落影空间——模糊集合的概率描述

Falling Space——the Probabilistic Description of Fuzzy Subsets

中文摘要:

      

英文摘要:

      In this paper we discuss some problems concerning the fuzzy statistics and the random subsets. The falling space, a framwork treating the fuzzy subsets as random subsets, has been stated. In this space the measurability of random subsets is equivalent to the strong measurability. Applying the graph of random subsets, we give a correspondence theorem which combines the falling random subsets and the measurable fuzzy subsets. We study also the operations of fuzzy subsets. Finally, we discuss the problems on fuzzy probability by means of the concept of random subset, and some interesting results may be found.