Pythagorean Fuzzy Set And Its Application In Multi-attribute Decision Making

Pythagoras fuzzy set is an effective extension of intuitionistic fuzzy set,which can better express decision information.As a new kind of intuitionistic fuzzy sets,the related research of Pythagoras fuzzy sets needs to be further improved.In this paper,the properties of Pythagorean fuzzy sets and the application of Pythagorean fuzzy numbers in multi-attribute decision making are studied.(1)Considering the interaction between membership degree and non-membership degree,the operation formulas between different Pythagorean fuzzy numbers are defined,and the related properties are discussed.(2)In view of the shortcomings of the existing scoring function and accuracy function,a new scoring function and accuracy function of Pythagoras fuzzy number are defined after considering the information of support,opposition and hesitation.On this basis,a new ranking method is obtained.Compared with the old sorting method,the new sorting method not only absorbs more uncertain information,but also has a more direct sorting process.(3)Inspired by intuitionistic fuzzy entropy,the axiomatic definition and calculation formula of Pythagorean fuzzy entropy are defined,which enriches Pythagorean fuzzy set theory.(4)According to the new Pythagorean fuzzy number formula and ranking method,a multi-attribute decision making method based on Pythagorean fuzzy number is proposed.Finally,the method is applied to a practical example,which shows that the method can effectively solve the actual multi-attribute decision making problem,and can be further applied to risk management,artificial intelligence and other research fields.