Compactness in fuzzy topological spaces
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It is observed that it is possible to have degrees of compactness, which is called α-compactness (α a member of a designated lattice), and a Tychonoff Theorem is obtained for an arbitrary product of α-Compact fuzzy spaces and a 1-point compactification.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1978-03-01 and is currently open access. It has received 242 citations till now. The article focuses on the topics: Compact space & Tychonoff's theorem.read more
Citations
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An introduction to intuitionistic fuzzy topological spaces
TL;DR: The basic concepts of the so-called “intuitionistic fuzzy topological spaces” are constructed, the definitions of fuzzy continuity, fuzzy compactness, fuzzy connectedness and fuzzy Hausdorff space are introduced, and several preservation properties and some characterizations concerning fuzzy compactity and fuzzyconnectedness are obtained.
Book ChapterDOI
Fuzzy Topological Spaces
TL;DR: In mathematics, certain notions of topology are also abstractions of classical concepts in the study of real or complex functions, including open sets, continuity, connectedness, compactness, and metric spaces.
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Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
Ulrich Höhle,Alexander P. Sostak +1 more
TL;DR: This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory.
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Fuzzy topological vector spaces II
TL;DR: The notion of a bornological fuzzy linear space is given and some of the properties of such a space are investigated.
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On a canonical representation of fuzzy numbers
TL;DR: This paper proposes two parameters, value and ambiguity, for fuzzy number representation and uses them to obtain canonical representations and to deal with fuzzy numbers in decision-making problems.
References
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Journal ArticleDOI
Normality in fuzzy topological spaces
TL;DR: In this article, the notion of normality in topological spaces is extended to fuzzy topologies, and a fuzzy topological space is constructed in terms of a Urysohn type lemma.
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The fuzzy tychonoff theorem
TL;DR: In this article, the authors define cl∞-monoids, which are used to measure the degree of membership of points in sets, and define L- or "fuzzy" sets are defined, and suitable collections of these are called L-topological spaces.
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Fixed points, separation, and induced topologies for fuzzy sets
TL;DR: This paper considers how a topology for a set 3 may give rise to an “induced fuzzy topology” for S, thus characterizing the fuzzy subsets of % which may naturally be considered “open” and furnishing a concrete class of examples of the “fuzzy topologies” defined by C. L. Chang.