Fuzzy groups, fuzzy functions and fuzzy equivalence relations.
type: Item
instance of: scholarly article
title: Fuzzy groups, fuzzy functions and fuzzy equivalence relations.
zbMATH Open document ID: 1066.20076
DOI: 10.1016/S0165-0114(03)00301-4
author: Yanyan Li
published in: Fuzzy Sets and Systems
publication date: 2004-08-20T00:00:00Z
review text: The paper applies the notion of fuzzy functions with respect to fuzzy equalities introduced by the first author [cf. Fuzzy Sets Syst. 106, No. 2, 239-246 (1999; Zbl 0934.03067); J. Math. Anal. Appl. 252, No. 1, 495-517 (2000; Zbl 0973.03071); Int. J. Gen. Syst. 32, No. 2, 123-155 (2003; Zbl 1028.03044); ibid. 157-175 (2003; Zbl 1028.03045); ibid. 177-201 (2003; Zbl 1028.03046)]. The main goal of the paper is a comparison between properties of fuzzy groups [cf., e.g., \textit{N. Kuroki}, Inf. Sci. 53, No. 3, 203-236 (1991; Zbl 0714.20052); ibid. 75, No. 3, 201-211 (1993; Zbl 0808.20052)] and vague groups [cf. \textit{M. Demirci}, J. Math. Anal. Appl. 230, No. 1, 142-156 (1999; Zbl 0949.20050)] with applications to fuzzy subgroups and vague groups on the real line. Final results of the paper are very restrictive: reduce a fuzzy case to the crisp one. For example (Theorem 5.4), any admissible fuzzy equivalence relation on the real line reduces to a two-valued function (like the characteristic function of the identity relation). Similarly, fuzzy numbers considered as fuzzy groups reduce to fuzzy points (Corollary 5.5) or to triangular fuzzy numbers (Example 5.10).
Mathematics Subject Classification ID: 20N25
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 08A72
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 26E50
zbMATH DE Number: 2093611
zbMATH Keywords: fuzzy functions
zbMATH Keywords: fuzzy equivalences
zbMATH Keywords: fuzzy equalities
zbMATH Keywords: fuzzy groups
zbMATH Keywords: vague groups
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: fuzzy subgroups
reviewed by: Józef Drewniak
MaRDI profile type: Publication
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full work available at URL: s0165-0114(03)00301-4
OpenAlex ID: W1986645676
description: scientific article; zbMATH DE number 2093611