Decision-making Method And Its Application In Hesitant Fuzzy Environment

In a multi-attribute decision-making problem,when facing a certain problem,decision makers usually hesitate.As an important tool for solving uncertainty problems,the hesitant fuzzy set can better express the evaluation results of decision makers' hesitation.Therefore,in recent years,people often use hesitant fuzzy sets when solving multi-attribute decision-making problems.This article aims to introduce a series of applications of hesitant fuzzy sets in multi-attribute decision-making.The multi-attribute decision model in the hesitant fuzzy environment is evaluated based on the integration of attribute information,so the integration of hesitant fuzzy information is the key to the decision-making process.Based on this,this paper first proposes the weighted hesitant fuzzy priority average operator and the weighted hesitant fuzzy priority geometry operator,and then proves that these two types of operators satisfy the basic properties of general operators.A multi-attribute group decision-making model based on this operator is constructed,and the decision-making model is applied to actual case analysis,and the validity of the proposed model is further illustrated by this example.Secondly,since hesitant fuzzy entropy is also an important tool for integrating data,this article summarizes a new axiomatic definition of hesitant fuzzy entropy,constructs an exponential hesitant fuzzy element entropy measurement formula,and gives the entropy definition of hesitation fuzzy set and entropy measure formula at the same time.Based on this,the entropy is compared with the existing hesitant fuzzy entropy through the calculation results of several hesitant fuzzy elements,and the final analysis shows that the exponential hesitation fuzzy entropy is effective.Finally,using the exponential hesitation fuzzy entropy,a multi-attribute decision model based on the entropy weight method is constructed,and the practicality of the exponential hesitation fuzzy entropy is analyzed through specific cases.This article mainly has the following two innovations: First,the weighted hesitant fuzzy priority operator addresses issues such as the lack of attribute information membership and the priority relationship of attribute information that may appear in the existing multi-attribute group decision-making process,and makes full use of the decision maker's evaluation data for a certain attribute,so that the final evaluation results are more comprehensive;Second,the exponential hesitant fuzzy entropy proposed in this paper can not only satisfy the existing basic criteria for the axiomatic definition of fuzzy entropy,but also deal with the fuzzy entropy of some special hesitant fuzzy elements,so that the fuzziness of hesitant fuzzy elements can be fully expressed.Therefore,the entropy theory of hesitant fuzzy sets has been further improved.