliers’ ability to harmlessly deal with pollution and their efforts to protect the ecological environment. The second is the cost of energy consumed by agricultural products and the ability to develop new clean technologies, which shows the economic profitability of the organization and the level of waste disposal. From the perspective of sustainability combined with the weight of indicators, the two were in line with objective cognition and scientific laws. The results show that suppliers should first consider possible ecological damage and pollution control, and then they should pay attention to controlling product cost and technological innovation for disposal.Figure 3
Proportion of total weight.


## 5.4. Decision Matrix Normalization

Experts scored the qualitative indicators of the four suppliers, and then the maximum value method was used to decompose the fuzzy numbers to obtain the true values of the qualitative indicators of each supplier. The quantitative values obtained approximately accurate values through statistical data and simulation. Finally, the initial decision matrix composed of qualitative indicators and quantitative indicators is shown in Table16.Table 16
Initial decision matrix.
Index/supplierC1C2C3C4maxcjmincjb1 ISO 14000 certification0.77160.780.66750.75130.780.6675b2 environmental policy and plan0.43380.64560.360.6750.6750.36b3 environmental restoration0.64640.71950.36480.86130.86130.3648b4 environmental governance0.65630.60.4080.62250.65630.408b5 energy consumption518532568504568504b6 logistics costs132016321893110018931100b7 product net price253027152900230029002300b8 air pollutant production545558525852b9 wastewater production130015201890110018901100b10 solid waste generation433046504882421048824210b11 reusability505532606032b12 biodegradable products625043757543b13 use recycled materials303228383828b14 use of hazardous substances120130150105150105b15 reduce food additives0.38630.40770.24090.41250.41250.2409b16 green R & D and innovation0.22880.23340.17130.21760.23340.1713Among them, the yellow part indicates that the indicator is a cost-based indicator, and the rest are benefit-based indicators. Then, the above indicators were divided into cost-type indicators and benefit-type indicators, and they were substituted into formulas (10) and (11), respectively. The standardized decision matrix is shown in Table 17.Table 17
Normalized decision matrix.
Index/supplierC1C2C3C4b1 ISO 14000 certification0.9259100.7456b2 environmental policy and plan0.23430.906701b3 environmental restoration0.56720.714401b4 environmental governance10.773300.8639b5 energy consumption0.78130.562501b6 logistics costs0.72260.329101b7 product net price0.61670.308301b8 air pollutant production0.66670.501b9 wastewater production0.74680.468401b10 solid waste generation0.82140.345201b11 reusability0.64290.821401b12 biodegradable products0.59380.218801b13 use recycled materials0.20.401b14 use of hazardous substances0.66670.444401b15 reduce food additives0.84730.972001b16 green R & D and innovation0.9259100.7456


## 5.5. Computing Dominance

After obtaining the normalized decision matrix and the weight of each indicator, the predominanceδai,ak of supplier ai relative to supplier ak with respect to indicator cj was calculated according to equation (13), where θ takes 2.25 [34]. Then, according to equation (12), the matrix of comparative advantages between suppliers was obtained as shown in Table 18.Table 18
Dominant comparison matrix.
C1C2C3C4TdεaiC10−4.39453.2165−15.5640−16.74200.7476C2−8.933203.0584−17.6883−23.56310.6643C3−24.7402−22.84350−30.3814−77.96510C4−0.05380.39253.587903.92661The advantage comparison matrix was standardized according to equations (14) and (15) to obtain the comprehensive score εai of each supplier: εa1=0.7476, εa2=0.6643, εa3=0, and εa4=1. Sorting by size shows that a4 was the best supplier, and the enterprise should choose supplier a4 to supply fresh agricultural products.As shown in Figure4, the overall advantage of each supplier and the trend of the final comprehensive score were the same. Compared with other suppliers, supplier C4 had a maximum advantage of 3.9266 and the highest overall score of 1, followed by suppliers C1, C2, and C3. The figure shows that the overall advantage of supplier C3 was far lower than that of other manufacturers. From the above calculations, it can be seen that the largest of the cost-based indicators came from C3. This means that, in terms of environmental pollution and product costs, supplier C3 had the highest proportion compared with other manufacturers, so it had the lowest sustainability and the lowest ranking. Supplier C4 was mostly in the bottom position regarding cost-based indicators, and mostly in the first place in efficiency-based indicators. This shows that supplier C4 achieved a better balance between economic development, social responsibility, and environmental protection than other manufacturers, which ultimately makes it the most sustainable and gives it the highest comprehensive score.Figure 4
Dominance and comprehensive score table.


## 5.6. Sensitivity Analysis

The purpose of the sensitivity analysis is to verify whether there are differences in the results of the selection of sustainable suppliers of fresh agricultural products under differentθ values (representing the different ability of decision-makers to avoid risks). In this paper, two values of θ = 3, 4 [34] were used for sensitivity analysis. Table 19 shows the comprehensive scores of various suppliers under different attenuation coefficients. According to Table 19, as the attenuation coefficient increased, the scores of suppliers C1 and C2 declined. This is because the ability of decision-makers to avoid risks became weaker and weaker, resulting in more errors in the judgment of suppliers. Figure 5 reflects the comprehensive score trend of various suppliers under different attenuation coefficient θ values. It can be seen that under the four different θ values, no matter how the decision-makers’ circumvention ability changed, the final supplier selection results tended to be consistent.Table 19
Comprehensive supplier scores under different attenuation coefficients.
Attenuation coefficient/supplierC1C2C3C42.250.74760.66430130.74450.66120140.74060.657401Figure 5
Comprehensive scores under different attenuation coefficients.


## 6. Conclusion

At present, there are very few studies that evaluate the sustainability of fresh agricultural product suppliers, and most indicators are selected based on economic indicators or financial indicators. However, noneconomic indicators such as social responsibility and environmental protection should be considered under the requirements of sustainable development. Therefore, this paper comprehensively considered the impact of economic development, social responsibility, and environmental protection (that is, the triple bottom line) on the sustainability of the supply of fresh agricultural products, and it built a more reasonable index system based on reference to the selection criteria of conventional suppliers. The evaluation system can help future decision-makers in selecting sustainable fresh agricultural product suppliers. This paper also combined intuitionistic fuzzy AHP and TODIM multiattribute decision-making methods to select sustainable suppliers.When determining the index weight, the traditional supplier selection methods such as AHP, ANP, and DEMATEL cannot accurately deal with the uncertainty of expert evaluation information, and the decision information lacks scientific quantitative means. The fuzzy AHP method can better deal with the fuzziness of natural language and transform fuzzy information into accurate numbers. This fully considers the uncertainty in expert evaluation and better guarantees that the original information is not distorted.When ranking suppliers, the supplier ranking methods such as DEA, PROMETHEE, and TOPSIS do not consider the decision-maker's subjective preference behavior, which often loses a lot of qualitative information. TODIM multiattribute decision-making method takes into account the psychological behavior of decision-makers, which can deal with environmental uncertainty and ensure the original information is not distorted.In the field of sustainable supplier selection of fresh agricultural products, from the perspective of sustainability, most of the previous literature did not consider the combination of fuzzy weight determination method and traditional supplier ranking method to select fresh agricultural products suppliers. Therefore, based on the concept of sustainability, this paper uses FAHP and TODIM to select the best supplier. In order to verify the feasibility of the proposed integration method, an example sensitivity analysis was carried out in this paper. According to the final calculation results, it was found that intuitionistic fuzzy AHP and TODIM were feasible and effective for supplier selection.In summary, this article is based on the “triple bottom line” theory to assess and enrich the sustainability model of fresh agricultural products suppliers. This research fills the gap of applying the “triple bottom line” theory and the IFAHP-TODIM method to the selection of sustainable suppliers of fresh agricultural products. Finally, the limitations and future research directions of this article are as follows:(1)
The model adopted in this paper still cannot avoid subjectivity in determining the weight of each indicator, so further research is needed.(2)
Due to the lack of research in this field, the evaluation index system in this article may not be universally applied. In the future, it is necessary to adjust the selection of indicators according to the actual economic and policy situation of various regions, so as to make the decision more effective.(3)
The future research can also start from the weight section. Further, the combination of subjective and objective weights makes the decision more reliable.(4)
The supplier selection of fresh agricultural products can make decisions more accurately with the help of big data and other data mining algorithms.



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*Source: 4792679-2020-12-04.xml*