模糊拟度量的拟度量族特征  

A Characterization of a Fuzzy Quasi-metric in Terms of a Family of Quasi-metrics

作　　者：田恪明 吴健荣[1] TIAN Ke-ming;WU Jian-rong(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《模糊系统与数学》2020年第3期13-18,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11971343);苏州科技大学研究生校级科研创新项目(SKCX18-013)。

摘　　要：本文讨论了Kramosil和Michalek意义下模糊拟度量空间的结构问题。通过引入星拟度量族的概念,给出了模糊拟度量的拟度量族特征,即:一个模糊拟度量当且仅当是由一族单调增且上半连续的星拟度量族生成的。This paper deals with the structure problem of a fuzzy quasi-metric space in the sense of Kramosil and Michalek.After introducing the concept of the family of star quasi-metrics,a characterization of a fuzzy quasi-metric in terms of a quasi-metric family is given.That is,a function is a fuzzy quasi-metric if and only if it can be induced by a star quasi-metric family which is both increasing and upper semi-continuous.

关 键 词：模糊拓扑 模糊拟度量 拟度量 分解定理 

分 类 号：O189[理学—数学]