Based On Fuzzy Sets, Vague Sets, Fuzzy Metric Study

In this thesis, by use of fuzzy sets as the research object, we firstly study some properties of the general fuzzy entropy and inclusion measure and discuss their mutual induced relations. Furthermore, we get the mutual induced formula. This work enriches the theory of fuzzy measure. The concepts of divergence measure and local divergence measure of fuzzy sets in finite universe are simply introduced, and some relative properties of the local divergence measure are discussed. Therefore, several construction methods of local divergence measure are mainly studied. Moreover, by use of vague sets as the research object, we introduce the definitions ofσ-similarity measure andσ-inclusion measure of vague sets in finite universe and present some properties of them. Finally, we study the mutual induced relations betweenσ-similarity measure andσ-inclusion measure of vague sets, and get the mutual induced formulas.