A note on compactness in a fuzzy setting
TL;DR: Fuzzy filter bases are used to introduce the notion of Compactness in fuzzy setting and the expected basic properties of compactness are explored.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1990-01-03. It has received 23 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.
Citations
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TL;DR: This work studies some relations between separability in fuzzy topological spaces and one in fuzzy hyperspaces and investigates some properties of axiom of countability in fuzzy hyperspaces.
Abstract: We study some relations between separability in fuzzy topological spaces and one in fuzzy hyperspaces. And we investigate some properties of axiom of countability in fuzzy hyperspaces.
2 citations
Journal Article•
05 Aug 2013-World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
TL;DR: In this article, a new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space, is introduced and it is established that this class lies between fuzzy closed set and fuzzy generalized closed sets.
Abstract: A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
1 citations
TL;DR: By introducing fuzzy upper and lower correspondence between fuzzy topological spaces, the fuzzy version of the topological intersection theorem is proved.
1 citations
Cites methods from "A note on compactness in a fuzzy se..."
...While doing so we use the notions of fuzzy compactness and fuzzy connectedness given in [6, 10, 11, 2, 8, 15], respectively....
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01 Jan 2015
TL;DR: Several characterizations and properties of this newly defined multifunction have been studied and the mutual relationships of this fuzzy multifunction with fuzzy upper (lower) -precontinuous multifunctions have been established.
Abstract: This paper deals with a new type of fuzzy multifunction, viz., fuzzy upper (lower) -continuous multifunction. Several characterizations and properties of this newly defined multifunction have been studied here. Also the mutual relationships of this fuzzy multifunction with fuzzy upper (lower) -precontinuous multifunctions [8] have been established here.
1 citations
24 Jun 2012
TL;DR: F fuzzy strong-precompactness and fuzzystrong-preclosed spaces are introduced in fuzzy topological spaces by means of fuzzy strongly preopen sets and fuzzy stronglypreclosed sets.
Abstract: In this paper, fuzzy strong-precompactness and fuzzy strong-preclosed spaces are introduced in fuzzy topological spaces by means of fuzzy strongly preopen sets and fuzzy strongly preclosed sets The concepts of fuzzy strong-precompactness and fuzzy strong-preclosed spaces are defined and fuzzy filterbases are used to characterize these concepts
1 citations
References
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TL;DR: This paper explores the foundations of, generalizes, and continues the work of Zadeh in [I] and [2].
2,375 citations
1,997 citations
995 citations
TL;DR: It will be shown in a following publication that contrary to the results obtained up to now, the Tychonoff-product theorem is safeguarded with fuzzy compactness.
894 citations
TL;DR: In this paper, the authors studied the different kinds of compactness notions that have been introduced up to this time and studied the implications that exist between the different notions, and in Section 5 they gave some concluding remarks.
264 citations