Approaches And Applications To Multiple Attribute Decision Making Under Pythagorean Fuzzy Environment

In real life,decision making problems widely exist in many fields such as economy,society and management.Among them,multiple attribute decision making and preference relations play important roles.With the development of economy and society,decision making problems become more and more complicated,and decision makers are more inclined to give vague and uncertain evaluation information.As a generalization of intuitionistic fuzzy sets,Pythagorean fuzzy sets have greater flexibility,and have received widespread attention from scholars at home and abroad in recent years.This paper studies several methods and applications of multiple attribute decision making in Pythagorean fuzzy environment.The structure of this paper is arranged as follows:Chapter 1 mainly introduces the research background and significance of this paper.At the same time,it analyzes and summarizes the research situations at home and abroad,and puts forward the problems to be studied in this paper.Chapter 2 introduces fuzzy set,hesitant fuzzy set,intuitionistic fuzzy set,Pythagorean fuzzy set,Pythagorean hesitant fuzzy set,Pythagorean fuzzy aggregation operators,intuitionistic fuzzy preference relations,TOPSIS method and grey relational analysis.Chapter 3 proposes a Pythagorean hesitant fuzzy multiple attribute decision making method based on prospect theory and grey correlation degree.Firstly,defining the Pythagorean hesitant fuzzy grey correlation degree and the Pythagorean hesitant fuzzy prospect value function.Then,based on the grey correlation degree,the difference set of each solution with respect to the positive and negative ideal solutions is defined,and the Pythagorean fuzzy decision matrix is converted into a value matrix by combining the prospect value function.Finally,the Pythagorean fuzzy grey relational multiple attribute decision making method based on prospect theory is presented,and the superiority of the new method is verified by an example.Chapter 4 presents a Pythagorean hesitant fuzzy multiple attribute decision making method based on projection model.Firstly,a Pythagorean hesitant fuzzy projection model is proposed according to the least common multiple expansion method.Secondly,for the multiple attribute decision making problem where the attribute weight information is completely unknown,an attribute weight determination model based on maximizing variance is proposed.Finally,a Pythagorean hesitant fuzzy TOPSIS method based on the projection model is proposed,and the effectiveness of this method is proved by the example of performance evaluation of financial enterprises.Chapter 5 develops a multiple attribute decision making method based on additive Pythagorean fuzzy preference relations.Firstly,a new Pythagorean fuzzy weight determination model is proposed based on additive consistent Pythagorean fuzzy preference relations.Then,the definition of Pythagorean fuzzy preference relations with acceptable consistency is given,and an additive consistency adjustment algorithm is developed for Pythagorean fuzzy preference relations that do not satisfy acceptable additive consistency.Finally,a multiple attribute decision making method based on additive consistency Pythagorean fuzzy preference relations is proposed,and by comparison with other methods,the validity and rationality of the proposed method are verified.Finally,the conclusion chapter summarizes the research results and gives a prospect for the future research.