In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filt...In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of （∈γ, ∈γ Vqδ）-intuitionistic fuzzy soft filters of BL-algebras.展开更多
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
The authors introduce the notions of （∈, ∈ ∨q）-fuzzy Boolean （implicative, positive implicative, and fantastic） filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and des...The authors introduce the notions of （∈, ∈ ∨q）-fuzzy Boolean （implicative, positive implicative, and fantastic） filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an （∈, ∈ ∨q）fuzzy filter in a BL-algebra is Boolean （implicative） if and only if it is both positive implicative and fantastic.展开更多
基金Supported by the Graduate Independent Innovation Foundation of Northwest University(YZZ12061)
文摘In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of （∈γ, ∈γ Vqδ）-intuitionistic fuzzy soft filters of BL-algebras.
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.
基金the Key Science Foundation of Education Committee of Hubei Province,China,under Grant No.D200729003
文摘The authors introduce the notions of （∈, ∈ ∨q）-fuzzy Boolean （implicative, positive implicative, and fantastic） filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an （∈, ∈ ∨q）fuzzy filter in a BL-algebra is Boolean （implicative） if and only if it is both positive implicative and fantastic.
