TY - EJOU
AU - Katican, Tugce
AU - Oner, Tahsin
AU - Rezaei, Akbar
AU - Smarandache, Florentin
TI - Neutrosophic *N*-Structures Applied to Sheffer Stroke BL-Algebras
T2 - Computer Modeling in Engineering \& Sciences
PY - 2021
VL - 129
IS - 1
SN - 1526-1506
AB - In this paper, we introduce a neutrosophic *N*-subalgebra, 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.
KW - Sheffer stroke BL-algebra; (ultra) filter; neutrosophic *N*-subalgebra; (ultra) neutrosophic *N*-filter
DO - 10.32604/cmes.2021.016996