A theory of vague lattices based on many-valued equivalence relations. I: General representation results
type: Item
instance of: scholarly article
title: A theory of vague lattices based on many-valued equivalence relations. I: General representation results
zbMATH Open document ID: 1067.06006
author: Mustafa Demirci
published in: Fuzzy Sets and Systems
publication date: 2005-04-21T00:00:00Z
review text: Fuzzy orderings in the sense of \textit{U. Bodenhofer} [Fuzzy Sets Syst. 137, No. 1, 113--136 (2003; Zbl 1052.91032)] are extended to integral, commutative, complete, quasi-monoidal lattices in the sense of the author [Int. J. Gen. Syst. 32, No. 2, 123--155 (2003; Zbl 1028.03044)] and defined as vague orderings. Known notions of fuzzy orderings due to \textit{U. Bodenhofer} [loc. cit.] and \textit{U. Höhle} and \textit{N. Blanchard} [Inf. Sci. 35, 133--144 (1985; Zbl 0576.06004)] are seen as special cases of vague orderings. The author then defines the concept of vague lattice and shows how such lattices can be constructed, represented and algebraically characterized. Other related papers are due to the same author [Int. J. Gen. Syst. 32, No. 2, 157--175 (2003; Zbl 1028.03045); ibid. 32, No. 2, 177--201 (2003; Zbl 1028.03046); ibid. 32, No. 5, 431--458 (2003; Zbl 1051.93019)].
reviewed by: Salvatore Sessa
Mathematics Subject Classification ID: 06D72
zbMATH DE Number: 2160228
zbMATH Keywords: Fuzzy lattice
zbMATH Keywords: Fuzzy ordering
zbMATH Keywords: Fuzzy equivalence relation
zbMATH Keywords: Fuzzy equality
zbMATH Keywords: Indistinguishability operator
MaRDI profile type: Publication
full work available at URL: j.fss.2004.06.017
OpenAlex ID: W2018761380
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DOI: 10.1016/J.FSS.2004.06.017
description: scientific article; zbMATH DE number 2160228