Neutrosophic N-structures on Sheffer stroke BG-algebras

Tahsin Oner; Neelamegarajan Rajesh; Akbar Rezaei; Ibrahim Senturk

Authors

Tahsin Oner Ege University;
Neelamegarajan Rajesh Rajah Serfoji Government College;
Akbar Rezaei Payame Noor University;
Ibrahim Senturk Ege University;

Keywords:

Sheffer stroke (BG-algebra), ideal, neutrosophic N-subalgebra, neutrosophic N-ideal.

Abstract

The study defines a neutrosophic N-subalgebra and a level set of a neutrosophic N-structure on
Sheffer stroke BG-algebras. It appears that these concepts are integral to understanding the behavior of
neutrosophic logic within the framework of Sheffer stroke BG-algebras. The study establishes a relationship
between subalgebras and level sets on Sheffer stroke BG-algebras. Specifically, it proves that the level set of
neutrosophic N-subalgebras on this algebra is its subalgebra, and vice versa. This indicates a tight connection
between these two concepts within the given algebraic structure. It is stated that the family of all neutrosophic
N-subalgebras of a Sheffer stroke BG-algebra forms a complete distributive lattice. This suggests that there is a
well-defined structure and order among these subalgebras, allowing for systematic analysis. The study describes
a neutrosophic N-ideal of a Sheffer stroke BG-algebra and provides some of its properties. Additionally, it is
shown that every neutrosophic N-ideal of a Sheffer stroke BG-algebra is also its neutrosophic N-subalgebra,
though the inverse is generally not true. This highlights the specific characteristics and behavior of neutrosophic
N-ideals within the given algebraic context.

DOI 10.5281/zenodo.21480805