Neutrosophic N-structures on Sheffer stroke UP-algebras
Aiyared Aiyared, Aiyared Iampan, Neelamegarajan Rajesh · International Journal of Neutrosophic Science · 2025
The study defines a neutrosophic N-subalgebra and a level set of a neutrosophic N-structure on Sheffer stroke UP-algebras. It appears that these concepts are integral to understanding the behavior of neutrosophic logic within the framework of Sheffer stroke UP-algebras. The study establishes a relationship between subalgebras and level sets on Sheffer stroke UP-algebras. Specifically, it proves that the level set of neutrosophic Nsubalgebras on this algebra is its subalgebra, and vice versa. This indicates a tight connection between these concepts within the given algebraic structure. It is stated that the family of all neutrosophic N-subalgebras of a Sheffer stroke UP-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 UP-algebra and provides some of its properties. Additionally, it is shown that every neutrosophic N-ideal of a Sheffer stroke UP-algebra is also its neutrosophic N-subalgebra, though the inverse is generally not true. This highlights the specific characteristics and behavior of neutrosophic Nideals within the given algebraic context.