On\(n\)-fold fuzzy positive implicative ideals of BCK-algebras

Abstract

We consider the fuzzification of the notion of an $n$-fold positive implicative ideal. We give characterizations of an $n$-fold fuzzy positive implicative ideal. We establish the extension property for $n$-fold fuzzy positive implicative ideals, and state a characterization of ${\text{PI}}^n$-Noetherian BCK-algebras. Finally we study the normalization of $n$-fold fuzzy positive implicative ideals.