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

Document Type : Research Paper


1 Department of Mathematics, Ege University, Izmir, Turkey

2 Department of Mathematics, Izmir University of Economics, Izmir, Turkey

3 Department of Mathematics, Payame Noor University, Tehran, Iran



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.


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