%0 Journal Article %T Neutrosophic $\mathcal{N}-$structures on Sheffer stroke BE-algebras %J Journal of Mahani Mathematical Research %I Shahid Bahonar University of Kerman %Z 2251-7952 %A Oner, Tahsin %A Katican, Tugce %A Svanidze, Salviya %A Rezaei, Akbar %D 2022 %\ 01/01/2022 %V 11 %N 1 %P 121-143 %! Neutrosophic $\mathcal{N}-$structures on Sheffer stroke BE-algebras %K SBE-algebra %K (implicative) SBE-filter %K neutrosophic N− subalgebra %K (implicative) neutrosophic N−filter %R 10.22103/jmmrc.2021.18565.1176 %X 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. %U https://jmmrc.uk.ac.ir/article_3122_65be36521efc8627d6bfb4c6df494a9f.pdf