Neutrosophic N-structures on Sheffer stroke BE-algebras

Abstract

In this study, a neutrosophic N-subalgebra, a (implicative) neutrosophic N-filter, level sets of these neutrosophic 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-subalgebras ((implicative) neutrosophic N-filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then it is proved that the family of all neutrosophic N-subalgebras of a SBE-algebra forms a complete distributive modular lattice. We present relationships between upper sets and neutrosophic N-filters of this algebra. Also, it is given that every neutrosophic N-filter of a SBE-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. It is demonstrated that a neutrosophic N-structure on a SBE-algebra defi ned by a (implicative) neutrosophic N-filter of another SBE-algebra and a surjective SBE-homomorphism is a (implicative) neutrosophic N-filter. We present relationships between a neutrosophic N-filter and an implicative neutrosophic N-filter of a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N-functions and some properties are examined.