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

In this study, a neutrosophic \mathcal{N}-subalgebra, a (implicative) neutrosophic \mathcal{N}- filter, level sets of these neutrosophic \mathcal{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 \mathcal{N}- subalgebras ((implicative) neutrosophic \mathcal{N}-filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then we present relationships between upper sets and neutrosophic \mathcal{N}-filters of this algebra. Also, it is given that every neutrosophic \mathcal{N}-filter of a SBE-algebra is its neutrosophic \mathcal{N}-subalgebra but the inverse is generally not true. We study on neutrosophic \mathcal{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 \mathcal{N}-functions and some properties are examined.

کلیدواژه ها:

SBE-algebra ، (implicative) SBE-filter ، neutrosophic N− subalgebra ، (implicative) neutrosophic N−filter