Hesitant Fuzzy Multi-attribute Decision-making Method And Application Based On Divergence Measure

The hesitance fuzzy set can describe the opinions of different decision makers on a certain scheme in the form of set and can reflect the real decision information of decision makers.Divergence measure is a measure method used in random distribution to describe the degree of difference between two random distributions.Since the element values of the hesitating fuzzy set are all between 0 and 1,which conforms to the application criteria of the divergence measure,this paper adopts the divergence measure method to study the degree of difference of the relevant information of the hesitating fuzzy set.The research content of this paper mainly includes the following aspects.(1)The data completion method of hesitating fuzzy element is studied.In this paper,based on the existing methods of fuzzy metadata complement for hesitation,the Matthew effect theory is proposed to complete the data,that is,to judge the degree of risk decision of decision maker by using quantitative method,and then select the appropriate element value to complete the data.(2)The problem of hesitating fuzzy divergence measure is studied.According to the axiomatic definition of hesitant fuzzy divergence measure,the axiomatic definition of the divergence measure of hesitant fuzzy element is presented,and the symmetric chi-square divergence measure of the hesitant fuzzy element is presented.On this basis,the symmetric chi-square divergence measure of hesitating fuzzy sets is proposed in this paper.In order to consider the importance of weights,a weighted symmetric chisquare divergence measure of hesitating fuzzy is proposed.(3)Hesitation fuzzy divergence measure is applied to multi-attribute decision making.Firstly,the hesitating fuzzy multi-attribute decision making model based on symmetric divergence measure is proposed,and the optimal scheme is obtained by using TOPSIS method to sort the schemes,and the feasibility and effectiveness of the method are proved by numerical examples.Secondly,the divergence measure of hesitating fuzzy element is used to construct the prospect value function,and the comprehensive prospect value is used to make multi-attribute decision,and an example is given to prove the effectiveness of this method.Finally,the hesitant fuzzy multiattribute decision-making model based on symmetric divergence measure is applied to the evaluation and decision-making of ecological protection and high-quality development of the Yellow River Basin,and the index system of the Yellow River Basin is constructed.Through the application of this method,the ecological protection and high-quality development of different cities are evaluated.