Translation of Neutrosophic INK-Algebra

Wadei Faris AL-Omeri; M Kaviyarasu; M Rajeshwari

Authors

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, Tamilnadu-600062,India;
M Rajeshwari School of Engineering, Presidency University, Bangalure,India;

Keywords:

INK-algebra; Translation INK-ideal; Neutrosophic translation INK-ideal; Neutrosophic translation INK-subalgebra

Abstract

This study investigates the philosophical foundations of the neutrosophic set(NS), as rst proposed
by Smarandache. It clari es the connection between single-valued Nss and their function as a specialized subset
in the larger context of Nss, particularly in the elds of science and engineering. This paper investigates neutro
sophic 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 def
initions and theorems are added in the article, providing comprehensive insights complexities of NINK-A.

DOI: 10.5281/zenodo.10905892