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This study investigates the philosophical foundations of the neutrosophic set (NS), as first proposed by Smarandache. It clarifies the connection between single-valued Nss 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 oftheir 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.