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 ...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.展开更多
文摘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.
