Neutrosophic $mathcal{N}-$structures on Sheffer stroke BE-algebras

In this study, a neutrosophic N−N−subalgebra, a (implicative) neutrosophic N−N− filter, level sets of these neutrosophic N−N−structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic N−N− subalgebras ((implicative) neutrosophic N−N−filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then we present relationships between upper sets and neutrosophic N−N−filters of this algebra. Also, it is given that every neutrosophic N−N−filter of a SBE-algebra is its neutrosophic N−N−subalgebra but the inverse is generally not true. We study on neutrosophic N−N−filters of SBE-algebras by means of SBE-homomorphisms, and present relationships between mentioned structures on a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N−N−functions and some properties are examined.