A supplier selection method based on Pythagorean fuzzy sets and VIKOR

Abstract

The present invention proposes a supplier selection method based on Pythagorean fuzzy sets and VIKOR, which belongs to the technical field of supplier evaluation and selection. The supplier selection method based on Pythagorean fuzzy sets and VIKOR includes: using Pythagorean fuzzy sets to evaluate candidate suppliers and the importance of evaluation indicators; according to the evaluation data, the subjective weight and objective weight of the evaluation indicators are calculated respectively, and the combined weight is obtained; according to the evaluation of the alternative solutions and the weights of each evaluation indicator, the VIKOR method based on Pythagorean fuzzy sets is used to sort the candidate suppliers and determine the best supplier.

Description

Technical Field

[0001] The invention belongs to the technical field of supplier selection, and in particular relates to a supplier selection method based on Pythagorean fuzzy sets and VIKOR. Background Art

[0002] In the modern business environment, the performance of an enterprise depends largely on its management of the supply chain. Supply chain management needs to integrate many links in the supply chain, such as suppliers, production departments, and sales departments, in order to reduce the cost of the supply chain, promote the exchange of logistics and information flow, and improve the overall performance of the enterprise. As an upstream enterprise in the supply chain, suppliers play a vital role in the competitiveness of the entire supply chain and the output of the economic and social benefits of the enterprise. Therefore, as an important part of supply chain management, finding and selecting suitable suppliers is the key to the sustainable development of enterprises. Through supplier evaluation and selection, enterprises can effectively improve performance and customer satisfaction. In addition, a qualified supplier can help enterprises avoid risks in raw material supply while maintaining a competitive position. Supplier selection has now become a very basic component for enterprises and industries to improve their interests.

[0003] When choosing a suitable supplier, various evaluation indicators are often involved, including price, quality, delivery time, service and corporate reputation. Therefore, enterprise supplier selection can be regarded as a complex multi-criteria decision-making problem. Due to the complexity and uncertainty of expert evaluation, many existing supplier selection methods cannot accurately express the expert evaluation. In addition, in terms of determining the weights of evaluation indicators, many studies only calculate based on subjective weights or objective weights, without considering the two together. These factors will affect the final supplier ranking results. Therefore, it is necessary to propose a more accurate supplier ranking method.

[0004] Pythagorean fuzzy sets consist of membership and non-membership, which can more flexibly and accurately express the complexity and uncertainty of expert evaluation information in the supplier evaluation process. So far, Pythagorean fuzzy sets have been successfully applied to solve many decision-making problems in the real world.

[0005] The VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method is a multi-criteria decision-making method based on multiple ideal solutions. It determines the ranking of alternative solutions according to the degree of proximity between the alternative solutions and the ideal solutions. The characteristic of the VIKOR method is that it considers maximizing group utility and filtering and minimizing individual regrets when ranking alternative solutions, thereby weighing which solution is the most reasonable under the conditions of multiple influencing factors. At present, it has been widely used in many fields. For decision makers, the VIKOR method is an intuitive supplier ranking method. Summary of the invention

[0006] In order to overcome the defects of existing supplier selection methods in terms of inaccurate supplier evaluation, evaluation index weight calculation and alternative supplier ranking, this paper proposes a supplier selection method based on Pythagorean fuzzy sets and VIKOR. By combining the Pythagorean fuzzy set and VIKOR methods, an innovative supplier method is proposed, thereby improving the efficiency and accuracy of supplier selection.

[0007] The present invention is achieved through the following technical solutions:

[0008] The technical solution of the present invention is a supplier selection method based on Pythagorean fuzzy sets and VIKOR, comprising the following steps:

[0009] S1. Use the Pythagorean fuzzy weighted average operator to aggregate the evaluations of the candidate suppliers and calculate the collective Pythagorean fuzzy evaluation matrix;

[0010] S2, using the Pythagorean fuzzy weighted average operator to obtain the collective Pythagorean fuzzy weights of the evaluation indicators, and calculating the subjective weights of the standardized evaluation indicators;

[0011] S3. Calculate the objective weight of the evaluation index;

[0012] S4, calculating the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution for each evaluation index;

[0013] S5, calculating the normalized Pythagorean fuzzy distance;

[0014] S6. Calculate the group utility value and individual regret value of each solution respectively;

[0015] S7, calculating the compromise evaluation value of each candidate supplier;

[0016] S8. Sort the alternative suppliers and determine the best option.

[0017] This technical solution verifies the applicability and effectiveness of the method through an example selected from a hospital information management system in Shanghai.

[0018] To more clearly illustrate the technical solution of the present invention, assume that there are l evaluation experts DM k (k=1,2,...,l) is responsible for m suppliers A i (i=1,2,...,m) based on n evaluation indicators C j (j=1,2,...,n) to make an evaluation, To evaluate the expert DM k Evaluation of the mth supplier based on the nth evaluation index. Suppose the evaluation expert DM k The Pythagorean fuzzy evaluation matrix is ​​given as Furthermore, in the supplier selection method proposed in the present invention, the weights of the evaluation experts are known.

[0019] Based on the above settings, the supplier selection method includes the following steps:

[0020] Step 1 aggregates the personal evaluation matrix of evaluation experts.

[0021] The Pythagorean fuzzy weighted average operator is used to convert the evaluation matrix of each evaluation expert into Aggregate into collective supplier Pythagorean fuzzy evaluation matrix R = (r ij ) m×n .

[0022]

[0023] Step 2: Calculate the subjective weight of the evaluation index.

[0024] Assume that the weight of the evaluation index is C j By evaluation expert DM k Provided and expressed as The collective Pythagorean fuzzy weights of the evaluation indicators (ω j ) can be obtained by using the Pythagorean fuzzy weighted average operator. The calculation formula is as follows:

[0025]

[0026] where ω j =(μ j ,ν j ),j=1,2,...,n is the importance weight of the jth indicator.

[0027] Based on collective Pythagorean fuzzy weight ω j , the subjective weight of the evaluation index can be obtained by the following formula:

[0028]

[0029] Among them, π j =1-μ j -ν j and

[0030] Step 3: Calculate the objective weight of the evaluation index

[0031] In this study, the entropy weight method is used to calculate the objective weight of the evaluation index. The basic idea of ​​the entropy weight method is to determine the objective weight according to the size of the index variability. Generally speaking, the smaller the information entropy of the evaluation index, the greater the role it plays in the comprehensive evaluation and the greater its weight. Based on the collective supplier evaluation matrix R, the Pythagorean fuzzy information entropy E of each evaluation index is j The calculation method is as follows:

[0032]

[0033] Then, the objective weight of the evaluation index The calculation formula is:

[0034]

[0035] in and

[0036] Step 4: Determine the Pythagorean fuzzy positive ideal solution for each evaluation index and the Pythagorean fuzzy negative ideal scheme Where j = 1, 2, ..., n.

[0037]

[0038]

[0039] Step 5: Calculate the normalized Pythagorean fuzzy distance

[0040]

[0041] in:

[0042]

[0043]

[0044] Step 6: Calculate the group utility value S of each solution i and individual regret value R i

[0045] The group utility value S of each plan iIt can be obtained by the following formula:

[0046]

[0047] Individual regret value R of each solution i It can be obtained by the following formula:

[0048]

[0049] in, is the combined weight of the evaluation indicators, Indicates the relative importance of the subjective weight and objective weight of the indicator. The value of can be any number between 0 and 1. In this study, The value of is 0.5.

[0050] Step 7: Calculate the compromise evaluation value Q of each alternative supplier i

[0051] The compromise evaluation value Q of each alternative supplier i It can be obtained by the following formula:

[0052]

[0053] in v and (1-v) represent the weights of the group utility maximization strategy and the individual regret maximization strategy, respectively. Usually, the value of v is assumed to be 0.5.

[0054] Step 8: Sort the alternative suppliers and determine the best solution.

[0055] According to S i , R i , Q i Then, a compromise sorting scheme (A (1) ), when the scheme satisfies the following two conditions at the same time, it is the best sorting result:

[0056] Condition 1: Acceptable advantage. Q(A (2) )-Q(A (1) )≥1 / (m-1), where A (2) Indicates the supplier ranked second in the Q sorting results.

[0057] Condition 2: Acceptable stability in the decision-making process. Supplier A (1)It is the optimal solution in the ranking of S and / or R at the same time. The compromise solution obtained from this can meet the stability of the decision-making process. When v>0.5, it means that the interests of the majority of the group are taken into account; when v≈0.5, it means that both the interests of the group and individual objections are taken into account; when v<0.5, it means that the result depends on the veto of the minority.

[0058] If the above conditions cannot be met at the same time, a set of compromise solutions that meet the following rules can be obtained: When only condition 1 is met but condition 2 is not met, then A (1) and A (2) is a compromise solution; when condition 1 is not met, according to Q(A (M) )-Q(A (1) )<1 / (m-1)The maximum value M obtained by all suppliers A (M) All are ideal solutions.

[0059] The beneficial effects of the present invention are as follows: (1) The proposed supplier selection method can more accurately describe uncertain decision information and is suitable for complex and uncertain environments. (2) Combining the advantages of subjective weight and objective weight methods, the combined weight method can obtain more accurate evaluation index weights. (3) Combining the VIKOR method to rank alternatives can improve the reliability of the ranking results, overcome the defects of the existing supplier ranking method, and obtain more accurate supplier ranking results. DETAILED DESCRIPTION

[0060] The technical solution of the present invention is further described in detail below in conjunction with specific embodiments.

[0061] The embodiments described below are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] This embodiment applies the proposed supplier selection method to an actual case of selecting an information management system for a hospital in Shanghai. For a hospital, a good information management system can improve the degree of information sharing between departments and thus improve the efficiency of hospital operations. Therefore, it is crucial for a hospital to choose a suitable information management system.

[0063] 4 evaluation experts DM k (k=1,2,...,4) were invited to participate in the supplier evaluation process. They evaluated four candidate suppliers (A1, A2, A3, A4) based on five evaluation indicators. The five evaluation indicators considered in this embodiment are function (C1), reliability (C2), availability (C3), maintainability (C4) and price (C5).

[0064] During the evaluation process, the evaluation experts evaluated the candidate suppliers based on the evaluation indicators using the language described in Table 1, and evaluated the importance of the indicators using the language described in Table 2. The specific evaluation results are shown in Tables 3 and 4. Since the four evaluation experts have different professional knowledge and backgrounds, the expert weights in the evaluation process are: 0.15, 0.20, 0.30, and 0.35 respectively.

[0065] Table 1 Supplier evaluation language terms

[0066]

[0067] Table 2 Language terms for indicator importance evaluation

[0068]

[0069] Table 3 Experts’ evaluation of alternative suppliers

[0070]

[0071] Table 4 Experts’ evaluation of the importance of indicators

[0072]

[0073] In this embodiment, the proposed supplier selection method is applied to the evaluation and selection of hospital information management systems. The main steps are as follows:

[0074] Step 1: After quantifying the language evaluation using Pythagorean fuzzy numbers, the collective Pythagorean fuzzy evaluation matrix of the candidate supplier evaluation can be obtained by applying the Pythagorean fuzzy weighted average operator mentioned in formula (1). The specific results are shown in Table 5.

[0075] Step 2: The evaluation of the evaluation experts on the importance of the evaluation indicators can be aggregated through formula (2). The results are shown in the last row of Table 5. Then, through formula (3), the subjective weight of the standardized evaluation indicators can be calculated. The results are shown in Table 6.

[0076] Step 3: Based on the subjective weighting method, the Pythagorean fuzzy information entropy of each evaluation index can be calculated by formula (4). In addition, the objective weight of the evaluation index can be obtained by formula (5). The specific results are shown in Table 7.

[0077] Table 5 Collective Pythagorean fuzzy evaluation matrix and collective Pythagorean fuzzy weight

[0078]

[0079] Table 6 Collective Pythagorean fuzzy evaluation matrix and subjective weights

[0080]

[0081] Table 7 Pythagorean fuzzy information entropy and objective weight

[0082]

[0083] Step 4: Among the five evaluation indicators, function, reliability, availability and maintainability belong to benefit indicators, and price belongs to cost indicators. Based on this, the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution for each evaluation indicator can be determined. The results are shown below.

[0084] f1 * =(0.761,0.084),f2 * =(0.761,0.084),f3 * =(0.739,0.108),f4 * =(0.577,0.366),

[0085] f5 * =(0.857,0.071);

[0086] f1 - =(0.446,0.518),f2 - =(0.569,0.379),f3 - =(0.401,0.533),f4 - =(0.492,0.436),

[0087] f5 - =(0.814,0.087).

[0088] Step 5: According to formula (8), the standardized Pythagorean fuzzy distance can be calculated. The specific results are shown in Table 6.

[0089] Step 6: The group utility value S and individual regret value R of the four alternative suppliers can be calculated using formulas (11)-(12). The results are shown in Table 8.

[0090] Table 8 S, R and Q values ​​of alternative suppliers

[0091]

[0092] Table 9: Ranking of alternative suppliers based on S, R and Q

[0093]

[0094] Step 7: The compromise evaluation value Q of the four alternative suppliers can be calculated by formula (13). The results are shown in Table 8.

[0095] Step 8: According to the ascending order of S, R and Q values, the three ranking results of the four alternative formulas are shown in Table 9. Based on Table 9, the ranking of the four alternative suppliers based on Q value is: A2>A1>A3>A4. Therefore, among the many alternatives, supplier A2 is the most suitable to provide the required information management system for this hospital.

[0096] This embodiment is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A supplier selection method based on Pythagorean fuzzy sets and VIKOR, comprising the following steps: S1. Use the Pythagorean fuzzy weighted average operator to aggregate the evaluation of the candidate suppliers and calculate the collective Pythagorean fuzzy evaluation matrix. The collective Pythagorean fuzzy evaluation matrix R = (r ij ) m×n The calculation formula is: S2. Use the Pythagorean fuzzy weighted average operator to obtain the collective Pythagorean fuzzy weight of the evaluation index, and calculate the subjective weight of the standardized evaluation index. The calculation formula for the collective Pythagorean fuzzy weight of the evaluation index is: where ω j =(μ j ,ν j ),j=1,2,...,n is the importance weight of the jth evaluation index; Subjective weight of evaluation indicators The calculation formula is: in, π j = 1 - μ j - ν j and S3. Calculate the objective weight of the evaluation index. The calculation formula is: in and E j The calculation formula is: S4. Calculate the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution for each evaluation index. The calculation formulas for the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution for each evaluation index are: S5. Calculate the normalized Pythagorean fuzzy distance, the normalized Pythagorean fuzzy distance The calculation formula is: in: S6. Calculate the group utility value and individual regret value of each solution respectively. The group utility value S of each solution is i and individual regret value R i The calculation formula is: in, is the combined weight of the evaluation indicators, Indicates the relative importance of the subjective and objective weights of the indicators; S7. Calculate the compromise evaluation value of each alternative supplier and the compromise evaluation value Q of each solution. i The calculation formula is: in v and (1-v) represent the weights of the group utility maximization strategy and the individual regret maximization strategy, respectively; S8. Sort the candidate suppliers and determine the best solution, determine the reference value for ranking the candidate suppliers, and i , R i , Q i The alternative suppliers are sorted in ascending order of the value of , and then a compromise sorting scheme is obtained based on the three sorting results, and the best supplier is determined.

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