aspg-21-3426-1791475392 20261008160312 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Wadei Faris AL-Omeri Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid, Jordan M.Kaviyarasu Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R & D Institute of Science and Technology, Chennai, India Rajeshwari M. Department of Mathematics,Presidency University, Bangalore, India This paper investigates the theoretical basis of fermatean neutrosophic sets, which were first introduced by Smarandache, to clarify the relationship between single-valued fermatean neutrosophic sets and their role as specific subsets in the wider context of fermatean neutrosophic sets, particularly in science and engineering. This study investigates fermatean neutrosophic INK-ideals within INK-algebras using the translation concept, which is proposed as an extension of intuitionistic fuzzy sets. First, translation fermatean neutrosophic INKalgebras are presented and their fundamental features are studied. Furthermore, the research investigates properties related to the translation of INK-subalgebras and INK-ideals, as well as the dynamics of their unions, intersections, and multiplications for fermatean neutrosophic INK-ideals. The article adds definitions and theorems to provide a complete grasp of the problems of fermatean neutrosophic INK-algebras. 2025 135 146 3426 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250411 https://www.americaspg.com/journal/21/article/3426 https://www.americaspg.com/storage/61735276830.pdf