The Discussion And Expansion On Measurement Of Fuzzy Uncertainty

In general, the uncertainty of information includes probabilistic uncertainty, fuzzy uncertainty and resolutional uncertainty. In fuzzy information systems, fuzzy information entropy problem is at present a much more interesting issue that is very important from the theoretical as well as from the practical point view.This paper studied several aspects of quantitative measures of fuzziness as follows:In chapter two, as the development of the concept of fuzzy entropy, the new concepts of partial entropy, relative entropy and relative entropy coefficients of fuzzy sets were defined firstly. Then some properties of them were analyzed in detail, and the relation between the relative entropy and fuzzy divergence, discrimination information was established. Finally this paper point out application of relative entropy coefficient in pattern recognition.In chapter three, this paper extended (k,q) -order generalized probabilistic entropy and q -order Shannon probabilistic entropy to the fuzzy sets theory, and introduced (k, q) -order generalized entropy and q -order Shannon entropy of fuzzy sets for the first time. Proved q -order Shannon fuzzy entropy satisfied four axiom conditions of entropy. Then the relationship between q -order Shannon fuzzy entropy and q -order Renyi fuzzy entropy were discussed.In chapter four, gave the axiom definitions of entropy, distance measure and similarity measure of mtuitionistic fuzzy sets, and discussed basic relations among them. Then a -entropy, a -distance measure and a -similarity measure of intuitionistic fuzzy sets are discussed and the relations among them are given.In chapter five, Based on the axiom definitions of distance measure and similarity measure respectively in chapter four, some new entropy formulas of intuitionistic fuzzy sets are induced.In chapter six, gave the axiom definitions of (-)entropy, (-)distance measure and (-)similarity measure of interval valued intuitionistic fuzzy sets, and discussed basic relations among them.GUO Xiaozhi (computing mathematics) Directed by Prof. XIN Xiaolong...