Quality Risk Evaluation of the Food Supply Chain Using a Fuzzy Comprehensive Evaluation Model and Failure Mode , Effects , and Criticality Analysis

Evaluating the quality risk level in the food supply chain can reduce quality information asymmetry and food quality incidents and promote nationally integrated regulations for food quality. In order to evaluate it, a quality risk evaluation indicator system for the food supply chain is constructed based on an extensive literature review in this paper. Furthermore, a mathematical model based on the fuzzy comprehensive evaluation model (FCEM) and failure mode, effects, and criticality analysis (FMECA) for evaluating the quality risk level in the food supply chain is developed. A computational experiment aimed at verifying the effectiveness and feasibility of this proposed model is conducted on the basis of a questionnaire survey. The results suggest that this model can be used as a general guideline to assess the quality risk level in the food supply chain and achieve the most important objective of providing a reference for the public and private sectors when making decisions on food quality management.


Introduction
In 2016, the State Council of the People's Republic of China issued guidelines on food safety work.These provisions emphasized improving the quality of edible agricultural products, strengthening risk prevention and control measures, promoting quality management throughout the food supply chain, and accelerating nationally integrated regulations for food safety.These guidelines highlight China's attention to quality risk management in the food supply chain [1].
Food quality is defined as the access of all people to sufficient, safe, and nutritious food that meets their dietary needs and food preferences for an active and healthy life [2,3].Food quality covers a broad area that can be characterized by a set of different risk factors [4][5][6], such as the agricultural conditions [7], production process [8], use of antimicrobials [9], and consumer demand [10,11].These factors can be represented by various indicators such as environmental pollution, microbial contamination, logistics, warehousing, and transportation.The risk indicators are related to the food supply chain processes [12] and can be evaluated and documented on the basis of imprecise inputs.The data of these processes are imprecise and difficult to quantify since they pertain to both the resilience of the food supply chain and the consumer demand and supply channels such as retail outlets and restaurants.Therefore, it is difficult to use traditional data-based approaches to evaluate food quality.Addressing this challenge requires the managers to develop some precise methods for assessing the risk level of all factors in every link of the food supply chain [13] and calculating them as a whole [14].Unfortunately, few related studies have been done.
The quality risk level of food is defined as the potential hazard which is caused by unsafe practices in the food supply chain.The uncertainty of the ability to acquire safe foods is also called food insecurity and can be measured by the risk level of food quality [15].And the quality risk level of food security is an important problem related to the food supply chain environment.One effective solution to solve this problem is to build an evaluation indicator system based on the fuzzy sets theory [16].Several studies have considered that building the indicator system is the first step in assessing the quality risk, and many research results have been made, such as in the case of Wang et al. who developed an index system to evaluate the transparency of the supervision of food safety in China as a prerequisite for an accurate evaluation of the food safety risk level.Jie et al. analyzed the supply chain performance of Australian cattle producers based on food supply chain performance indicators [17].Turi et al. proposed aggregate indicators to assess the performance of the food supply chain by considering economic, social, and environmental development [18].Nilsson et al. proposed total quality indicators for the food production chain [19].Salvo et al. focused on the toxic inorganic pollutants in foods from agricultural producing to evaluate the risks for consumers [20].In these studies, however, the evaluation objects were only a single link not the whole food supply chain.Moreover, the food quality risk supervision at the national level is missed in these studies.Therefore, the existing literature cannot provide an effective guidance for the quality risk evaluation throughout the whole food supply chain, which means that a comprehensive and systematic study on the area of quality risk evaluation in the food supply chain is still missing.
Many affecting factors of the quality risk evaluation in the food supply chain exhibit highly fuzzy uncertainty and cannot be analyzed quantitatively.Therefore, it is difficult to evaluate the level of quality risk by a single, defined management criterion [21].To address this fuzzy uncertainty problem, in 1965, Zadeh proposed the concept of fuzzy sets, which laid the foundation for the application of the fuzzy comprehensive evaluation model (FCEM) in risk management [22].The FCEM is a method to evaluate fuzzy mathematics, which can transform a qualitative evaluation into a quantitative evaluation [23][24][25].Combined with other methods, the greatest feature of the FCEM is that it can integrate the intuition and fuzziness of human thinking, thus circumventing the unity of results required by traditional mathematical methods [26].Therefore, the FCEM has become an effective multifactor decision-making tool for comprehensive evaluations [27] and real-word problem solving in areas such as international relations [28], aircraft flight safety [29], swine building environment [23], health, safety, and environmental management [30], regional water resources capacity [31], and teaching performance [32].Therefore, in this paper, an FCEM for modeling these uncertainties and assessing food quality risk level is developed to determine the overall food quality risk by monitoring various independent risk factors and indictors in the food supply chain.
The rest of this paper is structured as follows.Section 2 describes the construction of a quality risk evaluation indicator system that covers the whole food supply chain based on an extensive literature review.Section 3 proposes an FCEM for the quality risk evaluation of the food supply chain based on FCEM and FMECA.Section 4 verifies the effectiveness and feasibility of the model using a computational experiment, and Section 5 presents the conclusions.

Quality Risk Evaluation Indicator System for the Food Supply Chain
To ensure the accuracy and effectiveness, a quality risk evaluation indicator system that covers the entirety of the food supply chain should be established before evaluating food quality risk.Existing research on this system has been very limited.There is no ready-made quality risk evaluation indicator system for the food supply chain [13].Here, the effective approach to establishing the preliminary indicator framework is to analyze the existing literature and the laws and regulations of food safety regulatory [58].On this basis, the quality risk evaluation indicator system for the food supply chain can be built by the method which is based on the fuzzy analytic hierarchy process (FAHP) proposed by Wang et al. [59], shown as Table 1.
(1) Raw Material Supply Risk.The risk of raw material supply involves the raw materials produced by human pollution, natural pollution, and other factors that lead to pesticide residues, pathogen pollution, and illegal additives during the process of planting or breeding, which results in long-term or short-term harm to human health [34].Raw material supply risk is a source of food quality risk, including soil pollution, air pollution, water pollution, heavy metal pollution, illegal use of additives, residual inputs, microbial contamination, pathogenic bacteria pollution, and transgenic technology risk.
(2) Production and Processing Risk.This risk arises when the safety management and production environment during the processes of production and packaging are not compliant with regulations; this risk could lead to possible food contamination and illegal additives and produce potential safety hazards to human health.As this link involves the food quality and safety in the whole food industrial chain, its impact is relatively large.The main quality risk evaluation indicators included in this link are illegal use of additives, contamination with foreign matter, inability to wash a food product clean, presence of detergent residue, pathogen contamination, microbial contamination, uncertified processing equipment, nonstandardized processing personnel operation, insufficient processing environment, insufficient processing equipment, inappropriate packaging, insufficient packaging quality, uncertified packaging logo, insufficient assurance of (5) Government Regulatory Risk.In the food industry, manufacturers may add chemical additives to augment the appearance or the taste of food.This process may increase food demand and sales profits but cause health problems among consumers [53].The government can take punitive measures to regulate such risky behavior and benefit from the tax income generated by the increased revenues arising from such additives.An analysis of the current status of China's food quality regulations reveals that the quality risk evaluation indicators regarding government regulation include imperfect regulatory system, supervisory staff level, supervisor moral hazard, supervision channels, regulatory organization regulatory, agency efficiency, regulatory process management, regulatory results feedback, and regulatory detection technology.

Fuzzy Comprehensive Evaluation Method.
FCEM is a method based on the membership degree theory in fuzzy mathematics, which transform the qualitative evaluation into quantitative evaluation [27,60,61].It has now become an effective multifactor decision-making tool for comprehensive evaluation.Combined with experts grading method, FCEM can make a full reflection on the fuzziness of evaluation criteria and the influence factors and produce evaluation results closer to the actual situation [62].The typical FCEM process could be shown in Figure 1.Shown as Figure 1, the typical process of FCEM could be divided into five stages; the main task in the 1st stage is to establish a scientific set of indicators which is determined by the situation of evaluation objective; this indicators set will lay the foundation for the application of FCEM.In the 2nd stage, the assessment comment set of evaluation objective and the criterion used to reflect the standard of scoring should be established and proposed; this will provide the data foundation for quantifying the results of assessment comment.Each element in the set of indicators makes a different contribution to the realization of risk assessment; the weights of these factors are important and different; therefore, in the 3rd stage, the weight matrixes which are determined by the contribution of the evaluation objective should be built and measured.There are many ways to build the weight matrix, such as analytic hierarchy process (AHP), entropy, and FMECA; the criterion for the selection of these methods is whether the proposed method could satisfy the characteristics and requirements of the evaluation objectives.In the 4th stage, a fuzzy comprehensive assessment matrix which could reflect the risk level of assessment objective should be established on the basis of the construction results of weight matrixes.Combined with the assessment comment set, the fuzzy comprehensive assessment matrix, the value of the whole, and each evaluation objective should be calculated in 5th stage, which will provide a reference for managers to make risk management decisions.

Construction of the Food Quality Risk Evaluation Model
Using FCEM.The process of food quality risk evaluation in the food supply chain is a typical FCEM process.According to Section 3.1, using FCEM to evaluate the level of food quality risk in the food supply chain could be divided into five stages: (1) construct the food quality risk evaluation indicator set, (2) establish the food quality risk assessment comment set, (3) determine the weight matrix, (4) establish the comprehensive assessment matrix, and (5) finalize the FCEM [63].
In the first stage, construct a food quality risk evaluation indicator set , which is composed of the evaluation objects   and their corresponding evaluation indicators   , shown as follows: where  is the food quality risk evaluation indicator set,  is the number of evaluation objects,   ( ∈ [0, ]) is the th evaluation object,   is the th food quality risk evaluation indicator of   , and  is the number of food quality risk evaluation indicators in   .
In the second stage, establish the food quality risk assessment comment set L to describe the fuzzy logic relationship among different indicators.Here, L is a collection  of five comments used to evaluate the food quality risk level according to the criterion of the FCEM, shown as follows: where L is the food quality risk assessment comment set and ℓ 1 , ℓ 2 , ℓ 3 , ℓ 4 , and ℓ 5 are the comments representing the food quality risk levels of "Terrible," "Unacceptable," "Fair," "Acceptable," and "Desirable."These levels are represented by scores of 1, 2, 3, 4, and 5.The risk assessment comment set L can be expressed as follows: According to this criterion, the fuzzy comprehensive evaluation matrixes  and   ( = 1, 2, . . ., ) can be determined by where  = { where  and    are the weight vectors of food quality risk evaluation objects and indicators.  and    are the weights of   and   .The values of   and    can be calculated by the method of FMECA.
In the fourth stage, establish the comprehensive assessment matrix  to reflect the food quality risk level of each evaluation objective by where  is the fuzzy comprehensive assessment matrix that can reflect the food quality risk level of the evaluation objective,   is the fuzzy comprehensive assessment matrix of   , and  is the fuzzy comprehensive assessment matrix set.
Finally, finalize the FCEM.Recording the food quality risk level and each evaluation objective as  and   , combined with L, , and   , the values of  and   can be calculated by where  and   are the food quality risk levels of  and   .  is the set of   s' food quality risk levels.According to (9), the food quality risk levels of  and   can be obtained.

Determinants of the Weight Vectors Using FMECA.
According to Section 3.2, when applying the FCEM to evaluate the food quality risk level, the weight of indicator is very important.Generally, the weights of indicators during the application of the FCEM are usually given based on the experience of various experts, which leads to the limitation of subjectivity.To reduce this subjectivity, this paper takes the FMECA as the method to determine the weight vectors of evaluation indicators.FMECA is a safety and reliability analysis tool, which has been widely used for the identification of system/process potential failures, their causes, and consequences.This method focuses on "discussions before system failure" per the notion that "prevention is better than cure" [64].FMECA provides an appropriate method to determine the weights of the elements depending on the occurrences of food quality risk parameters, their severity, the detection, and ability to control or compensate for the loss after a failure [64].According to the FMECA, the weights of the indicators can be calculated by where    is the cross-sectional area of the evaluation object   and    is the cross-sectional area of the evaluation indicator   .  is the occurrence probability of   .  is the severity after the occurrence of   .  is the likelihood of detection of   , and   is the ability to control or compensate for the loss following the occurrence of   .The values of   ,   ,   , and   can be obtained by the experts grading method (EGM), where   ∈ [1,5],   ∈ [1,5],   ∈ [1,5], and   ∈ [1,5].The principles of expert evaluation are shown as ( 11)- (14).
where 1 <   < 5.The higher the value of   , the higher the probability of   .
where 1 <   < 5.The higher the value of   , the worse the severity after the occurrence of   .
where 1 <   < 5.The higher the value of   , the lower the likelihood of detection of   .
1 most difficult to control or compensate for the loss 5 least difficult to control or compensate for the loss where 1 <   < 5.The higher the value of ℎ  , the easier to control or compensate for the loss after the occurrence of   .

Computational Experiment and Results
Henan is an important province of China, with a population of 107.22 million in 2017, accounting for 7.8% of China's total population.Thus, Henan plays an important role in China's food consumption.Food quality directly affects people's health and economic development; therefore, improving food quality and safety and making the food chain more ecofriendly are the development goals pursued by Henan Province.However, Henan is a large agricultural province; the food supply chain from farm to fork includes so many links such as raw material supply, production and processing, logistics, warehousing and transportation, and sales and consumption.In such a food supply chain, there are many risk factors that could affect the food quality level at each link.The probability of occurrences and the severity of each occurrence are uncertain; thus, identifying the risk factors and evaluating the risk level of each link in the food supply chain are the prerequisite for controlling the food quality.
This issue aligns with the problem addressed by the model proposed in this paper.Therefore, the food supply chain of the Henan Province (FSCHP) is taken as a computational experiment to introduce the process of food quality risk evaluation in order to verify the validity and effectiveness of the proposed model.According to Table 1 and the process of risk evaluation described in Section 3.2, the risk evaluation indicator set of FSCHP  can be constructed as shown in Table 2.
In Table 2,  is the risk evaluation indicator set of FSCHP. is the number of evaluation objects in , in which  = 5.   ( ∈ [1, ]) is the th evaluation object,   is the th risk evaluation indicator of   , and  is the number of risk evaluation indicators.As shown in Table 2, the number of FSCHP's risk evaluation indicators is According to the criterion of FCEM and (2), the risk assessment comment set of FSCHP L can be established, where L = {ℓ 1 , ℓ 2 , ℓ 3 , ℓ 4 , ℓ 5 } = {1, 2, 3, 4, 5}.To aggregate the risk assessment comments of the FSCHP and establish the fuzzy comprehensive evaluation matrixes  and   ( = 1, 2, . . ., ), a questionnaire survey was designed (shown as Appendix A).The objectives of this survey included five categories of respondents-farmers, food processing enterprises, logistics and warehousing enterprises, retailers and consumers, and government regulators-to ensure the accuracy of the survey results.A total of 1000 questionnaires were issued, and 898 were returned, which included 22 unfinished and 27 identical questionnaires; these 49 questionnaires were considered invalid according to the statistical principles.Thus, 849 questionnaires were considered valid and completed questionnaires.The recovery rate and the valid questionnaire rate were 89.8% and 84.9%.Therefore, the results of this survey are robust and effective and thus can be used for further analyses.
According to the results of the assessment comments of the risk evaluation indicators, the fuzzy comprehensive evaluation matrixes of evaluation objects  can be constructed.Here, this paper takes the evaluation object  2 ( 2 was selected because the number of risk evaluation indicators of  2 is the highest) as an example to introduce the calculation process of the fuzzy comprehensive evaluation matrix  2 .
By analyzing the results of the survey questionnaires, the assessment comment of evaluation objective  2 can be obtained, as shown in Table 3.
In Table 3, the level of comment of risk evaluation indicator   can be calculated by   = Frequency(   )/ ∑ 5 =1 Frequency(   ), where Frequency(   ) is the number of times that the objectives of this questionnaire survey scored   as   ( = 1, 2, 3, 4 or 5).Then, the fuzzy comprehensive evaluation matrix  2 can be established as follows: Similarly, the fuzzy comprehensive evaluation matrix of the other evaluation objects  1 ,  3 ,  4 , and  5 can be established as follows: Weight vectors are very important in determining the food quality risk level and can be calculated by FMECA according to Section 3.3.To calculate the weights of evaluation objects and risk indicators, five experts on food quality risk management were invited to score the values of   ,   ,   , and   with the principles of ( 11)-( 14) (the scoring table is shown in Appendix B).The scoring results of the evaluation objects are shown in Table 4. Taking the average as the final score, the weights of evaluation objects   can be obtained according to (10): According to (8), the fuzzy comprehensive assessment matrix of evaluation objects can be calculated: According to ( 6)- (7), the fuzzy comprehensive assessment matrix  can be established:  According to (9), the level of FSCHP's food quality risk  and the level of evaluation objects   can be calculated: The food quality risk levels of evaluation objects are shown in Figure 2.
According to the calculation results, the risk level of FSCHP's food quality  is 3.273.This means that the risk level of FSCHP is much higher than the average level of risk comments of 2.5, more than 30.29%; it indicates that the risk level of FSCHP's food quality is relatively higher and requires scientific management in the process of supply chain management.
In Figure 2, the value of FSCHP's food quality risk assessment in descending order is sales and consumption risk  4 ; logistics, warehousing, and transportation risk  3 ; government regulatory risk  5 ; production and processing risk  2 ; raw material supply risk  1 .Comparing the calculation results, the conclusion that the risk levels of sales and consumption risk  4 and logistics, warehousing and transportation risk  3 , which are similar and equal to 3.09 and 3.06, are the highest two of the risk evaluation of FSCHP could be obtained.Meanwhile, the values of other indictors in FSCHP's quality risk  5 ,  2 , and  1 which are equal to 2.99, 2.85, and 2.82 can be also obtained; these values are 3.25%, Analyzing this phenomenon, we can find that the reason why the risk levels of sales and consumption risk and the logistics, warehousing, and transportation risk are the highest is because there are too many uncontrollable factors such as cold chain hardware supporting facilities, cold chain logistics information transmission, poor sanitation in cooking facilities, and poor sanitation in dining establishments existing in these management processes, and the standard of them is missing or implemented poorly or supervised poorly.The results are consistent with the actual situation of the FSCHP.Therefore, if managers want to control the food quality risk of the FSCHP effectively, sales and consumption and the logistics, warehousing, and transportation are the key factors that should be addressed first.What is more, seen from Figure 2, we can find that the raw material supply risk  1 in FSCHP is the lowest, which is because Henan is one of the largest agricultural provinces in China, and in order to improve the food quality, the standardized food cultivation model has been promoted and accepted by all farmers, which makes a great contribution to achieving the goal of controlling the food quality from its source [65].
Through the statistical analysis of the existing literature, it can be found that a lot of studies have been carried out to explore food quality in the food supply chain, such as Fearne, Hornibrook, and Dedman who conducted two exploratory case studies of retailer-led quality assurance schemes (QAS) for beef in Germany and Italy and found that QAS have the potential to reduce perceived risk and increase consumer confidence in specific fresh beef products [66]; Ting et al. took the quality sustainability in the food supply chain as research object and proposed a supply chain quality sustainability decision support system to support managers in food manufacturing firms to define good logistics plans in order to maintain the quality and safety of food products [67]; Chen et al. presented a mutually supporting analytical model and exploratory case to study the managerial and policy issues related to quality control in food supply chain management with a focus on the Chinese dairy industry and discussed numbers of important managerial and policy insights and implications in managing the global food supply chain quality and risk [68].These studies and findings have already provided a valid reference for controlling the food quality in the supply chain food; however, many of them are focused on the quality or risk control in a single link [66,67] or some independent aspects [68] in the food supply chain, which could only provide a basis for the quality and risk management of the single or independent aspect not the whole food supply chain.Compared with these literatures, the evaluation model proposed in our paper based on the FCEM and FMECA can be used as a general guideline to assess the quality risk level of the food supply chain as a whole by the integration of all links in the food supply chain; what is more, it can achieve the most important objective by measuring and sorting the risk level of different links.These superiorities, which could be obtained by comparing with other methods, not only could reflect the potential in evaluating the quality and risk level in food supply chain but also could make up the gap between the traditional food risk evaluation from the aspect of single or independent link and the modern food risk evaluation from the aspect of the whole food supply chain and provide a reference for the public and private sectors when making decisions on food quality management.

Conclusion
The food industry in China is facing various challenges, including but not limited to reducing food waste, improving food quality and safety, and becoming more ecofriendly.To address these challenges and improve the food quality, it is critical to implement efficient and effective quality and operations management measures by identifying food quality risk factors and evaluating the risk levels of each link in the food supply chain.This study adopted a comprehensive approach to establish a fuzzy evaluation model for food quality risk evaluation.Through an extensive literature review, a quality risk indicator system for the food supply chain covering five evaluation objectives and 55 quality risk evaluation indicators was built to provide a basis for evaluating the food quality risk level.Then, the methods of FCEM and FMECA were applied based on surveys of experts to evaluate the food quality risk level.The results of a computational experiment suggest that this approach is reasonable for evaluating the food quality risk level.
The resulting quality risk evaluation model of the food supply chain can be used as a general guideline to highlight the most important objectives regarding the level of food quality risk evaluation according to the results of the computational experiment.Furthermore, the evaluation model provides a useful foundation for future case analyses.The government agencies responsible for food quality in supply chain management may adopt this model to assess the food quality risk level of each region.A food industry sector might also apply this model to review the strengths and weaknesses of its current food quality risk management so that better quality management plans could be developed for the food supply chain.In addition, compared with other provinces, it is clear that the food quality risk levels of the same objects, such as sales and consumption risk and logistics, warehousing, and transportation risk, are different due to the differences in cold chain logistics technology and eating habits.This finding  Shaanxi Province (nos.2017S028 and 2016R026).The managers who participated in this study are also greatly appreciated for giving their time and sharing their experiences.
contribution of evaluation objective Reflect the risk level of evaluation objective Calculate the level of whole evaluation objective Construct the set of evaluation indicators Finalize the results of evaluation

Table 1 :
Quality risk evaluation indicator system for the food supply chain.
(4)Sales and Consumption Risk.The sales and consumption risk involves food contamination, deterioration, and contamination with harmful substances due to expired shelf life, food fraud, improper sales environments, or improper consumption of food, which poses a potential hazard to human health.The quality risk evaluation indicators in this link include selling expired food, falsifying the date of production, false reporting of food ingredients, poor sanitation in dining establishments, poor sanitation conditions, improper disposal of waste food, poor sanitation in cooking facilities, improper eating methods, and insufficient storage environment.

Table 2 :
Risk evaluation indicator set of FSCHP .

Table 3 :
Assessment comment of evaluation objective  2 .

Table 4 :
Values of Figure 2: Food quality risk levels of evaluation objects.7.77%, and 8.74% lower than the highest evaluation object  4 .