On fuzzy spaces and fuzzy group theory
type: Item
instance of: scholarly article
title: On fuzzy spaces and fuzzy group theory
zbMATH Open document ID: 0832.20088
DOI: 10.1016/0020-0255(94)90079-5
author: V. Pereyra
published in: Information Sciences
publication date: 1996-02-22T00:00:00Z
review text: The notion of fuzzy set was generalized in many directions, e.g.: \(L\)-fuzzy sets [\textit{J. A. Goguen}, J. Math. Anal. Appl. 18, 145--174 (1967; Zbl 0145.24404)], probabilistic sets [\textit{K. Hirota}, Fuzzy Sets Syst. 5, 31--36 (1981; Zbl 0442.60008)], intuitionistic fuzzy sets [\textit{K. Atanassov}, Fuzzy Sets Syst. 20, 87--96 (1986; Zbl 0631.03040)], Boolean fuzzy sets [\textit{C. A. Drossos}, Fuzzy Sets Syst. 37, 287--307 (1990; Zbl 0712.03045)]. Here a notion of fuzzy space is introduced and fuzzy groupoids on fuzzy spaces are examined (formally without structure of crisp groupoid, but practically with equivalent conditions). Results are compared to properties of Rosenfeld's fuzzy groupoids [cf. \textit{A. Rosenfeld}, J. Math. Anal. Appl. 35, 512--517 (1971; Zbl 0194.05501), \textit{L. Biacino, G. Gerla}, Inf. Sci. 33, 181--195 (1984; Zbl 0562.06004)].
Mathematics Subject Classification ID: 20N25
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 08A35
zbMATH DE Number: 694932
zbMATH Keywords: fuzzy sets
zbMATH Keywords: fuzzy functions
zbMATH Keywords: fuzzy homomorphisms
zbMATH Keywords: \(M\)-lattices
zbMATH Keywords: \(L\)-fuzzy sets
zbMATH Keywords: fuzzy groupoids
zbMATH Keywords: fuzzy spaces
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0020-0255(94)90079-5
OpenAlex ID: W2050155886
cites work: Some properties of fuzzy groups
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cites work: Q4091811
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description: scientific article; zbMATH DE number 694932