Vague Sets Of Fuzzy Measure Research

In the real world,there exists a large of information that is fuzzy, uncertain, incomplete. Information science is a course in order to solve the uncertainty of information, to obtain information. Now, the main processing of fuzzy information theory is Fuzzy Set puting forward by Zadeh, however, the people gradually found there are still some fuzzy information that cannot process using Fuzzy Set Theory in the real world.In1993,Taiwan scholars WL.Gau and S.M.Chen presented the Vague Set Theory.It is a special form of Fuzzy Set.The Vague Set has stronger ability to express uncertain information. Vague Set Theory in the academic circles attracted many scholars and researchers’attention, some scholars of Vague technology applied in information processing and control decision. But since the Vague was established only twenty years, his theory is not perfect, applied domain also needs to be further expanded. Therefore, This paper from the Vague Set based on the relationship between fuzzy metric, discuss the new method of fuzzy information measure. This paper first discusses the Vague fuzzy metric:distance measure,similarity measure, fuzzy entropy and the relationship between the three. Analysis current induction formula, and then two new induction formulas more concise, more directly reveals the three fuzzy metric properties and the relationship between each other.Then through the research of similarity theory, an analysis of existing similarity measure formula, find the defects existing in the existing formula. On this foundation,a formula is put forward that conforms to the intuitive sense and conforms to the similarity measure of Vague Sets axiomatic definition. Through several typical examples proved that the new formula to calculate the similarity measure is superior and practical.Finally the paper studies the fuzzy entropy theory.On the basis of the axiomatic definition,from the geometry the paper deduce a new properties of fuzzy entropy of Vague sets.Then an analysis based on the defect of the existing fuzzy entropy formula.The paper put forward a new calculating formula of the fuzzy entropy and proves that the new formula is consistent with the fuzzy entropy axiomatic definition.Through several examples of existing validated the new calculation formula that make up some defects of the existing formula and the new calculation formula is more rational.