Fuzzy Set-valued Information Systems And Their Homorphisms Based On Data Compression

A fuzzy set-valued information system means an information system where its information values are fuzzy sets.Homomorphism is a mathematical tool to study relationships between them.This article studies fuzzy set-valued information systems and their homomorphisms based on data compression.In chapter 1,the research background,current situation and development trend of fuzzy set-valued information systems,as well as the main work of this paper are presented.In chapter 2,the concepts of binary relation and fuzzy set are reviewed,and the concept of a fuzzy set-valued information system is put forward.In chapter 3,the distance between information values of a fuzzy set-valued information system is discussed,the tolerance relation on this information system is presented,information structures of this fuzzy set-valued information system are described,the dependence and information distance between these information structures are proposed,as well as properties of information structures are received,then the group and lattice characteristics of information structures in a fuzzy set-valued information system are obtained.In chapter 4,four uncertainty measurements for fuzzy set-valued information systems are researched,and the effectiveness analysis of these uncertainty measurements is carried out.As an application,the optimal selection of information structures based on ?-rough entropy for fuzzy set-valued information systems has been presented.In chapter 5,the concept of homomorphism between fuzzy set-valued information systems,and ?-reduction in fuzzy set-valued information systems are put forward,as well as invariant characteristics of fuzzy set-valued information systems under homomorphisms are obtained.