Theoretical Research And Application Of Dual Hesitant Fuzzy Sets

Fuzzy theory is mainly used to solve problems that have ambiguity and uncertainty,this theory will study a range from precise mathematical extended to fuzzy this area.Practice shows that fuzzy sets and their extended models play a very important role in solving problems with ambiguity and uncertainty.However,the real world is extremely complex,and the fuzzy set theory proposed by Zadeh can't be applied to all fuzzy problems.Therefore,scholars at home and abroad have extended the traditional fuzzy sets.For example,Atanassov proposed the concept of intuitionistic fuzzy sets by considering membership,non-membership and hesitation at the same time,so as to deal with uncertain problems more flexibly.However,some scholars consider the degree of membership,and the degree of non-membership may not be a certain number,but an interval.Therefore,a new concept of interval-valued intuitionistic fuzzy sets is proposed.For another example,decision makers may be hesitant when making evaluations.At this time,some scholars have proposed hesitating fuzzy sets to solve this potential problem.Therefore,fuzzy sets have many extended models.This article mainly based on the two concepts of interval-valued intuitionistic hesitant fuzzy sets and intuitionistic dual hesitant fuzzy sets,the following work is done:(1)In chapter 2,based on the concept of interval-valued intuitionistic hesitant fuzzy sets,the distance measure of interval-valued intuitionistic hesitant fuzzy sets is first studied,and the related definition and its standard Hamming distance measure formula are given,and then proved it shows that the formula proposed in this paper is reasonable,and then gives its weighted Hamming distance measure,standard Euclidean distance measure,weighted Euclidean distance measure and Hausdorff distance measure.Secondly,the correlation coefficient and weighted correlation coefficient of interval-valued intuitionistic hesitant fuzzy sets are studied,and the definition,properties and necessary proofs of the correlation are given.Thirdly,the entropy of interval-valued intuitionistic hesitant fuzzy sets is studied,and the calculation formula of its entropy is given.Finally,the application of interval-valued intuitionistic hesitant fuzzy sets in the multi-attribute group decision-making problem is given.First,the comprehensive weighting method is used to determine the comprehensive weight of each attribute when the subjective and objective weights are known,and then based on the interval respectively.Two algorithms are given for the distance measure and correlation coefficient of the interval-valued intuitionistic hesitant fuzzy sets.Finally,an example is given.Algorithm 1 and Algorithm 2 are used to calculate respectively.The calculation results show that the calculation results of the two algorithms are not completely consistent.But for decision makers,the final choice is exactly the same.Therefore,whether it is a basic distance measure or based on correlation coefficients,interval-valued intuitionistic hesitant fuzzy sets can describe the uncertainty of the problem well and are practical and effective.(2)In chapter 3,based on the concept of intuitionistic dual hesitant fuzzy sets,the distance measure of intuitionistic dual hesitant fuzzy sets is first studied,and the related definition and its standard Hamming distance measure formula are given.Then it is explained by proof rational formula proposed,which in turn gives the weighted Hamming distance measurement,a standard Euclidean distance measure,the weighted Euclidean distance measure and Hausdorff distance measure.Secondly,the correlation coefficients and weighted correlation coefficients of intuitionistic dual hesitant fuzzy sets are studied,and the relevant definitions,properties and necessary proofs are given.Thirdly,the entropy of the intuitionistic dual hesitant fuzzy sets is studied,and the calculation formula of its entropy is given.Finally,the application of intuitionistic dual hesitant fuzzy sets in multi-attribute group decision-making problems is given.First,based on the entropy of intuitionistic dual hesitant fuzzy sets,an attribute objective weight model is established,and then a comprehensive weighting method is used to determine the subjective and objective weights.Given the knowledge,the comprehensive weight of each attribute is then given two algorithms based on the distance measure and correlation coefficient of the intuitionistic dual hesitant fuzzy sets.Finally,an example is given,which is calculated using Algorithm 1 and Algorithm 2.The calculation results show that the calculation results of the two algorithms are not completely consistent,but for the decision maker,the final choice is exactly the same.Therefore,whether it is the basic distance measure or the correlation coefficient,the intuitionistic dual hesitant fuzzy sets can describe the uncertainty of the problem well and are practical and effective.