Generalized fuzzy connectives on \(MV\)-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.
scientific article; zbMATH DE number 1005669
scientific article