In this paper, we extend an important fixed point theorem for set-valued. A random fixed-point theorem for random set-valued semi-closed 1-set contraction mapping is obtained.
将集值半闭1 -集压缩映象的一个重要不动点定理随机化，得到随机集值半闭1 -集压缩映象的随机不动点定理。
The vague concept is explained by the random set and the contour function, and vague environments are explained with equality relation. Moreover, several examples are presented in the paper.
从两个方面讨论了模糊集合的语义，通过随机集合理论和等高线函数对模糊概念进行了说明，利用等价关系理论对模糊环境进行说明，同时结合一些具体实例加以详细讨论。
The vague concept is explained by the random set and the contour function, and vague environments are explained with equality relation. Moreover, several examples are presented in the paper.
从两个方面讨论了模糊集合的语义，通过随机集合理论和等高线函数对模糊概念进行了说明，利用等价关系理论对模糊环境进行说明，同时结合一些具体实例加以详细讨论。
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