Neutrosophic N-structures on strong Shefer stroke non-associative MV

Abstract

 The aim of the study is to examine a neutrosophic N -subalgebra, a neutrosophic N -filter, level sets of these neutrosophic N -structures and their properties on a strong Sheffer stroke non-associative MV-algebra. We show that the level set of neutrosophic N -subalgebras on this algebra is its strong Sheffer stroke nonassociative MV-subalgebra and vice versa. Then it is proved that the family of all neutrosophic N -subalgebras of a strong Sheffer stroke non-associative MV-algebra forms a complete distributive lattice. By defining a neutrosophic N -filter of a strong Sheffer stroke non-associative MV-algebra, it is presented that every neutrosophic N -filter of a strong Sheffer stroke non-associative MV-algebra is its neutrosophic N -subalgebra but the inverse is generally not true, and some properties