Generalized fuzzy connectives on \(MV\)-algebras
type: Item
instance of: scholarly article
title: Generalized fuzzy connectives on \(MV\)-algebras
zbMATH Open document ID: 0874.06010
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-04-29T00:00:00Z
review text: \textit{S. V. Ovchinnikov} [ibid. 92, 234-239 (1983; Zbl 0518.04003)] studied negations in the algebra \([0,1]^X\) of the fuzzy sets defined on the set \(X\).The author considers the above algebra as an \(MV\)-algebra in the sense of \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)]. In this general framework, three negation operators are defined and corresponding classes of \(MV\)-algebras are characterized. Stronger representation theorems are obtained then for fuzzy negations and for generalized conorms.
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1005669
zbMATH Keywords: algebra of fuzzy sets
zbMATH Keywords: \(MV\)-algebra
zbMATH Keywords: negation operators
zbMATH Keywords: fuzzy negations
zbMATH Keywords: generalized conorms
author: Peter L. Belluce
reviewed by: Antonio Di Nola
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5214
OpenAlex ID: W1973598789
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DOI: 10.1006/JMAA.1997.5214
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description: scientific article; zbMATH DE number 1005669