Three-way Decisions On Pythagorean Fuzzy Sets Based On Dominance Relations

With the development of science and technology,the data that people faced becomes more and more complex,and how to express the uncertainty of information more accurately is a hot research topic.Pythagorean fuzzy sets that are extension of intuitionistic fuzzy sets describe information through the degree of membership and the degree of non-membership,and require that the sum of the squares of the degrees of membership and non-membership is less than or equal to 1.In addition,a lot of data faced in real life has a preference relation,that is,the relation of “excellent” or“inferior”.In this case,the equivalence relation is no longer practical,and the dominance relation is more suitable at this time.Due to the complexity and uncertainty of the data,what kind of measures should be taken is also a problem to be solved.The three-way decision is an extension of the two-way decision.A boundary domain is added,and the elements that cannot be judged based on current information are divided into the boundary domain.Three-way decision theory has been successfully applied to feature selection,image recognition,text processing,recommendation system,group decision making and so on.Therefore,this paper explores three-way decision on Pythagorean fuzzy sets based on the dominance relation,which makes the research results of Pythagorean fuzzy sets richer.The main content of this article is as follows:(1)Three-way decision on Pythagorean fuzzy sets based on the dominance relation is studied.First,the dominance relation is defined on Pythagorean fuzzy set,and then two conditional probabilities in Pythagorean fuzzy sets are defined according to the dominance class obtained by division.Finally,combined with three-way decision,two three-way decision models on Pythagorean fuzzy sets are explored,and algorithms of two three-way decision models are listed respectively.(2)Discuss three-way decision on Pythagorean fuzzy multisets based on distance dominance relation.First,Pythagorean fuzzy sets and multisets are combined to define Pythagorean fuzzy multisets,and basic operations are defined.Then a distance dominance relation is defined on Pythagorean fuzzy multisets,and some related properties are studied.Finally,a three-way decision model and group decision model of Pythagorean fuzzy multisets are discussed.