TY  - EJOU
AU  - Katican, Tugce 
AU  - Oner, Tahsin 
AU  - Rezaei, Akbar 
AU  - Smarandache, Florentin 

TI  - Neutrosophic <i>N</i>-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 <i>N</i>-subalgebra, a (ultra) neutrosophic <i>N</i>-filter, level sets of these neutrosophic <i>N</i>-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 <i>N</i>-subalgebras on the algebraic structure is its quasi-subalgebra and vice versa. Then we show that the family of all neutrosophic <i>N</i>-subalgebras of a Sheffer stroke BL-algebra forms a complete distributive lattice. After that a (ultra) neutrosophic <i>N</i>-filter of a Sheffer stroke BL-algebra is described, we demonstrate that every neutrosophic <i>N</i>-filter of a Sheffer stroke BL-algebra is its neutrosophic <i>N</i>-subalgebra but the inverse is generally not true. Finally, it is presented that a level set of a (ultra) neutrosophic <i>N</i>-filter of a Sheffer stroke BL-algebra is also its (ultra) filter and the inverse is always true. Moreover, some features of neutrosophic <i>N</i>-structures on a Sheffer stroke BL-algebra are investigated.
KW  - Sheffer stroke BL-algebra; (ultra) filter; neutrosophic <i>N</i>-subalgebra; (ultra) neutrosophic <i>N</i>-filter

DO  - 10.32604/cmes.2021.016996