Research On Three-way Government Decision Covering Rough Set Model Based On Pythagorean Fuzzy Environment

As a mathematical tool for processing fuzzy information,Pythagorean fuzzy set deals with uncertain problems from both the degree of membership and the degree of non-membership which meets the condition that the square sum of its membership degree and non-membership degree cannot exceed 1,and obtain decision-making behavior that is more in line with human thinking.As another mathematical tool to deal with fuzzy in-formation,decision-theoretic rough set theory provides a new method to solve the problem of risk decision by means of three-way decision methods.So far,the fusion of Pythagorean fuzzy set and decision-theoretic rough set is relatively rare.Therefore,how to integrate Pythagorean fuzzy set with covering decision-theoretic rough set to construct a new model has certain significance for the research of three branch decision problems.This paper investigates the covering decision-theoretic rough sets in the Pythagorean fuzzy environment,and the main research contents are as follows:(1)The concepts of Pythagorean fuzzy ?-covering and Pythagorean fuzzy?-neighbor-hood are proposed.Based on the Bayesian decision procedure,a Pythagorean fuzzy?-covering decision-theoretic rough set model is constructed.Some interesting properties of the expected loss related to the model are also investigated.(2)Based on the Pythagorean fuzzy ?-covering decision-theoretic rough set model,the expected loss is established by using Pythagorean fuzzy numbers.And the corre-sponding three decision-making are derived.Finally,an example is provided to verify the effectiveness and scientificity of Pythagorean fuzzy ?-covering decision-theoretic rough set.(3)Based on the Pythagorean fuzzy ?-covering decision-theoretic rough set model,we introduce the concept of multi-granulation,construct two kinds of multi-granulation Pythagorean fuzzy ?-covering decision-theoretic rough set models:optimistic multi-granu-lation Pythagorean fuzzy ?-covering decision-theoretic rough set and pessimistic multi-granulation Pythagorean fuzzy ?-covering decision-theoretic rough set,and establish the corresponding three-way decision rules,respectively.Finally,an example is provided to verify the effectiveness and scientificity of the novel model.