Title
The complete lattice (S(X), <=) of smooth fuzzy topologiesThe complete lattice (S(X), <=) of smooth fuzzy topologies
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Amsterdam,
Subject
Mathematics
Computer. Automation
Source (journal)
Fuzzy sets and systems: an international journal of soft computing and intelligent. - Amsterdam
Volume/pages
125(2002):2, p. 145-152
ISSN
0165-0114
ISI
000173284000002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Smooth fuzzy topologies are an extension of both crisp topologies and fuzzy topologies, in the sense that not only the objects are fuzzified, but also the axiomatics. In this article, we will complete the proof of the result given in (Chattopadhyay et al., Fuzzy Sets and Systems 49 (1992) 237), stating that the collection of smooth fuzzy topologies, equipped with the pointwise order, is a complete lattice. To this end, we will establish a subbase and base lemma for these by proving that any valuation function can be modified to construct a gradation of openness. (C) 2002 Elsevier Science B.V. All rights reserved.
E-info
https://repository.uantwerpen.be/docman/iruaauth/80d19c/b7c2453.pdf
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