（T）Fuzzy积分的收敛定理与表现定理

Fuzzy测度与积分是Fuzzy数学的一个活跃分支,三角范数的引入为这一分支的研究提供了有力的工具。本文在文献[9]的基础上,以三角范数为主要工具,对(T)Fuzzy积分进行了进一步的讨论,主要得到了以下结果:(1)关于积分与极限可交换的两个收敛定理;(2)Fatou定理在(T)Fuzzy积分情况下的推广;(3)M~ 中正线性连续泛函的表现定理。

Convergent and Representation Theorem of (T)Fuzzy Integral

Fuzzy measure and integral are a vigorous branch in fuzzy mathematics. The introduction of the theory of triangular norms offers the research of this branch with powerful tool. Based on the reference No.9, the authors have made some discussions on (T)Fuzzy integral, obtaining the following results: (1) two convergent theorems about interchangeability between integral symbol and limit symbol; (2) popularization of Fatou's theorem under the case of (T)Fuzzy integral; (3) representation theorem of a kind of positive linear continuous functional in space M .