模糊值函数极限与连续的模糊结构元表述

Structured element representation of limit and continuity of fuzzy-valued function

在模糊值函数的模糊结构元表述理论的基础上,利用[-1,1]上同序标准单调函数类上的距离诱导出模糊值函数空间上的距离,证明了模糊实数空间与[-1,1]上同序单调函数类同胚.模糊数空间和模糊值函数空间上的与距离相关的所有性质都可以在一类单调函数类上得到.在此基础上,给出了模糊值函数极限与连续的定义,证明了相应的一些性质.

According to the fuzzy structured element representation theorem of fuzzy-valued function, the space distance of fuzzy-valued function was induced from the space distance of standard bounded monotone function on [-1,1], and they were proved to be homeomorphie. It showed that all properties of fuzzy number and fuzzy-valued function relating to distance can be obtained by this family of standard bounded monotone function. On this basis, the limit and continuity of fuzzy-valued function were defined, and its some relative properties were proved.