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: The concepts of fuzzy H-continuity and fuzzy strongly closed graph, respectively are introduced and some of their properties are investigated.
Abstract: We introduce the concepts of fuzzy H-continuity and fuzzy strongly closed graph, respectively and investigate some of their properties.
04 Dec 2019
TL;DR: In this article, the concept of fuzzy almost generalized b-continuous mappings in Sostak's Fuzzy Topological Spaces was introduced and several interesting properties of these mappings are also given.
Abstract: In this paper, we introduce and characterize the concept of fuzzy almost generalized b-continuous mappings in Sostak’s Fuzzy Topological Spaces. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy r-fuzzy T12 b-space, r-fuzzy gb- space, r-fuzzy regular gb-space and r-fuzzy generalized b-compact space. It is seen that a fuzzy almost generalized b-continuous mapping from a r-fuzzy T12 b-space to another fuzzy topological space becomes fuzzy almost continuous mapping.
Journal Article•
TL;DR: The fuzzy T 2 -axioms due to Hutton andReilly, Ganguly and Saha and Sinha and Sinhas are characterized by using thenotion of fuzzy closure, and the relation between these axioms is studied.
Abstract: . In this paper, the fuzzy T 2 -axioms due to Hutton andReilly, Ganguly and Saha and Sinha are characterized by using thenotion of fuzzy closure. As consequences, we study the relationbetween the fuzzy T 2 -axioms and give some examples which showthat the axiom of fuzzy compactness, due to Ganguly and Saha, isnot compatible with the fuzzy T 2 -axioms. 1. IntroductionSeveral fuzzy T 2 -axioms have been defined in different ways and in-vestigated by many authors, such as Hutton and Reilly [4], Gangulyand Saha [3] and Sinha [5]. In particular, Sinha characterized these ax-ioms and compared them. In Section 2, we provide another equivalentcondition for these axioms and study the relation between them.In [2], Ganguly and Saha introduced a new notion of fuzzy compact-ness and proved that this notion satisfies almost all the properties ofcompactness of set topology. But, in spite of the remarkable results,the notion is not compatible with some fuzzy T 2 -axioms. In Section 3,we explain this fact.Throughout this paper, we write a fuzzy topological space in shortas an fts. For a fuzzy set A in an fts X, the set {x ∈ X|A(x) > 0},denoted by A
Cites background from "A note on compactness in a fuzzy se..."
...0X and 1X denote, respectively, the constant fuzzy sets taking the values 0 and 1 on X. For definitions and notations which are not explained in this paper, we refer to [ 2 ],[3] and [5]....
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...Definition 3.2. ([ 2 ]) A fuzzy set A in an fts X fuzzy GS-compact if every fuzzy open covering U of A has a finite subcollection {Uj|j = 1,··· ,n} of U such that [n j=1Uj A....
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...In [ 2 ], Ganguly and Saha introduced a new notion of fuzzy compactness and proved that this notion satisfies almost all the properties of compactness of set topology....
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...Definition 3.1. ([ 2 ]) A collection U = {Ui|i 2 I} of fuzzy open sets in X is called a fuzzy open covering of a fuzzy set A in X if...
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References
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TL;DR: This paper explores the foundations of, generalizes, and continues the work of Zadeh in [I] and [2].
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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