Multi-attribute Group Decision-making Supplier Selection Method Based on Intuitionistic Fuzzy Theory

Abstract

The present invention discloses a multi-attribute group decision-making supplier selection method based on intuitionistic fuzzy theory, comprising the following steps: first, converting the acquired expert semantic evaluation values into intuitionistic fuzzy numbers with different hesitations to form an intuitionistic fuzzy evaluation matrix; second, determining attribute weights using the proposed improved intuitionistic fuzzy entropy, aggregating attribute information using IFWA to obtain an expert comprehensive evaluation matrix; then, determining expert weights using the proposed improved intuitionistic fuzzy distance, aggregating expert information using IFWA to obtain a comprehensive decision matrix for each supplier; finally, ranking using a scoring function method, obtaining a priority order for each supplier, and selecting the optimal supplier. Compared with traditional algorithms, the present invention adopts improved intuitionistic fuzzy entropy and intuitionistic fuzzy distance to determine attribute weights and expert weights, respectively, resulting in a more reasonable final ranking result and important theoretical significance and application value.

Description

Technical Field

[0001] The present invention relates to the field of multi-attribute decision-making, and in particular to a multi-attribute group decision-making supplier selection method based on intuitionistic fuzzy theory. Background Art

[0002] Supplier selection is a crucial aspect of procurement decisions. To minimize decision-making errors, experts from multiple fields typically evaluate and prioritize suppliers based on multiple attributes, such as product quality, price, and service. This is essentially a multi-attribute group decision-making problem. Due to the ambiguity of attribute information and the limitations of experts' professional expertise, practical experience, and personal preferences, the evaluation information provided by experts is often diverse and uncertain. Directly aggregating this information can have an unreasonable impact on the final evaluation, reducing the credibility of the results. Therefore, it is crucial to properly measure the diversity and uncertainty of evaluation information and determine attribute and expert weights.

[0003] Since Zadeh's fuzzy sets were proposed, multi-attribute group decision-making problems based on fuzzy sets have been extensively studied, as they can effectively capture the fuzzy nature of objective reality. Zadeh's fuzzy sets can only reflect two aspects of information: yes or no. However, due to the complexity of real-world problems and the uncertainty of information, coupled with the decision maker's limited time, energy, and incomplete understanding of the objective world, there is often a degree of hesitation in decision-making, making it difficult to accurately capture such situations using fuzzy sets. Therefore, Atanasso expanded and developed Zadeh's fuzzy set theory, proposing the concept of intuitionistic fuzzy sets. By adding a non-membership parameter, intuitionistic fuzzy sets can effectively capture the hesitation and uncertainty of decision makers in their judgments. They simultaneously consider membership, non-membership, and hesitation, and can describe fuzzy concepts that are neither one nor the other. This allows for a more nuanced portrayal of the fuzzy nature of the objective world and a reasonable measurement of the variability and uncertainty of information. After decades of development, intuitionistic fuzzy theory has garnered widespread attention and has been applied to solve problems in areas such as uncertainty modeling, pattern recognition, fault diagnosis, intelligent computing, and supplier selection.

[0004] Scholars have conducted extensive research on methods for determining attribute weights, often combining entropy theory with intuitionistic fuzzy numbers. Although many intuitionistic fuzzy entropies have been proposed, there is no universally recognized best intuitionistic fuzzy entropy. Ye et al. proposed a fuzzy entropy measure based on the cosine function in "Two effective measures of intuitionistic fuzzy entropy." Zeng et al. proposed a fuzzy entropy measure based on the difference between membership and non-membership in "Relationship between similarity measure and entropy of interval valued fuzzy sets." Varma et al. proposed an exponential-based fuzzy entropy measure in "Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning" using an exponential function. While these methods can address the uncertainty measurement problem of general intuitionistic fuzzy numbers, they lose their effectiveness when the difference between the membership and non-membership degrees of two intuitionistic fuzzy numbers is the same. In their paper "Approach for multi-attribute decision making based on novel intuitionistic fuzzy entropy and evidential reasoning," Yuan et al. proposed a new intuitionistic fuzzy entropy measure by considering the hesitancy and uncertainty of intuitionistic fuzzy numbers. In their paper "Research on a Multi-attribute Decision Making Method Based on a New Class of Intuitionistic Fuzzy Entropy," Liu et al. proposed an entropy measure based on the cosine function and hesitancy. While these methods consider the influence of hesitancy and can address the uncertainty of measurements when the difference between the membership and non-membership degrees of two intuitionistic fuzzy numbers is the same, they become ineffective when the membership and non-membership degrees are identical but the hesitancy degrees are different. Regarding methods for determining expert weights, researchers in various fields have proposed different types of similarity and distance measures for intuitionistic fuzzy sets, which have accelerated the development of intuitionistic fuzzy theory both theoretically and practically. However, many existing similarity and distance measures cannot handle certain specific situations in real-world problems.In their paper "Distances between intuitionistic fuzzy sets," Szmidt et al. proposed several intuitionistic fuzzy distance metrics based on Hamming distance and Euclidean distance. Grzegorzewski proposed an intuitionistic fuzzy distance metric based on the Hausdorff metric in their paper "Distances between intuitionistic fuzzy sets and / or interval-valued fuzzy sets based on the Hausdorff metric." While these methods offer certain advantages in measuring intuitionistic fuzzy distances, they can lead to unreasonable or counterintuitive results in certain situations. Therefore, distance and similarity metrics for intuitionistic fuzzy sets remain an open topic, attracting numerous researchers both domestically and internationally. More rational and optimized approaches are being sought to overcome the "blind spots" of existing methods. These issues can adversely affect decision outcomes and limit further development and improvement in group decision-making problems where attribute weights and expert weights are completely unknown. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-attribute group decision-making supplier selection method based on intuitionistic fuzzy theory, which can accurately and effectively make decisions on supplier selection decision problems where attribute weights and expert weights are completely unknown.

[0006] The technical solution adopted in the present invention is:

[0007] A. Determine supplier A = {A i ,i=1,2,…,n}, the evaluation attribute set is C={C j ,j=1,2,…,m}, the expert group set is D={D s ,s=1,2,…,k}, all attribute evaluation values constitute the semantic evaluation matrix Among them A i represents the i-th supplier, C j represents the jth evaluation attribute, D s represents the sth expert, Indicates expert D s For Supplier A i In attribute C j The original semantic evaluation value on ;

[0008] B. The original semantic evaluation value given by the expert is converted into an intuitionistic fuzzy number by using the original semantic evaluation value and intuitionistic fuzzy number conversion method proposed by Lin et al. in the article "Expert weight determination method based on hesitation and similarity and its application". Then we get the intuitionistic fuzzy evaluation matrix in is the intuitionistic fuzzy number of the intuitionistic fuzzy evaluation matrix, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number;

[0009] C. The intuitive fuzzy evaluation matrix obtained Through the following improved intuitionistic fuzzy entropy formula Get Expert D s About Attribute C j Intuitionistic fuzzy entropy in Indicates expert D s For Supplier A i About Attribute C j The degree of hesitation, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number;

[0010] D、By the experts s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy Through the following formula Get Expert D s Attribute C determined by the evaluation value j Weight in

[0011] E. The attribute weight obtained Through the following formula Aggregate attribute information to obtain the expert's comprehensive evaluation matrix in is the intuitionistic fuzzy number of the comprehensive evaluation matrix of the experts, Indicates expert D s About Supplier Ai The comprehensive evaluation membership of Indicates expert D s About Supplier A i The comprehensive evaluation non-membership degree, IFWA is the intuitionistic fuzzy weighted average operator;

[0012] F. The obtained expert comprehensive evaluation matrix The improved intuitionistic fuzzy distance is Calculate expert D p and D q Comprehensive evaluation of information differences D pq ,in For expert D s For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D P For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D q For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, Intuitionistic fuzzy divergence is used to measure the intuitionistic fuzzy number and The difference, Indicates expert D p About Supplier A i The comprehensive evaluation membership of Indicates expert D q About Supplier A i The comprehensive evaluation membership of Indicates expert D p About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D q About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D p About Supplier A i The comprehensive evaluation hesitation, Indicates expert D q About Supplier A i The comprehensive evaluation hesitation degree, p = 1, 2, ..., k, q = 1, 2, ..., k;

[0013] G. Differences in comprehensive evaluation information obtained from experts D pq By the following formula U pq =1-D pq Then we get expert D p and D qComprehensively evaluate the similarity of information and construct the similarity matrix U = [U pq ] k×k ;

[0014] H, the similarity matrix U obtained by pq ] k×k Through the following formula Get Expert D q The sum of similarities with other experts R q , and through the following formula Get Expert D q The weight w q ,in

[0015] I. Obtained expert weight w q pass Gather expert information and obtain the comprehensive decision matrix V″′=[d i ] 1×n , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix, μ i Indicates supplier A i The comprehensive decision-making membership, Indicates supplier A i The comprehensive decision non-membership degree,

[0016] J. Sort the obtained comprehensive decision matrices of each supplier by using the scoring function method;

[0017] The scoring function method is:

[0018] If S(d1)>S(d2), then d1>d2; if S(d1)<S(d2), then d1<d2; if S(d1)=S(d2), then make the following comparison: if H(d1)>H(d2), then d1>d2; if H(d1)<H(d2), then d1<d2; if H(d1)=H(d2), then d1=d2. Where, S(d1) and S(d2) are scoring functions, S(d i )=μ i -ν i , H(d1) and H(d2) are exact functions, H(d i )=μ i +ν i , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix.

[0019] The present invention takes the supplier selection decision problem based on the semantic evaluation information of experts as the application background. On this basis, the semantic evaluation information is transformed into the intuitive fuzzy number, and then the attribute information and expert information are aggregated. Finally, the scoring function method is used to sort and obtain the optimal supplier, which greatly improves the accuracy and efficiency of the supplier selection decision problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0023] like Figure 1 As shown, the present invention includes the following steps:

[0024] A. Determine supplier A = {A i ,i=1,2,…,n}, the evaluation attribute set is C={C j ,j=1,2,…,m}, the expert group set is D={D s ,s=1,2,…,k}, all attribute evaluation values constitute the semantic evaluation matrix Among them A i represents the i-th supplier, C j represents the jth evaluation attribute, D s represents the sth expert, Indicates expert D s For Supplier A i In attribute C j The original semantic evaluation value on .

[0025] B. Using the method for converting raw semantic evaluation values into intuitionistic fuzzy numbers proposed by Lin et al. in "Expert Weight Determination Method Based on Hesitation and Similarity and Its Application," the raw semantic evaluation values given by the experts were converted into intuitionistic fuzzy numbers. The raw semantic evaluation values were categorized into five levels: "very weak," "weak," "average," "strong," and "very strong." Given that most review experts have extensive experience, this patent categorized expert hesitancy into three levels: "very small," "small," and "average." The semantic evaluation granularity r = 0.5, and y = 0.1, 0.2, and 0.3, respectively, represent the three levels of hesitancy. The resulting semantic evaluation values and corresponding intuitionistic fuzzy numbers are shown in Table 1.

[0026] Table 1 Conversion between semantic evaluation value and intuitionistic fuzzy number

[0027]

[0028] Then we get the intuitionistic fuzzy evaluation matrix in is the intuitionistic fuzzy number of the intuitionistic fuzzy evaluation matrix, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number;

[0029] C. The intuitive fuzzy evaluation matrix obtained Through the following improved intuitionistic fuzzy entropy formula Get Expert D s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy in Indicates expert D s For Supplier A i About Attribute C j The degree of hesitation, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the transformation of semantic evaluation value and intuitionistic fuzzy number.

[0030] D、By the experts D s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy Through the following formula Get Expert D s Attribute C determined by the evaluation value j Weight in

[0031] E. The attribute weight obtained Through the following formula Aggregate attribute information to obtain the expert's comprehensive evaluation matrix in is the intuitionistic fuzzy number of the comprehensive evaluation matrix of the experts, Indicates expert D s About Supplier A i The comprehensive evaluation membership of Indicates expert D s About Supplier A i The comprehensive evaluation non-membership degree, IFWA (Intuitionistic Fuzzy Weighted Arithmetic) is an intuitionistic fuzzy weighted average operator.

[0032] F. The obtained expert comprehensive evaluation matrix The improved intuitionistic fuzzy distance is Calculate expert D p and D q Comprehensive evaluation of information differences D pq ,in For expert D s For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D P For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D q For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, Intuitionistic fuzzy divergence is used to measure the intuitionistic fuzzy number and The difference, Indicates expert D p About Supplier A i The comprehensive evaluation membership of Indicates expert D q About Supplier A i The comprehensive evaluation membership of Indicates expert D p About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D q About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D p About Supplier A i The comprehensive evaluation hesitation, Indicates expert D q About Supplier A i The comprehensive evaluation hesitation degree, p = 1, 2, ..., k, q = 1, 2, ..., k;

[0033] G. Differences in comprehensive evaluation information obtained from experts D pq By the following formula U pq =1-D pq Then we get expert D p and D q Comprehensively evaluate the similarity of information and construct the similarity matrix U = [U pq ] k×k .

[0034] H, the similarity matrix U obtained by pq ] k×k Through the following formula Get Expert D q The sum of similarities with other experts R q , and through the following formula Get the expert's weight w q ,in

[0035] I. Obtained expert weight w q pass Gather expert information and obtain the comprehensive decision matrix V″′=[d i ] 1×n , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix, μ i Indicates supplier A i The comprehensive decision-making membership, ν i Indicates supplier A i The comprehensive decision non-membership degree, IFWA (Intuitionistic Fuzzy Weighted Arithmetic) is an intuitionistic fuzzy weighted average operator.

[0036] J. Sort the comprehensive decision matrices of each supplier using the scoring function method, then obtain the priority order of each supplier and select the best supplier.

[0037] The scoring function method is:

[0038] If S(d1)>S(d2), then d1>d2; if S(d1)<S(d2), then d1<d2; if S(d1)=S(d2), then make the following comparison: if H(d1)>H(d2), then d1>d2; if H(d1)<H(d2), then d1<d2; if H(d1)=H(d2), then d1=d2. Where, S(d1) and S(d2) are scoring functions, S(d i )=μ i -ν i , H(d1) and H(d2) are exact functions, H(d i )=μ i +ν i , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix.

[0039] This invention takes the supplier selection decision problem based on expert semantic evaluation information as its application context. Based on this, it transforms semantic evaluation information into intuitionistic fuzzy numbers, then aggregates attribute information and expert information. Finally, it uses a scoring function method to rank and determine the optimal supplier, significantly improving the accuracy and efficiency of supplier selection decision problems. Specifically, when aggregating attribute information, the present invention proposes an improved intuitionistic fuzzy entropy method for calculating attribute weights. Existing intuitionistic fuzzy entropies fall into two categories. One type fails to consider the impact of hesitation on the degree of intuitionistic fuzzy uncertainty. This method becomes ineffective when the difference between the membership and non-membership degrees of two intuitionistic fuzzy numbers is the same. The other type considers the impact of hesitation on intuitionistic fuzzy entropy, but this method also becomes ineffective when the membership and non-membership degrees are exactly the same but the hesitation degrees are different. Based on this, the present invention proposes an improved intuitionistic fuzzy entropy method that effectively addresses the aforementioned issues. When aggregating attribute information, the present invention proposes an improved intuitionistic fuzzy distance method for calculating expert weights. To determine expert weights, researchers in various fields have proposed different types of similarity and distance metrics for intuitionistic fuzzy sets. However, existing similarity and distance metrics cannot handle certain specific situations in real-world problems and, in some cases, may even lead to unreasonable or counterintuitive results. These issues can have an undesirable impact on decision-making outcomes. This paper proposes an improved intuitionistic fuzzy distance, which is more reasonable and effective when processing expert information aggregation.

[0040] The following is a detailed description of the method and effects of the present invention using specific examples.

[0041] A. This patent is based on the problem of supplier selection decision-making. In the procurement decision-making, the selection of suppliers is carried out by a review team composed of experts from various fields such as technology, economy and related business representatives. The review team evaluates and selects suppliers based on many factors such as supplier qualifications, quality, price, service, etc., so the supplier A is determined to be {A i ,i=1,2,…,n}, the evaluation attribute set is C={C j ,j=1,2,…,m}, the expert group set is D={D s ,s=1,2,…,k}, all attribute evaluation values constitute the semantic evaluation matrix Among them A i represents the i-th supplier, C j represents the jth evaluation attribute, D s represents the sth expert, Indicates expert D s For Supplier A i In attribute C j The original semantic evaluation value on ;

[0042] B. Through the original semantic evaluation value and intuitive fuzzy number conversion method proposed by Lin et al. in the article "Expert weight determination method based on hesitation and similarity and its application", the original semantic evaluation value given by the expert is converted into an intuitive fuzzy number, where the original semantic evaluation value is divided into 5 levels: "very weak", "weak", "general", "strong", and "very strong". In view of the fact that most review experts have relatively rich experience, this patent divides the expert hesitation into 3 levels: "very small", "small", and "general". Then the intuitive fuzzy evaluation matrix is obtained in is the intuitionistic fuzzy number of the intuitionistic fuzzy evaluation matrix, Indicates expert D s For Supplier A i About Attribute C j The membership degree, Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number;

[0043] C. The intuitive fuzzy evaluation matrix obtained Through the following improved intuitionistic fuzzy entropy formula Get Expert D sAttribute C determined by the evaluation value j Intuitionistic fuzzy entropy in Indicates expert D s For Supplier A i About Attribute C j The degree of hesitation, Indicates expert D s For Supplier A i About Attribute C j The membership degree, Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number;

[0044] Experiments using specific examples illustrate that the improved intuitionistic fuzzy numbers in the present invention are more effective in measuring the uncertainty between intuitionistic fuzzy numbers:

[0045] Example 1 Let B1 = {<x,0.5,0.3> |x∈X},B2={<x,0.3,0.1> |x∈X}, are two fuzzy sets, which can be obtained by calculating different intuitionistic fuzzy entropies:

[0046]

[0047] E 2 (B1)=E 2 (B2) = 1 - 0.2 = 0.8;

[0048]

[0049] E(B1)=0.5695<E(B2)=0.7695.

[0050] From Example 1, we can see that the membership and non-membership of B1 and B2 have the same difference, but the hesitation of B2 is significantly greater than that of B1, that is, the uncertainty of B2 is also significantly greater than that of B1. Obviously, formula E 1 , E 2 and E 3 Because the influence of hesitation is not considered, the differences between them cannot be distinguished, which is insufficient. However, the improved credibility entropy proposed in this patent meets the requirements. 1 It is the intuitionistic fuzzy entropy proposed in the paper "Two effective measures of intuitionistic fuzzy entropy", E 2It is the intuitionistic fuzzy entropy proposed in the paper "Relationship between similarity measure and entropy of interval valued fuzzy sets", E 3 is the intuitionistic fuzzy entropy proposed in the paper “Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning”, and E is the improved intuitionistic fuzzy entropy in the patent of this invention.

[0051] Example 2 Let B1 = {<x,0.25,0.25> |x∈X},B2={<x,0.5,0.5> |x∈X}, are two intuitionistic fuzzy sets, and different intuitionistic fuzzy entropy calculations can be obtained:

[0052]

[0053]

[0054] E(B1)=0.7500>E(B2)=0.5000.

[0055] In Example 2, according to Formula E 4 、E 5 and E 6 The result of calculating the intuitionistic fuzzy entropy is 1. Although B1 and B2 have the same membership and non-membership, the hesitation of B1 is 0.5, while B2 has no hesitation. Obviously, the uncertainty of B1 is greater, and the result is obviously unreasonable. However, the improved credibility entropy proposed in this patent meets the requirements. 4 E is the intuitionistic fuzzy entropy proposed in the paper "Approach for multi-attribute decision making based on novel intuitionistic fuzzy entropy andevidential reasoning". 5 is the intuitionistic fuzzy entropy proposed in the paper "Research on a Multi-Attribute Decision-Making Method Based on a New Class of Intuitionistic Fuzzy Entropy," and E is the improved intuitionistic fuzzy entropy in this patent. Combining Examples 1 and 2, we show that the improved intuitionistic fuzzy number in this patent is more effective in measuring uncertainty between intuitionistic fuzzy numbers.

[0056] The improved direct fuzzy entropy in this patent invention not only takes into account the influence of membership and non-membership on uncertainty, but also takes into account the influence of hesitation. Therefore, when measuring the uncertainty of different intuitive fuzzy numbers, it can fully utilize the information contained in the intuitive fuzzy number itself, avoiding the loss of information, thereby achieving a more accurate and effective measurement of the difference in the degree of uncertainty between different intuitive fuzzy numbers.

[0057] Improved intuitionistic fuzzy entropy has the following three properties:

[0058] ①

[0059] ②

[0060] ③E=E c .

[0061] The proof is as follows.

[0062] ①If E=0, then that is to say Right now or μ B (x i )=0,ν B (x i )=1,π B (x i )=0, which is obviously a distinct set. If it is a distinct set, then obviously E=0.

[0063] ②If E=1, then that is to say Right now and Available if Then obviously E=1.

[0064] ③

[0065] D、By the experts s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy Through the following formula Get Expert D s Attribute C determined by the evaluation value j Weight in

[0066] E. The attribute weight obtained Through the following formula Aggregate attribute information to obtain the expert's comprehensive evaluation matrix in is the intuitionistic fuzzy number of the comprehensive evaluation matrix of the experts, Indicates expert D s About Supplier A i The comprehensive evaluation membership of Indicates expert D s About Supplier A i The comprehensive evaluation non-membership degree, IFWA is the intuitionistic fuzzy weighted average operator;

[0067] F. The obtained expert comprehensive evaluation matrix The improved intuitionistic fuzzy distance is Calculate expert D p and D q Comprehensive evaluation of information differences D pq ,in For expert D s For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D P For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D q For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, Intuitionistic fuzzy divergence is used to measure the intuitionistic fuzzy number and The difference, Indicates expert D p About Supplier A i The comprehensive evaluation membership of Indicates expert D q About Supplier A i The comprehensive evaluation membership of Indicates expert D p About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D q About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D p About Supplier A i The comprehensive evaluation hesitation, Indicates expert D q About Supplier A i The comprehensive evaluation hesitation degree, p = 1, 2, ..., k, q = 1, 2, ..., k;

[0068] Experiments using specific examples illustrate that the improved intuitionistic fuzzy numbers in the present invention are more effective in measuring the uncertainty between intuitionistic fuzzy numbers:

[0069] Example 3: There are two cases of intuitionistic fuzzy sets, where the intuitionistic fuzzy numbers B1 and B2 are shown in Table 2 below:

[0070] Table 2 Intuitionistic fuzzy numbers in Example 3

[0071]

[0072] The calculation results of different intuitionistic fuzzy distances are shown in Table 3:

[0073] Table 3 Intuitionistic fuzzy distances in different situations under Example 3

[0074]

[0075] From Example 3, we can see that there are differences between Case 1 and Case 2, but through and d G The calculation shows that the distances of case 1 and case 2 are the same, obviously and d G It violates the intuitive requirement and cannot distinguish their differences, which is insufficient. However, the intuitive fuzzy distance proposed in this patent can effectively distinguish the differences between them. and is the distance metric proposed in the paper “Distances between intuitionistic fuzzy sets”, d G is the distance metric proposed in the paper “Distances between intuitionistic fuzzy sets and / or interval-valued fuzzysets based on the Hausdorff metric”, and d is the intuitionistic fuzzy distance in the patent of this invention.

[0076] Intuitionistic fuzzy distance satisfies the following two properties:

[0077] ① When When D pq =0;

[0078] ②D pq =D qp .

[0079] The proof is as follows.

[0080] ①If Then D pq =0, when When, obviously at this time Then obviously D pq =0.

[0081] ②When D pq =D qp hour, Obviously D pq =D qp .

[0082] G. Differences in comprehensive evaluation information obtained from experts D pq By the following formula U pq =1-D pq Then we get expert D p and D q Similarity U of comprehensive evaluation information pq , and construct the similarity matrix U=[U pq ] k×k ;

[0083] H, the similarity matrix U obtained by pq ] k×k Through the following formula Get Expert D q The sum of similarities with other experts R q , and through the following formula Get the expert's weight w q ,in

[0084] I. Obtained expert weight w q pass Gather expert information and obtain the comprehensive decision matrix V″′=[d i ] 1×n , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix, μ i Indicates supplier A i The comprehensive decision-making membership, ν i Indicates supplier A i The comprehensive decision non-membership degree, IFWA (Intuitionistic Fuzzy Weighted Arithmetic) is an intuitionistic fuzzy weighted average operator;

[0085] J. Sort the obtained comprehensive decision matrices of each supplier using the scoring function method, then obtain the priority order of each supplier and select the best supplier;

[0086] The scoring function method is:

[0087] If S(d1)>S(d2), then d1>d2; if S(d1)<S(d2), then d1<d2; if S(d1)=S(d2), then make the following comparison: if H(d1)>H(d2), then d1>d2; if H(d1)<H(d2), then d1<d2; if H(d1)=H(d2), then d1=d2. Where, S(d1) and S(d2) are scoring functions, S(d i )=μ i -ν i , H(d1) and H(d2) are exact functions, H(d i )=μ i +ν i , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix.

[0088] The following specific experiments illustrate that the group decision-making method in this patent can effectively solve the supplier selection decision problem:

[0089] Example 4: Taking the procurement of a batch of general equipment by a certain army as an example, after prequalification, four suppliers (A1, A2, A3, A4) were identified. Due to space constraints, three experts (D1, D2, D3) were selected from each of the technical, economic and business fields to evaluate and select the best suppliers. The evaluation indicators include corporate reputation (C1), product quality (C2), service level (C3), and price suitability (C4).

[0090] Step 1: When the experts make the evaluation, they determine the evaluation hesitation level based on their own professional level and the information provided by the supplier. The evaluation values of all attributes of each supplier by each expert are obtained to form the original semantic evaluation value matrix V, as shown below:

[0091]

[0092]

[0093] Among them: superscript 1 represents the hesitation degree is "very small", superscript 2 represents the hesitation degree is "small", and superscript 3 represents the hesitation degree is "moderate".

[0094] Step 2: Using the original semantic evaluation value and intuitionistic fuzzy number conversion method proposed by Lin et al. in the article "Expert Weight Determination Method Based on Hesitation and Similarity and Its Application", the original semantic evaluation value given by the expert is converted into an intuitionistic fuzzy number, and then the intuitionistic fuzzy evaluation matrix V' is obtained as shown below:

[0095]

[0096]

[0097]

[0098] Step 3: Based on the obtained intuitionistic fuzzy evaluation matrix, the expert D is obtained through the improved intuitionistic fuzzy entropy formula. s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy The result is as follows:

[0099]

[0100]

[0101]

[0102] Step 4: Get the expert D s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy Identify expert D s Attribute C determined by the evaluation value j The weights are as follows:

[0103]

[0104]

[0105]

[0106] Step 5: Determine the expert D s Attribute C determined by the evaluation value j The weights of the attributes are aggregated through IFWA to obtain the comprehensive evaluation matrix V″ of the experts, as shown below:

[0107]

[0108] Step 6: Based on the obtained expert comprehensive evaluation matrix V″, the difference D of the expert comprehensive evaluation information is calculated by improving the intuitionistic fuzzy distance pq , and then the similarity U of the expert comprehensive evaluation information is obtained pq , forming the similarity matrix U as follows:

[0109]

[0110] Step 7: Calculate the sum of similarities R of the expert comprehensive evaluation information from the obtained similarity matrix U q , and then get the expert's weight w q, then gather expert information to obtain the comprehensive decision matrix V″′ of each supplier, as shown below:

[0111] V″′=[<0.6128,0.1895>,<0.6868,0.1500>,<0.6423,0.1701>,<0.6861,0.1633>]

[0112] Step 8: The obtained comprehensive decision matrix of each supplier is sorted using the scoring function method, and the result is A2>A4>A3>A1, so the optimal supplier is A2. The original evaluation values of the experts show that supplier A2 has the best evaluation value. The optimal supplier obtained by the method proposed in this patent is also A2, verifying the feasibility and effectiveness of the method proposed in this patent. This patent has the following main advantages: First, it determines the attribute weights through intuitive fuzzy entropy, which is more comprehensive and reasonable; second, it determines the expert weights through intuitive fuzzy distance to aggregate decision information, and the results are more objective; third, it uses the integral function method to sort the suppliers by their merits, which can clearly compare the evaluation indicators of each solution, which is conducive to making a choice.

[0113] Compared with traditional algorithms, the present invention utilizes a conversion method that considers hesitation to convert expert semantic evaluation values into intuitive fuzzy numbers with varying hesitations, thereby reducing the irrational impact of evaluation information uncertainty on evaluation results. Using an improved intuitive fuzzy entropy to weight attribute information effectively addresses the shortcomings of other existing intuitive fuzzy entropies when two intuitive fuzzy numbers have the same membership and non-membership differences, or when they have identical membership and non-membership degrees but different hesitations, thereby more rationally determining the weights of attribute information. Using an improved intuitive fuzzy distance to weight expert information effectively addresses the shortcomings of existing similarity and distance metrics in addressing certain specific situations in practical problems, thereby more rationally determining the weights of expert information. Finally, ranking is performed using a scoring function method, followed by obtaining a priority order for each supplier, selecting the optimal supplier, and obtaining a reasonable optimal supplier decision, which has important theoretical significance and application value.

[0114] In the description of the present invention, it should be noted that, for directional words, such as the terms "center", "horizontal", "longitudinal", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like, indicating directions and positional relationships, are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and cannot be understood as limiting the specific scope of protection of the present invention.

[0115] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present application described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0116] Note that the above are only preferred embodiments of the present invention and the principles of the technology used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention is described in detail through the above embodiments, the present invention is not limited to the specific embodiments described herein. Without departing from the concept of the present invention, it may also include many other effective embodiments, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A multi-attribute group decision-making supplier selection method based on intuitionistic fuzzy theory, characterized by: It includes the following steps: A. Determine supplier A = {A i ,i=1,2,…,n}, the evaluation attribute set is C={C j ,j=1,2,…,m}, the expert group set is D={D s ,s=1,2,…,k}, all attribute evaluation values constitute the semantic evaluation matrix Among them A i represents the i-th supplier, C j represents the jth evaluation attribute, D s represents the sth expert, Indicates expert D s For Supplier A i In attribute C j The original semantic evaluation value on ; B. Through the semantic evaluation value and intuitionistic fuzzy number conversion method, the original semantic evaluation value given by the expert is converted into an intuitionistic fuzzy number, and then the intuitionistic fuzzy evaluation matrix is obtained. in is the intuitionistic fuzzy number of the intuitionistic fuzzy evaluation matrix, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number; C. The intuitive fuzzy evaluation matrix obtained Through the following improved intuitionistic fuzzy entropy formula Get Expert D s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy in Indicates expert D s For Supplier A i About Attribute C j The degree of hesitation, Indicates expert D s For Supplier A i About Attribute C j The membership degree of Indicates expert D s For Supplier A i About Attribute C j The non-membership degree, membership degree and non-membership Obtained through the conversion of semantic evaluation value and intuitionistic fuzzy number; D、By the experts D s Attribute C determined by the evaluation value j Intuitionistic fuzzy entropy Through the following formula Get Expert D s Attribute C determined by the evaluation value j Attribute weight in E. The attribute weight obtained Through the following formula Aggregate attribute information to obtain comprehensive evaluation matrix of experts in is the intuitionistic fuzzy number of the comprehensive evaluation matrix of the experts, Indicates expert D s About Supplier A i The comprehensive evaluation membership of Indicates expert D s About Supplier A i The comprehensive evaluation non-membership degree, IFWA is the intuitionistic fuzzy weighted average operator; F. The obtained expert comprehensive evaluation matrix The improved intuitionistic fuzzy distance is Calculate expert D p and D q Comprehensive evaluation of information differences D pq ,in For expert D s For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D P For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, For expert D q For Supplier A i The intuitionistic fuzzy number of comprehensive evaluation, Intuitionistic fuzzy divergence is used to measure the intuitionistic fuzzy number and The difference, Indicates expert D p About Supplier A i The comprehensive evaluation membership of Indicates expert D q About Supplier A i The comprehensive evaluation membership of Indicates expert D p About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D q About Supplier A i The comprehensive evaluation non-membership degree, Indicates expert D p About Supplier A i The comprehensive evaluation hesitation, Indicates expert D q About Supplier A i The comprehensive evaluation hesitation degree, p = 1, 2, ..., k, q = 1, 2, ..., k; G. Differences in comprehensive evaluation information obtained from experts D pq By the following formula U pq =1-D pq Then we get expert D p and D q Comprehensively evaluate the similarity of information and construct the similarity matrix U = [U pq ] k×k ; H, the similarity matrix U obtained by pq ] k×k Through the following formula Get Expert D q The sum of similarities with other experts R q , and through the following formula Get the expert's weight w q ,in I. Obtained expert weight w q pass Gather expert information and obtain the comprehensive decision matrix V″′=[d i ] 1×n , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix, μ i Indicates supplier A i The comprehensive decision-making membership degree, ν i Indicates supplier A i The comprehensive decision non-membership degree, J. Sort the comprehensive decision matrices of each supplier using the scoring function method, then obtain the priority order of each supplier and select the best supplier.

2. The multi-attribute group decision-making supplier selection method based on intuitionistic fuzzy theory according to claim 1 is characterized by: The scoring function method specifically includes the following steps: If S(d1)>S(d2), then d1>d2; if S(d1)<S(d2), then d1<d2; If S(d1)=S(d2), then make the following comparison: if H(d1)>H(d2), then d1>d2; If H(d1)<H(d2), then d1<d2; If H(d1)=H(d2), then d1=d2; where S(d1) and S(d2) are scoring functions, S(d i )=μ i -ν i , H(d1) and H(d2) are exact functions, H(d i )=μ i +ν i , where d i =<μ i ,ν i > is the intuitionistic fuzzy number of the comprehensive decision matrix.

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