(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The study defines an intuitionistic fuzzy SUP-subalgebra and a level set of an intuitionistic fuzzy UP-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 UP-subalgebras and level sets on Sheffer stroke UP-algebras. Specifically, it proves that the level set of intuitionistic fuzzy SUP-subalgebras on this algebra is its subalgebra, and vice versa. It is stated that the family of all intuitionistic fuzzy SUP-subalgebras of a Sheffer stroke UP-algebra forms a complete distributive lattice. Additionally, it is shown that every intuitionistic fuzzy SUP-ideal of a Sheffer stroke UP-algebra is also its intuitionistic fuzzy SUP-subalgebra, though the inverse is generally not true. This highlights the specific characteristics and behavior of intuitionistic fuzzy SUP-ideals within the given algebraic context.