模糊度量空间中的伪度量结构及等距同构  

Pseudo-Metric Structure and Isometrical Isomorphism in Fuzzy Metric Spaces

作　　者：杨浩 吴健荣 YANG Hao;WU Jian-rong(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou Jiangsu 215009,China;Department of Radical Education,Nantong Institute of Technology,Nantong Jiangsu 226002,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009 [2]南通理工学院,基础教学学院,江苏南通226002

出　　处：《西南大学学报（自然科学版）》2021年第6期95-100,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971343).

摘　　要：由于模糊度量在彩色图像滤波等方面的成功应用,近年来该领域的研究引起了人们的重视.在将经典度量空间中的重要结论推广到模糊度量空间中的同时,研究方法上的创新显得特别重要.其中,将模糊度量分解为一族经典度量,建立模糊度量的分解定理无疑是十分有意义的.已有的分解定理主要是针对取小算子的模糊度量展开的,在应用上具有很大的局限性.本文引入了星伪度量族的概念作为对伪度量族概念的推广,利用这一概念,建立了针对取一般连续t-模的模糊度量的分解定理.同时,本文给出了模糊度量空间与伪度量族空间等距同构的充分条件和必要条件,由此建构起模糊度量与伪度量族之间的联系,为一般意义下的模糊度量的研究提供了一种新的有效途径.Due to the successful applications in such fields as color image filtering,the research about fuzzy metrics has attracted more and more attention in recent years.While many important results of classical metric spaces are generalized to fuzzy metric spaces,the innovation of research methodsis becoming increasingly important.No doubt,decomposition of fuzzy metrics into a family of classical metrics and establishment of decomposition theorems of fuzzy metrics are of great significance.The existing decomposition theorems,however,are mainly focused on fuzzy metrics with the minimum operator,and thus have great limitations in application.In this paper,the concept of family of star pseudo-metrics is introduced as a generalization of the family of pseudo-metrics.In addition,the sufficient and necessary conditions of isometric isomorphism between a fuzzy metric space and a family of pseudo-metric spaces are given,and the relationship between them is constructed,which provides a new and effective approach to the study of fuzzy metrics in the general sense.

关 键 词：模糊集 模糊度量 伪度量 分解 等距同构 

分 类 号：O189.13[理学—数学]