Generalized Fuzzy Connectives onMV-Algebras
Copyright policy )Generalized Fuzzy Connectives onMV-Algebras
\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.
\(MV\)-algebra, De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects), Applied Mathematics, algebra of fuzzy sets, fuzzy negations, Theory of fuzzy sets, etc., negation operators, generalized conorms, Analysis
\(MV\)-algebra, De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects), Applied Mathematics, algebra of fuzzy sets, fuzzy negations, Theory of fuzzy sets, etc., negation operators, generalized conorms, Analysis
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