Measure Of Fuzzy Information And Its Application

·Fuzzy set theory has been extremely widely applied since it was introduced, and the range of application is constantly being expanded, which makes measure of fuzzy information becoming more and more important.This thesis mainly focuses on three important measures of fuzzy information,i.e. entropy, similarity measure and distance measure.Firstly, the relationships among entropy, similarity measure and distance measure are studied on the fuzzy sets, and some new induction formulas are proposed.Secondly, though selective analysis of two definitions of entropy of intuitionistic fuzzy sets, a more reasonable axiomatic definition is proposed and how to construct this kind of entropy is also studied.Furthermore, according to the distance measure axiom definition, some formulas of distance measure of intuitionistic fuzzy sets in common use are proved to be unreasonable via some counter-examples, and some general forms of distance measure of intuitionistic fuzzy sets are presented.In addition, referring to the research on the relationships among entropy, similarity measure and distance measure on fuzzy sets, their relationships on intuitionistic fuzzy sets are discussed. Finally, the notions of generalized entropy, similarity measure and distance measure of intuitionistic fuzzy sets are first proposed in this paper. Some expressions of generalized entropy of intuitionistic fuzzy sets are presented and the approaches to obtain generalized similarity measure and distance measure through generalized entropy are given.The results of this thesis are of guiding significance to further research and application of measure of fuzzy information.