Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras

Tahsin Oner (Department of Mathematics, Ege University)
Tugce Katican (Department of Mathematics, Izmir University of Economics)
Akbar Rezaei (Department of Mathematics, Payame Noor University)

Journal of the Indonesian Mathematical Society
VOLUME 29 NUMBER 1 (MARCH 2023)

In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N −subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals.