Research On Extension Of Variable Precision Fuzzy Soft Rough Set Model

With the rapid development of information technology and communication technology,human beings are facing severe challenges brought by scientific modeling and effective decision-making of massive data.How to study the universal and reliable mathematical model and construct the robust and reliable calculation method is an important problem to be solved urgently.Rough set theory,fuzzy set theory and soft set theory are all mathematical tools devoted to analyzing and dealing with uncertainty problems.Combining the advantages of approximate description of rough set model,knowledge representation of fuzzy set theory and parametric expression of soft set theory,the constructed variable precision fuzzy soft rough set model has important practical significance for the existing models to deal with complex data,such as noise effect and lack of robustness of the model.In this thesis,the variable precision fuzzy soft rough set model and its extended model are proposed,which provide effective methods and theoretical basis for people to analyze and make decisions in complex fuzzy data environment.This thesis mainly studies from the following aspects:(1)In view of the lack of robustness of fuzzy data with noise and processing model,on the basis of variable precision rough set model and fuzzy soft set,firstly the fuzzy equivalent soft relation is constructed by defining the compound operation of fuzzy soft relation and inverse fuzzy soft relation,the variable precision fuzzy soft rough set model is proposed,its mathematical structure and theoretical characteristics are studied deeply,and its properties and important conclusions are presented and verified.Secondly,the uncertainty measurements of variable precision fuzzy soft rough set model are studied from the perspective of approximate space and approximate set by using five kinds of measurements such as information granularity,rough entropy,information entropy,combination entropy,condition entropy and using the other two kinds of measurements such as roughness and fuzzy entropy respectively,and the corresponding monotonicity conclusion is obtained.Finally,the validity of the model is verified by a concrete example with using the bounded product operator of fuzzy sets.(2)In view of the lack of robustness of the intuitionistic fuzzy data with noise and the processing model,on the basis of variable precision fuzzy soft rough set model set,firstly the intuitionistic fuzzy equivalent soft relation is constructed by defining the compound operation of intuitionistic fuzzy soft relation and inverse intuitionistic fuzzy soft relation,the variable precision intuitionistic fuzzy soft rough set model is proposed,its mathematical structure and theoretical characteristics are studied deeply,and its properties and important conclusions are presented and verified.Secondly,the uncertainty measurements of the variable precision intuitionistic fuzzy soft rough set model are studied from two perspectives of approximate space and approximate set similarly,and the corresponding monotonicity conclusion is obtained.Finally,using the score function,the exact function and the ordering rule of the intuitionistic fuzzy set,the validity of the model is verified by a concrete example.Variable precision fuzzy soft rough set and its extended model and the related research of the model proposed in this thesis provide theoretical support and calculation methods for the development of the basic theory of artificial intelligence and the modeling of complex environment data.The model and its extension have broad application prospects.