Neutrosophic N-Structures Applied to Sheffer Stroke BL-Algebras

In this paper, we introduce a neutrosophic Arsubalgebra, a (ultra) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties on a Sheffer stroke BL-algebra. By defining a quasi-subalgebra of a Sheffer stroke BL-algebra, it is proved that the level set of neutrosophic N-subalgebras on the algebraic structure is its quasi-subalgebra and vice versa. Then we show that the family of all neutrosophic N-subalgebras of a Sheffer stroke BL-algebra forms a complete distributive lattice. After that a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is described, we demonstrate that every neutrosophic N-filter of a Sheffer stroke BL-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. Finally, it is presented that a level set of a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is also its (ultra) filter and the inverse is always true, Moreover, some features of neutrosophic N-structures on a Sheffer stroke BL-algebra are investigated.