Implicative and Positive Implicative Ideals of Neutrosophic INK-algebras

This paper introduces and develops the concepts of implicative and positive implicative ideals within the framework of INK-algebras. These notions are subsequently extended to fuzzy and neutrosophic contexts, resulting in the definitions of fuzzy implicative ideals (FMI), fuzzy positive implicative ideals (FPMI), neutrosophic implicative ideals (NII), and neutrosophic positive implicative ideals (NPII). The structural properties of these ideals are investigated, including their behavior under intersection and union, where it is shown that intersection preserves the respective implicative properties, while union does not in general. Furthermore, we establish that the homomorphic pre-images of these ideals also preserve their respective fuzzy and neutrosophic implicative structures. The results contribute to a deeper understanding of ideal theory in INK-algebras under uncertainty, and open pathways for applications in fuzzy logic and neutrosophic systems.