Fuzzy points of equivalent fuzzy subsets

Authors:
V. Murali
Affiliations:
Department of Pure and Applied Mathematics, Rhodes University, P.O. Box 94, Grahamstown 6140, South Africa
Venue:
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Informatics and computer science intelligent systems applications
Year:
2004

Citing 3
Cited 12

On an equivalence of fuzzy subgroups I

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On flags and fuzzy subspaces of vector spaces

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On an equivalence of fuzzy subgroups II

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Semigroups characterized by (C,C,νqk)-fuzzy ideals

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Interval-valued (α,β)-fuzzy K-algebras

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Characterizations of hemirings by (@,@νqk)-fuzzy ideals

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Characterizations of regular ordered semigroups in terms of (α,β)-fuzzy generalized bi-ideals

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Generalized fuzzy interior ideals in semigroups

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Filters of ordered semigroups based on the fuzzy points

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A new type of fuzzy normal subgroups and fuzzy cosets

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

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Abstract

A natural equivalence relation on the set of all fuzzy subsets, generalizing the equality of crisp sets, was recently introduced and studied in various contexts such as finite fuzzy subsets, fuzzy vector space, finite fuzzy subfields and in the classification of finite Abelian groups. In this paper, we restrict this equivalence to the set of fuzzy points and study its effect on the relationship between fuzzy points and fuzzy subsets. All fuzzy subsets take a finite number of membership values in the real unit interval. An important tool for studying this equivalence relation is that of a keychain. This notion gives rise to the idea of a pinned-flag, their equivalences and index of fuzzy subsets.