Research On Soft Set And S Approximation Space Based On Pythagorean Fuzzy Set

Because of the incompleteness of knowledge in information system,many practical decision problems have great uncertainty.In recent years the research on uncertainty has become a hot topic in many fields,such as information science,decision science and so on.In order to deal with the problem of uncertainty,researchers have also put forward a series of mathematical theories,such as fuzzy set,rough set,soft set,Dempster-Shafter evidence theory and so on.However,the problem of uncertainty in real life is usually complex and multivariate,and a single theoretical model can not adapt to this situation.So we often need to extend the classical theoretical models or cross-fusing multiple models to give full play to their respective model advantages.This paper intends to apply Pythagorean fuzzy set theory to soft set theory and S approximation space theory,the specific contents are as follows:1.Pythagorean fuzzy set is a new generalization of fuzzy set,intuitionistic fuzzy set,which has been successfully applied in multi-attribute decision making,cluster analysis,pattern recognition and so on.This paper is based on Pythagorean fuzzy soft set model.Based on this model,a similarity measure and weighted similarity measure of Pythagorean fuzzy soft set based on membership degree,non-membership degree and hesitation degree are proposed.The properties of axiomatic definitions of these measures are studied,and the similarity measure formula is compared with the existing measure formula.Based on the defects of intuitionistic fuzzy entropy in the existing research,an improved calculation formula of intuitionistic fuzzy entropy is established,and the weight parameter is calculated by entropy weight method.Finally,the two similarity measure formulas are applied to the pattern recognition problem of building materials.2.S approximation space is a mathematical model proposed in recent years to solve uncertainty problems.This paper studies the cross-fusing model of S approximation space and Pythagorean fuzzy set,and then proposes the Pythagorean fuzzy S approximation space model.Firstly,this paper studies the properties of Pythagorean fuzzy S approximation space.Secondly,Pythagorean fuzzy S approximation space is studied by means of three-way decision methods.The definition and properties of thethree regions are given.The influence of threshold on universe division is also discussed.Thirdly,in order to adapt to the diversity of subjective and attribute conditions of decision makers in practical decision-making problems,based on the Pythagorean fuzzy S approximation model,the number of knowledge mappings is increased and the decision mappings are defined.Two special neighborhood system Pythagorean fuzzy S approximation space models are proposed,and the properties that their upper and lower approximations should satisfy are given respectively.Finally,using the Pythagorean fuzzy S approximation space model in the medical diagnosis example,three-way decision algorithms and sorting algorithms based on Pythagorean fuzzy objects are proposed.Above all,this paper mainly studies the similarity measure theory of the cross-fusing model for Pythagorean fuzzy set and soft set and Pythagorean fuzzy S approximation space theory.All these studies enrich Pythagorean fuzzy set theory on the one hand,and provide new ideas for other topics in soft set theory and S approximation space theory on the other hand.