刻画可双完备化的区间值模糊拟度量空间

doi:10.6040/j.issn.1671-9352.0.2013.548

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (10): 72-77.doi: 10.6040/j.issn.1671-9352.0.2013.548

刻画可双完备化的区间值模糊拟度量空间

陆汉川, 李生刚

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2013-11-03 出版日期:2014-10-20 发布日期:2014-11-10
作者简介:陆汉川(1977-),男,博士研究生,讲师,研究方向为格上拓扑学与模糊数学.E-mail:luhanchuan2004@163.com
基金资助:
国家自然科学基金资助项目(11071151);陕西省自然科学基金资助项目(2010JM1005);中央高校基本科研业务费专项资金项目(14SZYB08)

Characterization of bicompletable interval-valued fuzzy quasi-metric spaces

LU Han-chuan, LI Sheng-gang

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shanxi, China

Received:2013-11-03 Online:2014-10-20 Published:2014-11-10

摘要/Abstract

摘要： 在拟度量的背景下推广了区间值模糊度量的概念,主要结果如下:(1)给出了区间值模糊拟度量空间等距同构的扩张定理;(2) 证明了每个区间值模糊拟度量空间有双完备化且它是唯一达到等距同构的; (3)得到了区间值模糊拟度量空间双完备化的构造方法和区间值模糊拟度量空间可双完备化的等价刻画。

关键词: 区间值模糊拟度量空间, 区间值模糊拟度量双完备化, 双柯西序列, 等距同构

Abstract: We generalize the notions of interval-valued fuzzy metric in the quasi-metric background. The main results of this paper are: (1) the isometric extension theorem of interval-valued fuzzy quasi-metric space is given; (2) it is proved that every interval-valued fuzzy quasi-metric space has bicompletion and is unique up to isometry; (3) a method to construct the interval-valued fuzzy quasi-metric space bicompletion is given, and a equivalent characterization of interval-value fuzzy quasi-metric spaces is obtained which can be bicompletable.

Key words: interval-valued fuzzy quasi-metric bicompletion, isometry, interval-valued fuzzy quasi-metric spaces, bi-Cauchy sequence

中图分类号:

O189.13

陆汉川, 李生刚. 刻画可双完备化的区间值模糊拟度量空间[J]. 山东大学学报（理学版）, 2014, 49(10): 72-77.

LU Han-chuan, LI Sheng-gang. Characterization of bicompletable interval-valued fuzzy quasi-metric spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 72-77.

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刻画可双完备化的区间值模糊拟度量空间

Characterization of bicompletable interval-valued fuzzy quasi-metric spaces

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