模糊n-椭球数空间的拓扑性质  

The topological properties of the fuzzy n-ellipsoid number space

作　　者：刘小资 姜广浩 LIU Xiaozi;JIANG Guanghao(Center for Applied Mathematics of Guangxi,Yulin Normal University,Yulin 537000,China;School of Mathematics and Statistics,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]广西应用数学中心玉林师范学院,广西玉林537000 [2]淮北师范大学数学与统计学院,安徽淮北235000

出　　处：《纯粹数学与应用数学》2024年第3期510-525,共16页Pure and Applied Mathematics

基　　金：国家自然科学基金(12071188);广西高校中青年教师科研基础能力提升项目(2024KY0596);淮北师范大学自然科学结余经费资助项目(2023ZK029).

摘　　要：作为一类特殊的模糊数,模糊n-椭球数被广泛用于表示不精确或不确定环境中的多通道数字信号.本文研究赋予某类特殊度量后的模糊n-椭球数空间以及它的两个子空间的拓扑性质.探讨这三个空间的可分性与凸性,并证明它们都是绝对收缩核.最后,得到这三个空间都是道路连通、局部道路连通、可缩的度量空间.As a subclass of fuzz numbers,the fuzzy n-ellipsoid numbers are widely used to represent objects with multidimensional imprecise or uncertain attributes.In this paper,we study some topological properties of the fuzzy n-ellipsoid number space induced by a special metric and its two subspaces.The separability and convexity of above three spaces are discussed.And we show that both of them are absolute retracts.As a consequence,we finally obtain that these spaces are path-connected,locally path-connected and contractible.

关 键 词：模糊集 模糊数 模糊n-椭球数 绝对收缩核 度量空间 

分 类 号：O189.11[理学—数学]