Multiple Attribute Decision Making And Its Application Research Based On Dual Hesitant Fuzzy Sets

As an extension of fuzzy set,dual hesitant fuzzy set allows the membership hesitancy function and the non-membership hesitancy function two sets of possible values between 0 and 1 when the decision makers provide different opinions on the same scheme.Dual hesitant fuzzy set has been plenty of attention in the last few decades and achieved some good results due to the fact that they can be applied to many areas such as cluster analysis,approximate reasoning,image processing,medical diagnosis,decision making and information integration.So it has great theoretical significance and application of studying the multiple attribute decision making and application of dual hesitant fuzzy set.The research object of this paper is the dual hesitant fuzzy set,and the main contents and innovative work include:In chapter one,the historical backgrounds and current situations of dual hesitant fuzzy set theory and application are introduced,some related concepts of dual hesitant fuzzy sets are given in an introductory.The second chapter introduces aggregation of convex dual hesitant fuzzy set.This part establishes some basic concepts of convexity for dual hesitant fuzzy sets and investigates some properties and relationships among the convexity.Besides,in order to guarantee that the composition of dual hesitant fuzzy sets preserves convexity,we focus on aggregation functions for dual hesitant fuzzy elements,these aggregation functions are further extended for dual hesitant fuzzy sets as well as for the convex structures of these sets.The third chapter is about dual hesitant fuzzy probability.This part extends the notion of dual hesitant fuzzy probabilities by representing probabilities through the dual hesitant fuzzy number based on the intuitionistic fuzzy number,we also investigate some properties of dual hesitant fuzzy probability and apply it in color blindness.The fourth chapter proposes dual extended hesitant fuzzy set.This part develops the dual extended hesitant fuzzy sets,then studies the basic operations and the desirable properties of dual extended hesitant fuzzy elements in detail.At last,some correlation coefficients between dual extended hesitant fuzzy sets are developed to apply in investment problem.The fifth chapter discusses about distance measures of higher order dual hesitant fuzzy set.This part proposes new distance measures for dual hesitant fuzzy sets,which overcome some drawbacks of the existing distance measures.Meanwhile,we extend dual hesitant fuzzy set to its higher order type and refer to it as the higher order dual hesitant fuzzy set,in order to indicate higher order dual hesitant fuzzy sets have a good performance in information system project evaluation problem,we introduce several distance measures for higher order dual hesitant fuzzy sets based on our proposed new distance for dual hesitant fuzzy sets.The sixth chapter is the conclusion and outlook of the article.In this part,the main work and innovation of this paper are summarized,and we also discuss the future research work.