摘要
本文在超可测空间的基础上定义了模糊随机集,研究了严格正规模糊随机集的生成集和某些可测性问题;然后将严格正规模糊随机集作为变量取值的限制,定义了一种新的模糊随机变量,证明了它的可能性分布函数是一个随机过程,引进了模糊随机变量的F 样本集合,讨论了模糊随机变量的某些概率特征。
In this paper,a fuzzy random set is defined on the basis of the supermeasurable space,and the product set and some measurable properties of a strict normal fuzzy set are studied.Then,by taking the strict nor-mal fuzzy set as the restriction of a random variable,a new fuzzyrandom variable is defined and it is proved that its possibility distribu-tion function is a random process.Furthermore,the F-sample set of afuzzy random variable is introduced and some fuzzy probabilistic char-acteristics of the variable are discussed.
基金
霍英东教育基金
国家自然科学基金
关键词
模糊随机变量
概率
fuzzy random set
random variable product set
fuzzy random variable
R-F expectation.
