随机模糊集与随机集

本文研究了三个方面的工作：一是定义了一种模糊集上的可测结构，从而定义了随机模糊集，这些定义都与论域Ｘ上的拓扑结构无关。将通常意义下的集合看成特殊模糊集得到的通常集合上的超可测结构与文（３）中的定义一致；二是给出了随机模糊集、随机集的一些等价条件；三是研究了随机模糊集、随机集的分布与其有限维落影族的关系。

Random Fuzzy Sets and Random Sets

This article discusses three problems. First , it has defined the measurable structure on a fuzzy set on the basis of which the random fuzzy set is defined. These definitions have nothing to do with the topological structure of X fields of theory. The sets for normal sense are regarded as a super measurable structure of normal sets obtained from the special fuzzy sets , which is in accordance with the definition given in this article [3]. Second , it states some conditions of equal value of random fuzzy sets and random sets. Third , it studies the relationships between the distribution of random fuzzy sets and random sets and its finite falling shadow variety.