Interval-Valued Neutrosophic Fuzzy n-Fold Positive Implicative Ideals of BCK-Algebras: Properties and Characterizations

This paper investigation elucidates the notion of interval-valued neutrosophic fuzzy n-fold ideals in BCK-algebras, with a specific focus on interval-valued neutrosophic fuzzy n-fold BCK-ideal and interval valued neutrosophic fuzzy n-fold positive implicative ideals. A comprehensive examination of the characteriza tion theorems and extension properties of these ideals is undertaken. Notably, it is demonstrated that every interval-valued neutrosophic fuzzy n-fold BCK-ideal is an interval-valued neutrosophic fuzzy ideal, and every interval-valued neutrosophic fuzzy n-fold positive implicative ideal is an interval-valued neutrosophic fuzzy ideal. Furthermore, counterexamples are constructed to delineate the limitations of these concepts.