On the Topological Structure of KM Fuzzy Metric Spaces and Normed Spaces

被引：15
作者：
Xiao, Jian-Zhong [1 ]
Zhu, Xing-Hua [1 ]
Zhou, Hao [1 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
来源：
IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2020年 / 28卷 / 08期
关键词：
Extraterrestrial measurements; Probabilistic logic; Fuzzy sets; Information science; Topology; Fuzzy metric space; fuzzy normed space; locally convex; quasi-metric family; quasi-norm family; FIXED-POINT THEOREMS; MAPPINGS; DOMAIN;
D O I：
10.1109/TFUZZ.2019.2917858
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, some relations among the axioms of KM fuzzy metric spaces and KM fuzzy normed spaces are discussed, and some characterizations concerning the additional axiom are given. Also, a quasi-metric family and a quasi-norm family corresponding, respectively, to the KM fuzzy metric spaces and the KM fuzzy normed spaces are introduced and studied. Using their properties, the different topological structures of KM fuzzy metric spaces and KM fuzzy normed spaces with variable t-norm are described, and some new properties on these spaces are obtained. As their special cases, the topological structures and properties concerning GV fuzzy metric spaces and GV fuzzy normed spaces are presented.
引用
收藏
页码：1575 / 1584
页数：10
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