Standard fuzzy uniform structures based on continuous t-norms

被引：9

作者：

Gutierrez Garcia, J. ^{[2
]}

Romaguera, S. ^{[3
]}

Sanchis, M. ^{[1
]}

机构：

[1] Univ Jaume 1, Inst Univ Matemat & Aplicac Castello IMAC, Castellon de La Plana 12071, Spain

[2] Univ Pais Vasco Euskal Herriko Unibertsitatea, Dept Matemat, Bilbao 48080, Spain

[3] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

来源：

FUZZY SETS AND SYSTEMS | 2012年 / 195卷

关键词：

Fuzzy uniform structure; Fuzzy topological group; The fine fuzzy uniformity; The Stone-Cech fuzzy compactification; The Hausdorff-Bourbaki fuzzy uniformity; Fuzzy quasi-uniform structure; METRIC-SPACES; TOPOLOGICAL-GROUPS;

D O I：

10.1016/j.fss.2011.10.008

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper deals with fuzzy uniform structures previously introduced by the authors [Fuzzy uniform structures and continuous t-norms, Fuzzy Sets Syst. 161 (2009) 1011-1021]. Our approach involves a covariant functor psi from the category of fuzzy uniform spaces and fuzzy uniformly continuous mappings (in our sense) to the category of uniform spaces and uniformly continuous mappings. We show that psi is well-behaved with respect to some significant fuzzy uniform concepts. and its behavior provides a method to introduce notions of tine fuzzy uniform structure and Stone-tech fuzzy compactification in this context. Our method also applies to obtain fuzzy versions of some classical results on topological algebra and hyperspaces. The case of quasi-uniform structures is also analyzed. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：75 / 89

页数：15

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