Research On Pythagorean Fuzzy Multi-Attribute Decision Making Method Based On Regret Theory

With the rapid development of social and economy,traditional crisp numbers have been difficult to solve real-world decision-making problems.The concept of fuzzy set opens a new perspective for us to study uncertain information and it has attracted wide attention of scholars.Based on the theory of fuzzy set,the concepts of intuitionistic fuzzy set and Pythagorean fuzzy set have been put forward.Pythagorean fuzzy set is a further extension of intuitionistic fuzzy set.Compared with the intuitionistic fuzzy set,the Pythagorean fuzzy set has higher capacity in representing uncertain information and stronger applicability in describing fuzzy multi-attribute decision making information.Therefore,many scholars use the Pythagorean fuzzy set to study the multi-attribute decision-making problems and the results are fruitful.But there are still some areas that need to be improved.This paper supplements Pythagorean fuzzy multi-attribute decision-making on the basis of summarizing previous research results.In terms of attribute weight,this paper presents three kinds of weighting methods for Pythagorean fuzzy multi-attribute decision making problem with unknown attribute weight.In terms of decision model,this paper constructs two kinds of multi-attribute decision models: the Pythagorean multi-attribute decision model based on regret theory and the dynamic Pythagorean fuzzy multi-attribute decision model based on regret theory.The research contents and achievements of this paper include:(1)Score function based on Pythagorean fuzzy number.Because the size of the Pythagorean fuzzy number cannot be directly used for comparison,many scholars use the scoring function to convert the Pythagorean fuzzy number into a crisp number for comparison.A reasonable score function is an important guarantee for comparing the scientific results.Aiming at the shortcomings of the existing scoring function,this paper proposes a new scoring function to solve the problems of unreasonable definition and low discrimination of the existing scoring function.(2)Weighting method based on Pythagorean fuzzy information.For Pythagorean fuzzy multi-attribute decision weighting,this paper proposes three kinds of Pythagorean fuzzy multi-attribute decision making methods,which are subjective weighting method based on DEMATEL method,objective weighting method based on similarity principle and subjective objective comprehensive weighting method based on linear weighting method.(3)Multi-attribute decision making method based on Pythagorean fuzzy information.This paper proposes two decision-making models: Pythagorean multi-attribute decision making model based on regret theory and dynamic Pythagorean fuzzy multi-attribute decision-making model based on regret theory.In addition,the proposed fuzzy multi-attribute decision making of Pythagorean is applied to the selection of angel investors for start-ups.Firstly,the index system for the evaluation of start-ups is constructed,and then the method for angel investors to choose startups based on Pythagoras fuzzy information is designed to provide theoretical support for angel investors in choosing startups.