CN112506977B - Interval intuitionistic fuzzy multi-attribute group decision provider selection method - Google Patents
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Abstract
The invention discloses a method for selecting a decision provider of interval intuitionistic fuzzy multi-attribute groups, which comprises the steps of firstly, utilizing an existing operator to integrate decision matrixes of each expert to form an average decision matrix, splitting the decision matrix of each expert into a membership matrix, a non-membership matrix and a hesitation matrix, calculating the bidirectional projection values of the membership matrix and the non-membership matrix of each expert and the average decision matrix according to a value hesitation matrix by using an improved bidirectional projection formula, and finally, carrying out weighted fusion on three projection values to calculate the similarity of each expert and the groups so as to determine the weight of each expert. And finally, carrying out group decision through the determined weight, and selecting the optimal supplier. The method fully considers the definition and the effect of the interval intuitional fuzzy number, so that the decision result, namely the sequencing of suppliers, is more reasonable.
Description
Technical Field
The invention relates to a population decision-making method, in particular to a section intuitionistic fuzzy multi-attribute population decision-making provider selection method.
Background
The supplier selection is essentially a multi-attribute group decision problem, the evaluation method is an important exogenous force affecting the supplier selection, and the selection of an effective evaluation method is a major issue for the supplier selection. To describe the decision information, zadeh proposes the concept of fuzzy sets. However, with the occurrence of complex decision problems, only fuzzy sets containing membership are used to describe decision information that is already manifested as debilitation. Thus, to more fully describe complex decision problems, atanasov proposes an intuitive fuzzy set containing membership, non-membership, and hesitation. In a real-world situation, however, it is difficult to give accurate values describing membership and non-membership due to limited knowledge of the decision maker. Based on this, atanasov and gargo were first proposing interval intuitive ambiguity sets in 1989. The interval intuitionistic fuzzy set can better describe and describe the fuzzy characteristic of the decision information, so that the method is well applied.
The most studied about interval intuitionistic fuzzy multi-attribute group decision-making problems at present are expert weight determination, attribute weight determination, aggregation method determination, sequencing method determination and the like. For the same decision matrix, different expert weights may lead to different final decision results, and there are currently the following research methods to determine expert weights. Yue first establishes an ideal population decision, i.e. the mean of the population decisions. Expert weights are then determined from similarity measures between each individual decision and the ideal decision according to the TOPSIS concept. Zhang and Xu establish an optimal model based on consensus maximization to determine the weight of the expert by measuring the degree of consensus between individuals and groups. The Meng calculates the distance between the decision matrix of each expert and the decision matrix of the other expert to determine the expert weight. Wan defines the similarity of the interval intuitionistic fuzzy set, calculates the similarity between the experts based on the similarity, and determines the weight of the experts through the calculated similarity. An expert weight determination method based on unidirectional projection is proposed.
According to the above-mentioned literature study, the expert weights are mainly determined by similarity or proximity, but none of the above documents uses hesitation information in decision making, and the consideration is not comprehensive enough, and the definition of the interval intuitionistic ambiguity is not fully considered.
Disclosure of Invention
Aiming at the problem of supplier selection, the application provides a section intuitionistic fuzzy multi-attribute group decision method; according to the method, similarity of expert judgment is calculated according to judgment information given by an expert, so that group expert weights are determined, group comprehensive attribute values of suppliers are obtained according to the expert weights, and a sequencing result is given.
In order to achieve the above purpose, the technical scheme of the application is as follows: a method of interval intuitive fuzzy multi-attribute group decision provider selection, comprising:
constructing decision matrixes of all experts for evaluating the attributes of suppliers, and aggregating the decision matrixes to obtain an average decision matrix;
the average decision matrix and expert D k The decision matrix is divided into a membership matrix, a non-membership matrix and a hesitation matrix;
obtaining an average decision matrix and an expert D by utilizing an improved two-way projection formula k The bi-directional projection values of the membership matrix, the non-membership matrix and the hesitation matrix of the decision matrix are respectivelyWherein->And->Average decision matrix and expert D, respectively k A membership matrix, a non-membership matrix, and a hesitation matrix of the decision matrix;
obtaining the similarity of each expert and the group through the two-way projection values;
acquiring the weight of each expert;
after the expert weight is acquired, the comprehensive decision matrix X is obtained by aggregation, each row of the comprehensive decision matrix X is aggregated, the score is calculated according to the result, and finally the sequencing scheme is obtained.
Further, a decision matrix of all experts for evaluating the provider attributes is constructed, and the decision matrix is aggregated to obtain an average decision matrix, specifically:
in the case that expert decision opinion is an interval intuitionistic fuzzy number, let the supplier set be a= { a 1 ,A 2 ,...,A m Attribute set g= { G of vendor } 1 ,G 2 ,...,G n The decision expert set is d= { D } 1 ,D 2 ,...,D n -a }; for convenience, this time, the notation m= {1,2, M, n= {1,2, the N, t= {1,2, & gt, T }, set expert D k At A i Under the scheme, attribute G j The evaluation value of (a) is the intuitive fuzzy number of the intervalHesitation degree of->Expert D k The attribute evaluation value decision matrix for the provider is:
obtaining a decision matrix of each expert and reusing the formula
Aggregation is carried out to obtain an average decision matrix; wherein the method comprises the steps ofThe number of the intuitive fuzzy numbers is a group of interval, and n is the number of decision makers;
wherein the method comprises the steps of
And (i ε M, j ε N).
Further, the average decision matrix and expert D k The decision matrix is divided into a membership matrix, a non-membership matrix and a hesitation matrix, and specifically comprises the following steps:
further, an average decision matrix and expert D k The bi-directional projection values of the membership matrix, the non-membership matrix and the hesitation matrix of the decision matrix are respectively as follows:
the bi-directional projection value of the membership matrix is as follows:
wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided with
The bi-directional projection value of the non-membership matrix is as follows:
wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided withThe bi-directional projection value of the hesitation matrix is as follows: />
Wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided with
Further, the similarity between each expert and the group is obtained through the two-way projection value, specifically:(θ 1 ,θ 2 ,θ 3 ) Is obtained by averaging the intermediate value of each interval value of the membership degree matrix, the non-membership degree matrix and the hesitation degree matrix of the average decision matrix, and theta 1 +θ 2 +θ 3 =1; the higher the similarity, the higher the weight should be given to the expert, whereas the lower the similarity, the lower the decision value and the lower the weight should be given to the expert.
Further, the weight of each expert is calculated according to the similarity between each expert and the group:
wherein->
Further, after the expert weights are obtained, the decision matrix of all the experts is clustered through the calculated expert weights to obtain a comprehensive decision matrix X, then each row of the comprehensive decision matrix X is clustered, and a score is calculated according to the result, so that a sorting scheme is finally obtained, wherein the method comprises the following steps of:
by expert weights, by
Weighted arithmetic mean operator IIFWA for interval intuitionistic blurring, whereinFor a set of interval intuitional ambiguities, ω= (ω) 1 ,ω 2 ,…,ω n ) T Is->Is a weight vector of (2); aggregating all expert decision matrices to obtain a comprehensive decision matrix, aggregating each row of the comprehensive matrix, and calculating the score of each supplier according to the following formula:
wherein the method comprises the steps ofIs an interval intuitionistic fuzzy number and is finally utilized
Ranking the individual suppliers to obtain a ranked result and selecting an optimal supplier.
The invention has advantages over existing methods in terms of: the invention uses improved bi-directional projection to determine the similarity of the expert and the population to determine the expert weight. The defect that the traditional projection method has misjudgment of similarity in the application of the traditional projection method to the problems is overcome. And dividing the decision matrix into a membership degree matrix, a non-membership degree matrix and a hesitation degree matrix, respectively carrying out two-way projection, carrying out weighted fusion on the three projection values to determine the similarity of the expert and the group, and obtaining the weight of the expert. Compared with the prior art, the definition and the effect of the interval intuitionistic fuzzy number are fully considered, so that the decision result, namely the sequencing of suppliers is more reasonable.
Drawings
FIG. 1 is a flow chart of a method for selecting a block intuitive fuzzy multi-attribute group decision provider.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and to specific embodiments: this is taken as an example to describe the present application further.
Aiming at the problem of selecting the provider with the provider attribute evaluation value of interval intuitionistic fuzzy number by the expert, on the premise that the expert weight is completely unknown, the more similar the expert is to the group, the larger the weight is, and therefore, a weighted interval number matrix two-way projection formula is designed for determining the weight of the expert. The invention firstly uses the existing operators to integrate the decision matrix of each expert to form an average decision matrix, uses the decision matrix of each expert to split into a membership matrix and a non-membership matrix with value hesitation matrix, uses the improved bidirectional projection formula to calculate the bidirectional projection values of the membership matrix and the non-membership with value hesitation matrix of each expert and the average decision matrix, and finally carries out weighted fusion on the three projection values to calculate the similarity of each expert and the group so as to determine the weight of each expert. And finally, carrying out group decision through the determined weight, and selecting the optimal supplier.
In order to prove the effectiveness of the method provided by the invention, data of Zhang are used for comparison calculation. Plastic watch limited (FWCL) is a large well known manufacturer who has its own chain of watches in asia and whose board would like to choose a material provider to purchase critical parts in order to develop new products to achieve a market competitive advantage. The composition is d= { D 1 ,D 2 ,D 3 ,D 4 Decision committee composed of four experts from 5 qualified suppliers a= { a according to the following four attributes 1 ,A 2 ,A 3 ,A 4 ,A 5 Select suppliers (1) G 1 The quality of the product is achieved; (2) G 2 Is the relationship of intimacy; (3) G 3 For delivery capacity; (4) G 4 Is the experience time. In the actual decision process, the weights of the experts and attributes are typically determined by direct assignment by the manager (decision maker) or the AHP method. Here, it is assumed that the weight vector w= (W) of the attribute is known completely in advance 1 ,w 2 ,w 3 ,w 4 ) T ＝(0.3,0.2,0.3,0.2) T 。
Expert D 1 The decision matrix for the four attributes of the five suppliers is shown in the following formula, and the rest of the details are shown in Zhang literature.
Step one: constructing a decision matrix of four experts for evaluating the attributes of the suppliers, and aggregating the decision matrix to obtain an average decision matrix
Step two: splitting the average decision matrix into interval value membership matrixInterval value non-membership matrix->Zone value hesitation matrix ++>Wherein each interval value of the membership matrix represents the supply of an expert to a certain providerThe support degree of a certain attribute of the vendor, the non-membership degree represents the objectivity, and the hesitation degree represents the neutrality;
expert D k Is divided into interval value membership degree matrixInterval value non-membership matrix->Zone value hesitation matrix ++>Wherein each interval value of the membership matrix represents the support of an expert on a certain attribute of a certain supplier provider, the non-membership represents the objection, and the hesitation represents the neutrality. In D 1 For example, the following are shown:
step three: using improved two-way projection formula to calculate average decision matrixExpert D k Decision matrix->The bi-directional projection values of (2) are shown in the following table;
TABLE 1 expert D k Two-way projection values of decision matrix and average decision matrix
Step four: computation expert D k Similarity to population:
the preference degree of membership degree, non-membership degree and hesitation degree, namely the weight is 0.4,0.4,0.2, is obtained through calculation.
TABLE 2 expert D k Similarity to population
Step five: acquiring the weight of each expert
Wherein,
step six: and D, aggregating decision matrixes of all the experts by using the expert weight and aggregation formula obtained in the step five to obtain a comprehensive attribute evaluation matrix of five suppliers as follows:
the attribute weight is w= (W 1 ,w 2 ,w 3 ,w 4 ) T ＝(0.3,0.2,0.3,0.2) T And then, the data of each row of the comprehensive matrix is aggregated by using an aggregation formula to obtain the comprehensive interval intuitionistic fuzzy evaluation values of five suppliers, and the calculation score function is used as the following table:
TABLE 3 scoring of the various protocols
As shown in table 3: the sorting result of the five suppliers calculated by the invention is that
A 3 ＞A 5 ＞A 1 ＞A 4 ＞A 2 。
The method is compared with the following steps:
TABLE 4 sequencing results
TABLE 5 weights obtained by several methods
Ranking results analysis from overall suppliers: it can be seen from table 4 that the ordering result of other methods is not completely consistent with the ordering result of the method provided by the invention, but the trend is approximately the same, on one hand, the effectiveness of the method provided by the invention is illustrated, on the other hand, the ordering result obtained by aggregation is not the same as the weight obtained by the invention is different from the weight obtained by other methods, firstly, compared with Meng Junna unidirectional projection, the unidirectional projection is not strict enough when processing the problem, and the situation of misjudgment of similarity can be caused, so that the error in decision is caused, the method combines the mutual projection values among the matrixes, and in the process of processing the projection, the improved bidirectional projection of the invention considers the influence of the weight among the attributes on the projection value in the process of processing the projection, fully utilizes the information of the data, can eliminate the influence and more can illustrate the similarity of the two matrixes; compared with the Yue and Zhang methods, the above documents do not fully consider the definition of interval intuitionistic ambiguity numbers, and a group of interval intuitionistic ambiguity numbers comprise membership non-membership and hesitation information, which respectively represent that three attitudes are supported, opposite and neutral and have different meanings. According to the invention, the interval intuitionistic fuzzy decision matrix of each expert is disassembled to respectively calculate the similarity of the non-membership matrix and the hesitation matrix of the membership matrix, and then the three similarities are subjected to weighted fusion, so that not only can the hesitation information be considered, but also the definition and the action of the membership degree, the non-membership degree and the hesitation are fully considered, the determination of the similarity is more reasonable, the obtained expert weight is more reasonable, and the preferred ordering of suppliers is more reasonable.
Moreover, as can be seen from table 5, compared with the above method, the method of the invention has lower discrete degree on the determined expert weight, thus the decision expert power is more centralized, the expert weight ratio is scientific, and the consistency of the decision result is high. So the method is more reasonable.
In summary, the method fully considers the information between the data, compared with the traditional projection method, not only eliminates the situation of misjudgment of the similarity, but also considers the influence of the weight between the attributes on the calculated projection value, and the cited document is more fully considered by comparing with the hesitation information in decision. In addition, the dispersion degree of the expert weights determined by the method is low, so that the decision expert rights are more centralized, the expert weight ratio is scientific, and the consistency of the decision result is high. The vendor selection method of the present invention is more scientific and reasonable than the other three.
While the invention has been described with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (4)
1. A method for selecting a block intuitive fuzzy multi-attribute group decision provider, comprising:
constructing decision matrixes of all experts for evaluating the attributes of suppliers, and aggregating the decision matrixes to obtain an average decision matrix;
the average decision matrix and expert D k The decision matrix is divided into a membership matrix, a non-membership matrix and a hesitation matrix;
obtaining an average decision matrix and an expert D by utilizing an improved two-way projection formula k The bi-directional projection values of the membership matrix, the non-membership matrix and the hesitation matrix of the decision matrix are respectivelyWherein->And->Average decision matrix and expert D, respectively k A membership matrix, a non-membership matrix, and a hesitation matrix of the decision matrix;
obtaining the similarity of each expert and the group through the two-way projection values;
acquiring the weight of each expert;
after the expert weight is acquired, firstly assembling to obtain a comprehensive decision matrix X, assembling each row of the comprehensive decision matrix X, calculating a score according to the result, and finally obtaining a sequencing scheme;
constructing decision matrixes of all experts for evaluating the attributes of the suppliers, and aggregating the decision matrixes to obtain an average decision matrix, wherein the decision matrixes are specifically as follows:
in the case that expert decision opinion is an interval intuitionistic fuzzy number, let the supplier set be a= { a 1 ,A 2 ,...,A m Attribute set g= { G of vendor } 1 ,G 2 ,...,G n The decision expert set is d= { D } 1 ,D 2 ,...,D n -a }; the time history m= {1,2,., M }, N = {1,2,., N }, T = {1,2,., T }, set expert D k At A i Under the scheme, attribute G j The evaluation value of (a) is the intuitive fuzzy number of the intervalHesitation degree of->Expert D k The attribute evaluation value decision matrix for the provider is:
obtaining a decision matrix of each expert and reusing the formula
Aggregation is carried out to obtain an average decision matrix; wherein the method comprises the steps ofThe number of the intuitive fuzzy numbers is a group of interval, and n is the number of decision makers;
wherein the method comprises the steps of
And (i ε M, j ε N);
the average decision matrix and expert D k The decision matrix is divided into a membership matrix, a non-membership matrix and a hesitation matrix, and specifically comprises the following steps:
average decision matrix and expert D k The bi-directional projection values of the membership matrix, the non-membership matrix and the hesitation matrix of the decision matrix are respectively as follows:
the bi-directional projection value of the membership matrix is as follows:
wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided withThe bi-directional projection value of the non-membership matrix is as follows: />
Wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided with
The bi-directional projection value of the hesitation matrix is as follows:
wherein the method comprises the steps of
ω is the satisfaction ω= (ω) of the vector in the weight of each attribute 1 ,ω 2 ,…,ω n ) And is also provided with
2. The interval intuitionistic fuzzy multi-attribute group decision provider selection method of claim 1, wherein the similarity between each expert and the group is obtained by the bi-directional projection values, specifically:(θ 1 ,θ 2 ,θ 3 ) Is obtained by averaging the intermediate value of each interval value of the membership degree matrix, the non-membership degree matrix and the hesitation degree matrix of the average decision matrix, and theta 1 +θ 2 +θ 3 =1; the higher the similarity is, the higher the weight should be given to the expert, otherwise, the expert with smaller similarity has smaller decision value and is given toLess weight.
3. The interval intuitionistic fuzzy multi-attribute group decision provider selection method of claim 1, wherein each expert weight is calculated according to similarity between each expert and the group:wherein->
4. The interval intuitionistic fuzzy multi-attribute group decision provider selection method according to claim 1, wherein after the expert weights are obtained, the decision matrices of all the experts are gathered through the calculated expert weights to obtain a comprehensive decision matrix X, then each row of the comprehensive decision matrix X is gathered, and a score is calculated according to the result to finally obtain a sorting scheme, which is specifically as follows:
by expert weights, by
Weighted arithmetic mean operator IIFWA for interval intuitionistic blurring, whereinFor a set of interval intuitional ambiguities, ω= (ω) 1 ,ω 2 ,…,ω n ) T Is->Is a weight vector of (2); the decision matrix of all experts is aggregated to obtain a comprehensive decision matrix, each row of the comprehensive decision matrix is aggregated by the above formula, and the score of each supplier is calculated by the following formula:
wherein the method comprises the steps ofIs an interval intuitionistic fuzzy number and is finally utilized
Ranking the individual suppliers to obtain a ranked result and selecting an optimal supplier.
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