Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence
01 Aug 1980-Journal of Mathematical Analysis and Applications (JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS)-Vol. 76, Iss: 2, pp 571-599
About: This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1980-08-01 and is currently open access. It has received 995 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.
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TL;DR: This paper will give a characteristic of a field by a fuzzy ideal, as fuzzy invariant subgroups, fuzzy ideals, and to prove some fundamental properties of fuzzy algebra.
526 citations
01 Jan 2001
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.
Abstract: Topology has its roots in geometry and analysis. From a geometric point of view, topology was the study of properties preserved by a certain group of transformations, namely the homeomorphisms. Certain notions of topology are also abstractions of classical concepts in the study of real or complex functions. These concepts include open sets, continuity, connectedness, compactness, and metric spaces. They were a basic part of analysis before being generalized in topology.
473 citations
01 Jan 1999
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.
Abstract: This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems:
394 citations
TL;DR: The notion of a bornological fuzzy linear space is given and some of the properties of such a space are investigated.
387 citations
TL;DR: The definition of an (ϵ, ϵ v q)-fuzzy subgroup is slightly modified and some of the fundamental properties of such fuzzy subgroups are obtained.
324 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].
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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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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.
247 citations