从分解定理的角度对不同模糊度量的比较  

A comparative study of different fuzzy metrics from the perspective of decomposition theorem

作　　者：吴健荣 WU Jianrong(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2024年第4期69-75,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(11971343,12071225)。

摘　　要：本文首先回顾了模糊度量概念的两类主要形式,并指出了它们在定义上的差异。然后,引入了基础模糊度量空间的概念,它涵盖了大多数现有模糊度量的形式,并给出了它的分解定理。在此基础上,研究了模糊度量的一些特定公理与分解定理形式之间的内在关系,从而以分解定理的角度对不同的模糊度量的内涵进行了比较。所得到的结论对深入理解不同模糊度量的特征具有重要的意义;同时,也揭示了模糊度量与分明度量(族)之间的内在关系,为模糊度量理论的深入研究提供了新的思路。This paper first reviewed the two main versions of fuzzy metrics,and pointed out their differences in their definitions.Then,it introduced a concept of basic fuzzy metric space containing most of the existing fuzzy metrics and gave its decomposition theorem.On this basis,the author investigated the relationships between some special axioms of fuzzy metric and the decomposition theorems for various fuzzy metric spaces and conducted a comparative study of different fuzzy metrics from the perspective of decomposition theorem.The results obtained are of great significance to further understand the characteristics of different fuzzy metrics,and reveal the internal relationship between a fuzzy metric and a crisp metric(families).They provide a new way for the further study of fuzzy metric theory.

关 键 词：模糊拓扑 模糊度量 分解定理 

分 类 号：O159[理学—数学] O189.13[理学—基础数学]