Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, ...Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.展开更多
In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtai...In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).展开更多
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
文摘Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.
文摘In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).
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.
