直觉模糊数的表示和结构刻划

本文给出了直觉模糊数的表示定理:包括区间表示、函数表示、嵌入定理,并将直觉模糊数空间嵌入到一类特殊的二维模糊数空间—方模糊数空间,给出了直觉模糊数的结构定理;最后,利用方模糊数与一般二维模糊数的逼近定理,给出了二维模糊数的直觉模糊数逼近。

The Representation and Structure Characterizations of Intuitionistic Fuzzy Numbers

The intuitionistic fuzzy sets consider not only the degree of membership to a given set, but also the degree of rejection, which have been applied to the fuzzy optimization, fuzzy reasoning, decision making, etc. In this paper, the representation theorems of intervals, functions and embedding theorems of intuitionistic fuzzy numbers are given. In addition, we show that the intuitionistic fuzzy number space could be embedded into the 2-cell fuzzy number space which is a special 2-dimension fuzzy space, and the construction theorem of intuitionistic fuzzy numbers is discussed. Finally, similarly to the approximate theorem between 2-cell fuzzy numbers and 2-dimension fuzzy numbers, the approximation approach for 2-dimension fuzzy numbers by intuitionistic fuzzy numbers is presented.