A Hesitant Fuzzy Method for Evaluating Risky Cold Chain Suppliers Based on an Improved TODIM
Abstract
:1. Introduction
2. Relevant Literature
2.1. Cold Chain Supplier Evaluation
2.2. Common MultiAttribute DecisionMaking Methods
3. Construction of the Evaluation Index System for Cold Chain Logistics Suppliers
3.1. Quality and Safety Aspects
3.2. Price Cost Aspect
3.3. Service Level Aspect
3.4. Informatization and Standardization Level
3.5. Other Relevant Indicators
4. Index Weight Determination Method Based on Fuzzy Measure
4.1. Basic Concept of Hesitant Fuzzy Numbers
 (1)
 ${h}_{1}\cup {h}_{2}=H\{\mathrm{max}({\gamma}_{1},{\gamma}_{2}){\gamma}_{1}\in {h}_{1},{\gamma}_{2}\in {h}_{2}\}$;
 (2)
 ${h}_{1}\cap {h}_{2}=H\{\mathrm{min}({\gamma}_{1},{\gamma}_{2}){\gamma}_{1}\in {h}_{1},{\gamma}_{2}\in {h}_{2}\}$;
 (3)
 $\theta h=H\{(1{(1\gamma )}^{\theta}\left\}\right\gamma \in h\}(\theta >0)$;
 (4)
 ${h}^{\theta}=H\left\{{\gamma}^{\theta}\right\gamma \in h\}(\theta >0)$;
 (5)
 ${h}^{c}=H\{(1\gamma )(\gamma \in h)\}$;
 (6)
 ${h}_{1}\oplus {h}_{2}=H\{{\gamma}_{1}+{\gamma}_{2}{\gamma}_{1}{\gamma}_{2}{\gamma}_{1}\in {h}_{1},{\gamma}_{2}\in {h}_{2}\}$;
 (7)
 ${h}_{1}\otimes {h}_{2}=H\left\{{\gamma}_{1}{\gamma}_{2}\right{\gamma}_{1}\in {h}_{1},{\gamma}_{2}\in {h}_{2}\}$.
 (1)
 When$\eta $= 1, the extended value is $\overline{\lambda}={\lambda}^{+}$. The maximum of the hesitant fuzzy number should be added at this time. In this case, the decisionmaker is the type of risk preference.
 (2)
 When$\eta $= 0, the extended value is $\overline{\lambda}={\lambda}^{}$. At this time, the minimum in the hesitant fuzzy number should be added. In this case, the decisionmaker is the type of risk aversion.
 (3)
 When$\eta $= 1/2, the extended value is $\overline{\lambda}=$$({\lambda}^{+}+{\lambda}^{})/2$. At this time, the average of the maximum and minimum in the hesitant fuzzy number should be added. In this case, the decisionmaker is a of riskneutral type.
4.2. Fuzzy Measure and Generalized Shapely Function
5. Selection of Suppliers Based on TODIM
 If $S({\tilde{x}}_{ij}^{})S({\tilde{x}}_{wj}^{})>0$, then ${\phi}_{j}^{s}({x}_{i}^{},{x}_{w}^{})$ represents “gain”.
 If $S({\tilde{x}}_{ij}^{})S({\tilde{x}}_{wj}^{})=0$, then ${\phi}_{j}^{s}({x}_{i}^{},{x}_{w}^{})$ represents “neither gain nor loss”.
 If $S({\tilde{x}}_{ij}^{})S({\tilde{x}}_{wj}^{})<0$, then ${\phi}_{j}^{s}({x}_{i}^{},{x}_{w}^{})$ represents “loss”.
6. Case Study
6.1. A Case of Cold Chain Logistics Supplier Selection
6.2. Sensitive Analysis
6.3. Comparative Analysis
7. Conclusions
7.1. Managerial Implications
 By comparing the weights of various indicators, it can be found that product quality and cost are important factors in selecting suppliers. In the long run, the enterprise should maintain a good cooperative relationship with suppliers so as to ensure that the purchase price is relatively low. A revenue sharing contract can be signed with suppliers, which can ensure that the procurement cost is not too high and that the quality of products can be guaranteed.
 The different freshness of products affects the changes in the profits. Suppliers should make full use of their mature cold chain distribution system and cold storage to ensure the freshness of products and start a quality war.
 Suppliers are classified according to the sorting results, taking corresponding supplier development strategies according to the different results of supplier classification. The construction of the supplier evaluation system should be strengthened, for instance, by conducting a supplier performance evaluation. The evaluation cycle should adopt a combination of regular and irregular spot checks, and different incentives can be implemented for different suppliers.
7.2. Research Summary
 The evaluation index system of cold chain logistics suppliers is determined. Based on the characteristics of cold chain logistics suppliers, we conducted comprehensive literature research and screening to determine the evaluation index. Five firstclass indicators are determined, including quality and safety, price cost, service level, informatization and standardization level, and other relevant indicators. A total of 27 secondclass indicators are set to build the evaluation index system of cold chain logistics suppliers. The evaluation index system can provide a certain reference value for cold chain logistics enterprises when selecting suppliers.
 Considering the risky psychological preference behavior of decisionmakers, the HFSTODIM method is used to sort the candidate suppliers by analyzing decisionmaker’s risk attitudes.
 Considering the mutually influential relationship among indicators, the generalized Shapley function is used to analyze the importance degree of indicators. Next, the index weight is obtained, which is more in line with the reality.
 In light of the fuzzy characteristics of the evaluation information, hesitant fuzzy information is used to express the evaluation information of decisionmakers. The decisionmakers are allowed to give several possible values, which can increase the flexibility of the decisionmaker’s assignment and can more delicately describe the uncertainty of things, which is especially suitable for describing the real decisionmaking problem in the case of hesitation.
7.3. The Limitations and Research Prospects
 Enterprises usually have more than one supplier. Enterprises will divide suppliers into several groups according to the number of materials purchased, the importance of materials purchased, and the importance and reliability of suppliers to the enterprise. We only sort the suppliers and do not classify them.
 The selection of indicators has certain limitations. For example, there are many indicators of freshness, such as taste, color, and appearance. This paper integrates these small indicators, and how to judge the freshness quantitatively and qualitatively is not described in detail.
 With the rapid development of the cold chain logistics industry and the improvement of service quality awareness in the future, the influencing factors of cold chain logistics will be more complex, and the evaluation system will focus on a sub field of the cold chain, so the evaluation results will be more accurate.
 Any method has its advantages and disadvantages. This paper only conducts a preliminary research and exploration on the related problems of supplier evaluation based on the HFSTODIM method. In the future, we can try to use more methods, such as the related algorithms based on artificial intelligence, to study the cold chain suppliers and apply them to practical work.
Author Contributions
Funding
Institutional Review Board Statement
Conflicts of Interest
References
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Methods  Advantages  Shortcomings 

AHP 


TOPSIS 
 
VIKOR 


DEA 


ELECTRE 


FirstClass Indicators  SecondClass Indicators  Explanation 

Quality and safety aspects  Freshness [26,46,47]  The freshness, and the chemical, biological, sensory, and other properties of aquatic products need to meet the standards. 
The nutritive value [27,47]  This refers to the nutrients in food.  
Traceability [28,48]  Food safety can only be guaranteed if food traceability is realized.  
Food safety certifications [25,49]  There are the written guarantees or certificates of conformity given by a third party to the food.  
Quality assessment techniques [47]  Rational quality assessment can make up for the deficiency in quality monitoring.  
Price cost aspect  Relative price competitiveness [46]  Price measures are used to compete for market share with competitors. 
The volume discount rate [26,50]  Batch the discount amount as a percentage of the sales price.  
Transportation expenses [46,51]  Transportation expenses that are paid for transporting goods.  
Payment terms [25,51]  A specified discount is promised by the enterprise within a certain period of time.  
The reputation of suppliers [35,46]  The reputation of suppliers mainly depends on the actual performance, rather than advertising or other forms of publicity.  
Service level aspect  Order fillrate [51,52]  It refers to the degree of ability to meet customers’ inventory needs. 
Ontime delivery rate [50,52]  The ontime delivery rate is the percentage of ontime deliveries times of lowertier suppliers out of their total delivery times within a certain period of time.  
Supply flexibility [53,54]  Under the premise of the changing market demand, improving product quality and the delivery completion rate, flexible adjustment, and quickly returning goods comprise a comprehensive management and control model.  
Customer complaints [27,46,54]  Customer complaints are a behavioral mechanism to reduce cognitive imbalance when customers are dissatisfied with products or services.  
Customer satisfaction [48,54]  Customer satisfaction is a psychological reaction after customers’ needs are met.  
System of food recall [49,53]  When food producers and business operators find that the food does not meet food safety standards and may endanger the health of consumers, they shall report to the government departments according to the law and notify relevant producers and consumers.  
Informatization and standardization level  Information system [27,51,55]  This refers to the deployment of computer technology. 
The utilization of the information system [55,56]  The full use of the information system can effectively improve work efficiency.  
The scope of applied the information system [56,57]  Increasing the scope of applied information systems can enhance the competitiveness of enterprises.  
Logistics storage equipment [48,56]  This is the technical basis for organizing warehousing and logistics activities and reflects the logistics capacity of enterprises.  
The implementation of laws, regulations, and standards [25,27,46]  The strict implementation of relevant national laws and regulations leads to a high degree of food safety.  
Other relevant indicators  The quality of employees [43,46]  The cultivation and improvement of staff quality can directly affect the basic strength and development potential of the enterprise. 
Food safety training [48,49]  It is necessary to conduct safety and hygiene training for employees.  
Inventory capacity [47,54]  The higher the frequency of warehousing, the higher the efficiency and economic benefits of warehousing.  
Delivery reliability [47]  The delivery reliability refers to the degree to which enterprise’s orders are satisfied in time.  
Emergency capacity [58]  The operational mechanism is established to deal with food safety accidents.  
Information exchange capability [46]  It can also help enterprises obtain sustainable competitive advantages and finally adapt to the new economic normal. 
C_{1}  C_{2}  C_{4}  C_{4}  C_{5}  

A_{1}  H{0.7,0.8,0.9}  H{0.4,0.6,0.9}  H{0.4,0.9}  H{0.3,0.5,0.8}  H{0.6,0.8} 
A_{2}  H{0.2,0.4,0.6}  H{0.1,0.3,0.5}  H{0.4,0.7,0.8}  H{0.2,0.8}  H{0.5,0.6,0.7} 
A_{3}  H{0.1,0.5,0.9}  H{0.2,0.3,0.4}  H{0.3,0.4,0.7}  H{0.4,0.6,0.7}  H{0.3,0.8,0.9} 
A_{4}  H{0.2,0.4,0.5}  H{0.3,0.5,0.7}  H{0.1,0.9}  H{0.1,0.3,0.7}  H{0.4,0.5,0.8} 
A_{5}  H{0.5,0.6,0.8}  H{0.4,0.5,0.6}  H{0.7,0.8}  H{0.2,0.3,0.6}  H{0.2,0.4,0.6} 
A_{6}  H{0.6,0.8}  H{0.5,0.8}  H{0.2,0.8,0.9}  H{0.2,0.3,0.7}  H{0.1,0.3,0.5} 
C_{1}  C_{2}  C_{4}  C_{4}  C_{5}  

A_{1}  H{0.6, 0.9}  H{0.5,0.6,0.8}  H{0.3,0.7,0.9}  H{0.2,0.6,0.9}  H{0.7,0.8,0.9} 
A_{2}  H{0.5,0.6}  H{0.2,0.3}  H{0.5,0.6,0.8}  H{0.1,0.2,0.7}  H{0.4,0.6,0.7} 
A_{3}  H{0.3,0.4,0.8}  H{0.1,0.4}  H{0.2,0.6,0.7}  H{0.5,0.6,0.7}  H{0.5,0.6,0.7} 
A_{4}  H{0.2,0.5}  H{0.4,0.5,0.7}  H{0.4,0.5,0.9}  H{0.3,0.7}  H{0.4,0.6,0.8} 
A_{5}  H{0.5,0.6,0.7}  H{0.3,0.5,0.8}  H{0.6,0.8}  H{0.1,0.3}  H{0.3,0.4,0.6} 
A_{6}  H{0.6,0.8,0.9}  H{0.5,0.6,0.8}  H{0.1,0.8 }  H{0.3,0.6}  H{0.4,0.7} 
C_{1}  C_{2}  C_{4}  C_{4}  C_{5}  

A_{1}  H{0.1,0.5,0.9}  H{0.3,0.9}  H{0.4,0.6,0.9}  H{0.2,0.5,0.8}  H{0.6,0.8,0.9} 
A_{2}  H{0.6,0.7}  H{0.1,0.3}  H{0.4,0.6}  H{0.2,0.5,0.6}  H{0.5,0.7} 
A_{3}  H{0.5,0.9}  H{0.1,0.4,0,7}  H{0.4,0.6,0.7}  H{0.5,0.6,0.7}  H{0.3,0.8} 
A_{4}  H{0.2,0.4,0.5}  H{0.4,0.5,0.7}  H{0.1,0.4,0.9}  H{0.3,0.6,0.7}  H{0.4,0.5,0.8} 
A_{5}  H{0.4,0.6,0.8}  H{0.4,0.5,0.6}  H{0.7,0.8}  H{0.2,0.3,0.6}  H{0.2,0.4,0.6} 
A_{6}  H{0.8,0.9}  H{0.2,0.7}  H{0.1,0.9}  H{0.2,0.6,0.7}  H{0.3,0.5} 
C_{1}  C_{2}  C_{4}  C_{4}  C_{5}  

A_{1}  H{0.5,0.6,0.9}  H{0.4,0.5,0.9}  H{0.4,0.6,0.9}  H{0.2,0.5,0.8}  H{0.6,0.7,0.9} 
A_{2}  H{0.4,0.5,0.6}  H{0.1,0.2,0.4}  H{0.4,0.6,0.7}  H{0.2,0.3,0.7}  H{0.5,0.6,0.7} 
A_{3}  H{0.3,0.5,0.9}  H{0.1,0.3,0.5}  H{0.3,0.5,0.7}  H{0.5,0.6,0.7}  H{0.4,0.6,0.8} 
A_{4}  H{0.1,0.3,0.5}  H{0.4,0.5,0.7}  H{0.2,0.3,0.9}  H{0.2,0.4,0.7}  H{0.4,0.5,0.8} 
A_{5}  H{0.5,0.6,0.8}  H{0.4,0.5,0.7}  H{0.7,0.7,0.8}  H{0.2,0.2,0.6}  H{0.2,0.4,0.6} 
A_{6}  H{0.6,0.7,0.8}  H{0.4,0.4,0.8}  H{0.1,0.3,0.9}  H{0.2,0.4,0.7}  H{0.3,0.3,0.6} 
Fuzzy Measure  Value  Fuzzy Measure  Value  Fuzzy Measure  Value  Fuzzy Measure  Value 

$\mu ({C}_{1})$  0.8  $\mu ({C}_{1},{C}_{5})$  0.552  $\mu ({C}_{1},{C}_{2},{C}_{4})$  0.721  $\mu ({C}_{3},{C}_{4},{C}_{5})$  0.322 
$\mu ({C}_{2})$  0.4  $\mu ({C}_{2},{C}_{3})$  0.331  $\mu ({C}_{1},{C}_{2},{C}_{5})$  0.687  $\mu ({C}_{1},{C}_{2},{C}_{3},{C}_{4})$  0.894 
$\mu ({C}_{3})$  0.4  $\mu ({C}_{2},{C}_{4})$  0.461  $\mu ({C}_{1},{C}_{3},{C}_{4})$  0.673  $\mu ({C}_{1},{C}_{3},{C}_{4},{C}_{5})$  0.734 
$\mu ({C}_{4})$  0.2  $\mu ({C}_{2},{C}_{5})$  0.319  $\mu ({C}_{1},{C}_{3},{C}_{5})$  0.709  $\mu ({C}_{1},{C}_{2},{C}_{3},{C}_{5})$  0.882 
$\mu ({C}_{5})$  0.2  $\mu ({C}_{3},{C}_{4})$  0.345  $\mu ({C}_{1},{C}_{4},{C}_{5})$  0.564  $\mu ({C}_{1},{C}_{2},{C}_{4},{C}_{5})$  0.871 
$\mu ({C}_{1},{C}_{2})$  0.574  $\mu ({C}_{3},{C}_{5})$  0.376  $\mu ({C}_{2},{C}_{3},{C}_{4})$  0.461  $\mu ({C}_{2},{C}_{3},{C}_{4},{C}_{5})$  0.573 
$\mu ({C}_{1},{C}_{3})$  0.563  $\mu ({C}_{4},{C}_{5})$  0.176  $\mu ({C}_{2},{C}_{3},{C}_{5})$  0.412  $\mu ({C}_{1},{C}_{2},{C}_{3},{C}_{4},{C}_{5})$  1 
$\mu ({C}_{1},{C}_{4})$  0.521  $\mu ({C}_{1},{C}_{2},{C}_{3})$  0.788  $\mu ({C}_{2},{C}_{4},{C}_{5})$  0.369 
${\vartheta}^{1}({x}_{1},{x}_{1})$  0  ${\vartheta}^{1}({x}_{2},{x}_{1})$  −5.44  ${\vartheta}^{1}({x}_{3},{x}_{1})$  −3.69  ${\vartheta}^{1}({x}_{4},{x}_{1})$  −5.24  ${\vartheta}^{1}({x}_{5},{x}_{1})$  −4.77  ${\vartheta}^{1}({x}_{6},{x}_{1})$  −4.74 
${\vartheta}^{1}({x}_{1},{x}_{2})$  0.93  ${\vartheta}^{1}({x}_{2},{x}_{2})$  0  ${\vartheta}^{1}({x}_{3},{x}_{2})$  −0.05  ${\vartheta}^{1}({x}_{4},{x}_{2})$  −2.54  ${\vartheta}^{1}({x}_{5},{x}_{2})$  −2.09  ${\vartheta}^{1}({x}_{6},{x}_{2})$  −2.08 
${\vartheta}^{1}({x}_{1},{x}_{3})$  −1.00  ${\vartheta}^{1}({x}_{2},{x}_{3})$  −3.90  ${\vartheta}^{1}({x}_{3},{x}_{3})$  0  ${\vartheta}^{1}({x}_{4},{x}_{3})$  −4.18  ${\vartheta}^{1}({x}_{5},{x}_{3})$  −3.07  ${\vartheta}^{1}({x}_{6},{x}_{3})$  −3.87 
${\vartheta}^{1}({x}_{1},{x}_{4})$  0.95  ${\vartheta}^{1}({x}_{2},{x}_{4})$  −1.46  ${\vartheta}^{1}({x}_{3},{x}_{4})$  −0.27  ${\vartheta}^{1}({x}_{4},{x}_{4})$  0  ${\vartheta}^{1}({x}_{5},{x}_{4})$  −2.28  ${\vartheta}^{1}({x}_{6},{x}_{4})$  −1.57 
${\vartheta}^{1}({x}_{1},{x}_{5})$  −0.29  ${\vartheta}^{1}({x}_{2},{x}_{5})$  −2.39  ${\vartheta}^{1}({x}_{3},{x}_{5})$  −2.37  ${\vartheta}^{1}({x}_{4},{x}_{5})$  −1.98  ${\vartheta}^{1}({x}_{5},{x}_{5})$  0  ${\vartheta}^{1}({x}_{6},{x}_{5})$  −1.04 
${\vartheta}^{1}({x}_{1},{x}_{6})$  0.10  ${\vartheta}^{1}({x}_{2},{x}_{6})$  −2.45  ${\vartheta}^{1}({x}_{3},{x}_{6})$  −1.31  ${\vartheta}^{1}({x}_{4},{x}_{6})$  −0.83  ${\vartheta}^{1}({x}_{5},{x}_{6})$  −1.62  ${\vartheta}^{1}({x}_{6},{x}_{6})$  0 
${\mathrm{\Phi}}^{1}({x}_{1})$  1  ${\mathrm{\Phi}}^{2}({x}_{1})$  1  ${\mathrm{\Phi}}^{3}({x}_{1})$  1 
${\mathrm{\Phi}}^{1}({x}_{2})$  0  ${\mathrm{\Phi}}^{2}({x}_{2})$  0  ${\mathrm{\Phi}}^{3}({x}_{2})$  0 
${\mathrm{\Phi}}^{1}({x}_{3})$  0.49  ${\mathrm{\Phi}}^{2}({x}_{3})$  0.22  ${\mathrm{\Phi}}^{3}({x}_{3})$  0.37 
${\mathrm{\Phi}}^{1}({x}_{4})$  0.05  ${\mathrm{\Phi}}^{2}({x}_{4})$  0.26  ${\mathrm{\Phi}}^{3}({x}_{4})$  0.15 
${\mathrm{\Phi}}^{1}({x}_{5})$  0.11  ${\mathrm{\Phi}}^{2}({x}_{5})$  0.86  ${\mathrm{\Phi}}^{3}({x}_{5})$  0.44 
${\mathrm{\Phi}}^{1}({x}_{6})$  0.14  ${\mathrm{\Phi}}^{2}({x}_{6})$  0.55  ${\mathrm{\Phi}}^{3}({x}_{6})$  0.13 
$\theta =0.3$  $\theta =0.6$  $\theta =1$  $\theta =1.5$  $\theta =1.9$  $\theta =2$  
Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  
A_{1}  1  1  1  1  1  1  1  1  1  1  1  1 
A_{2}  0  6  0  6  0  6  0  6  0  6  0  6 
A_{3}  0.832  2  0.827  2  0.818  2  0.739  3  0.679  2  0.668  3 
A_{4}  0.136  5  0.132  5  0.119  5  0.115  5  0.102  5  0.092  5 
A_{5}  0.528  3  0.548  3  0.577  3  0.632  2  0.673  3  0.682  2 
A_{6}  0.279  4  0.261  4  0.254  4  0.244  4  0.24  4  0.224  4 
$\theta =2.5$  $\theta =3$  $\theta =3.5$  $\theta =4$  $\theta =5.5$  $\theta =6$  
Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  
A_{1}  1  1  1  1  1  1  1  1  1  1  1  1 
A_{2}  0  6  0  6  0  6  0  6  0  6  0  6 
A_{3}  0.663  3  0.658  3  0.655  3  0.651  3  0.646  3  0.643  3 
A_{4}  0.09  5  0.088  5  0.0.85  5  0.083  5  0.081  5  0.079  5 
A_{5}  0.699  2  0.707  2  0.714  2  0.723  2  0.731  2  0.738  2 
A_{6}  0.279  4  0.254  4  0.24  4  0.196  4  0.194  4  0.192  4 
$\theta =6.5$  $\theta =7$  $\theta =7.5$  $\theta =7.5$  $\theta =8$  $\theta =8.3$  
Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  
A_{1}  1  1  1  1  1  1  1  1  1  1  1  1 
A_{2}  0  6  0  6  0  6  0  6  0  6  0  6 
A_{3}  0.638  2  0.625  2  0.612  2  0.605  3  0.587  3  0.581  3 
A_{4}  0.078  5  0.076  5  0.075  5  0.074  5  0.073  5  0.072  5 
A_{5}  0.743  3  0.751  3  0.758  3  0.765  2  0.779  2  0.786  2 
A_{6}  0.19  4  0.188  4  0.187  4  0.185  4  0.183  4  0.18  4 
$\theta =8.6$  $\theta =9$  $\theta =9.3$  $\theta =9.5$  $\theta =9.9$  $\theta =10$  
Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  Value  Sort  
A_{1}  1  1  1  1  1  1  1  1  1  1  1  1 
A_{2}  0  6  0  6  0  6  0  6  0  6  0  6 
A_{3}  0.575  2  0.564  2  0.553  2  0.546  3  0.533  3  0.532  3 
A_{4}  0.071  5  0.071  5  0.07  5  0.07  5  0.069  5  0.069  5 
A_{5}  0.792  3  0.798  3  0.806  3  0.814  2  0.825  2  0.827  2 
A_{6}  0.177  4  0.175  4  0.173  4  0.171  4  0.17  4  0.169  4 
Evaluation Results  Sort Results  

HFSTODIM  $\mathrm{\Phi}{(A)}_{1}$ 1  $\mathrm{\Phi}{(A)}_{2}$ 0  $\mathrm{\Phi}{(A)}_{3}$ 0.397  $\mathrm{\Phi}{(A)}_{4}$ 0.123  $\mathrm{\Phi}{(A)}_{5}$ 0.368  $\mathrm{\Phi}{(A)}_{6}$ 0.262  ${A}_{1}\succ {A}_{3}\succ {A}_{5}\succ {A}_{6}\succ {A}_{4}\succ {A}_{2}$ 
HFTODIM  ${\mathrm{\Phi}}^{\prime}{(A)}_{1}$ 1  ${\mathrm{\Phi}}^{\prime}{(A)}_{2}$ 0.012  ${\mathrm{\Phi}}^{\prime}{(A)}_{3}$ 0.673  ${\mathrm{\Phi}}^{\prime}{(A)}_{4}$ 0  ${\mathrm{\Phi}}^{\prime}{(A)}_{5}$ 0.492  ${\mathrm{\Phi}}^{\prime}{(A)}_{6}$ 0.217  ${A}_{1}\succ {A}_{3}\succ {A}_{5}\succ {A}_{6}\succ {A}_{2}\succ {A}_{4}$ 
OPSTODIM  ${\mathrm{\Phi}}^{\u2033}{(A)}_{1}$ 1  ${\mathrm{\Phi}}^{\u2033}{(A)}_{2}$ 0  ${\mathrm{\Phi}}^{\u2033}{(A)}_{3}$ 0.585  ${\mathrm{\Phi}}^{\u2033}{(A)}_{4}$ 0.231  ${\mathrm{\Phi}}^{\u2033}{(A)}_{5}$ 0.234  ${\mathrm{\Phi}}^{\u2033}{(A)}_{6}$ 0.462  ${A}_{1}\succ {A}_{3}\succ {A}_{6}\succ {A}_{5}\succ {A}_{4}\succ {A}_{2}$ 
FHVIKOR  Q(A_{1}) 0  Q(A_{2}) 0.964  Q(A_{3}) 0.354  Q(A_{4}) 0.913  Q(A_{5}) 0.651  Q(A_{6}) 0.883  ${A}_{1}\succ {A}_{3}\succ {A}_{6}\succ {A}_{5}\succ {A}_{4}\succ {A}_{2}$ 
FHTOPSIS  C(A_{1}) 0.942  C(A_{2}) 0.33  C(A_{3}) 0.698  C(A_{4}) 0.303  C(A_{5}) 0.347  C(A_{6}) 0.475  ${A}_{1}\succ {A}_{3}\succ {A}_{6}\succ {A}_{5}\succ {A}_{2}\succ {A}_{4}$ 
FHSAW  S(A_{1}) 0.868  S(A_{2}) 0.298  S(A_{3}) 0.772  S(A_{4}) 0.411  S(A_{5}) 0.53  S(A_{6}) 0.372  ${A}_{1}\succ {A}_{3}\succ {A}_{5}\succ {A}_{4}\succ {A}_{6}\succ {A}_{2}$ 
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Zhang, Y.; Ye, C.; Geng, X. A Hesitant Fuzzy Method for Evaluating Risky Cold Chain Suppliers Based on an Improved TODIM. Sustainability 2022, 14, 10152. https://doi.org/10.3390/su141610152
Zhang Y, Ye C, Geng X. A Hesitant Fuzzy Method for Evaluating Risky Cold Chain Suppliers Based on an Improved TODIM. Sustainability. 2022; 14(16):10152. https://doi.org/10.3390/su141610152
Chicago/Turabian StyleZhang, Yongzheng, Chunming Ye, and Xiuli Geng. 2022. "A Hesitant Fuzzy Method for Evaluating Risky Cold Chain Suppliers Based on an Improved TODIM" Sustainability 14, no. 16: 10152. https://doi.org/10.3390/su141610152