TOPSIS And VIKOR Decision Methods Based On Pythagorean Fuzzy Set Representation

Intuitionistic fuzzy set,as an extension of traditional fuzzy set,has long been a hot issue.Pythagorean fuzzy set(PFS)is not only a generalization of traditional intuitionistic fuzzy set,but also a more comprehensive use of membership,non membership and hesitation to describe the fuzzy phenomenon of objective things than intuitionistic fuzzy set.In particular,it can deal with the decision-making problem of multi-attribute index information in a wider area.Their common ground is to consider the three attitudes of support,opposition and abstention at the same time,that is,they contain fuzzy information in three aspects:membership,non membership and hesitation,so that people can more objectively describe the essential characteristics of things.At present,TOPSIS method and VIKOR decision-making method have always attracted extensive attention of many scholars as dealing with multi-attribute decision-making problems.Their main feature is to calculate the index information such as positive and negative ideal solution,relative closeness and group utility value according to the initial decision-making matrix given by experts,so as to provide the optimal decision-making method for decision-makers.The main contents of this paper are arranged as follows.The first part:Background and research status of the topic.The second part:Preliminary knowledge.It mainly introduces the concepts of intuitionistic fuzzy sets(IFS)and Pythagorean fuzzy sets and their arithmetic operations.The third part:Based on the comparison between the distance of Pythagorean fuzzy number(PFN)and the minimum element(0,1),the concept of modulus and projection is proposed.The concept of bidirectional projection is introduced through positive and negative ideal values,and then a new VIKOR decision-making method is given according to the bidirectional projection of PFN.Finally,an example is given to verify the effectiveness of the method.The fourth part:This paper points out some shortcomings of the traditional score function,and then puts forward new score function,exact function and ranking criterion through risk preference factor.In addition,according to the ranking criteria of discrete fuzzy Choquet integral average operator and risk preference score function,a new Pythagorean fuzzy decision-making method is given,and an example is given to verify the effectiveness of the decision-making method.The fifth part:Considering the hesitation degree,the concepts of centroid coordinates and hesitation factor of PFN are introduced according to the geometric method,and then a new distance measure and similarity are proposed.Secondly,the weight formula of the existing priority integration operator is improved according to the PFN similarity,the method of Pythagorean fuzzy priority weighted average(PFPWA)integration operator is given,and the related properties of the integration operator are discussed.Finally,a new TOPSIS method is proposed by calculating the positive(negative)hesitation solution,two-way projection and closeness.An example is given to illustrate the effectiveness of this method in dealing with multi-attribute information.