Translation of Neutrosophic INK-Algebra.

This study investigates the philosophical foundations of the neutrosophic set(ℕS), as first proposed by Smarandache. It clarifies the connection between single-valued ℕs and their function as a specialized subset in the larger context of Nss, particularly in the fields of science and engineering. This paper investigates neutrosophic INK-ideals(NINK-Is) within INK-algebras(INK-A) by using the notion of translation, which is positioned as an extension of intuitionistic fuzzy sets. The notion of translation neutrosophic INK-algebras(NTINK-A) is introduced and their fundamental characteristics are explored. In addition, properties associated with the translation of INK-subalgebra(INK-Ss) and INK-ideals(INK-I) are investigated, along with the dynamics of their multiplications, unions, and intersections in the context of neutrosophic INK-ideals(NINK-I). Further definitions and theorems are added in the article, providing comprehensive insights complexities of NINK-A. [ABSTRACT FROM AUTHOR]