Fuzzy maximal ideals of BCI and MV algebras
Let \(X\) be a BCI-algebra and let \(F(X)\) be the set of all fuzzy ideals of \(X\) which have 0 as a value. Then a fuzzy ideal of \(X\) is fuzzy maximal if it is nonconstant and its normalization is a maximal element of \(F(X)\) under an obvious partial ordering. It is then shown that such a fuzzy ideal is normalized and takes on only the values 0, 1. Relations are established between ideals and fuzzy ideals, and fuzzy maximal and fuzzy prime ideals for MV-algebras. Finally, an explicit construction is given for fuzzy ideals in such algebras which are not constants and are not characteristic functions of ideals.
scientific article; zbMATH DE number 694934
scientific article