模糊数度量的单值函数表示  

Monotropic Function Representation of Metrics on Fuzzy-number Space

作　　者：李雪粉[1] 樊太和[1] 

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2015年第1期135-139,148,共6页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(61170110;11171308;61379018)

摘　　要：基于一个具体的三角模糊数作为结构元,给出了模糊数与定义于[-1,1]上的单调递增有界且上半连续的函数构成的集合之间的一一对应关系,从而得到了模糊数的单值函数表示。在上述表示基础上,给出了模糊数空间上的各种度量如上确界度量、Lp度量、sendograph度量的单值函数表现,从而将对模糊数的度量(拓扑)性质的研究完全转化为对普通单调递增有界且上半连续的函数空间中相应性质的研究。By taking a specific triangular fuzzy number as structural element, this paper gives a bijection between the set of all fuzzy numbers and the set of all bounded, monotonic increasing and upper semi-continuous functions defined on [- 1, 1], thus get a monotropic function representation of fuzzy number. On the basis of above representation, this paper gives the monotropic function representation of various metrics on fuzzy number space, such as the supremum metric, the Lp metrics, and the sendograph metric, so as to fully translate the study on metric （topology） properties of fuzzy numbers into the study on the corresponding properties on the space of all bounded, monotonic increasing and upper semi-continuous functions.

关 键 词：模糊数 度量 单值函数 同胚 

分 类 号：O175.14[理学—数学]