In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con...In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.展开更多
With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of...With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.展开更多
The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（...The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.展开更多
In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations betwe...In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.展开更多
基金Supported by the National Natural Science Foundation of China (61175055)the Innovation Term of Higher Education of Hubei Province,China (T201109)+1 种基金the Natural Science Foundation of Hubei Province (2012FFB01101)the Natural Science Foundation of Education Committee of Hubei Province (D20131903)
文摘In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
基金Supported by the National Natural Science Foundation of China(60875034)the Natural Science Foundation of Education Committee of Hubei Province(D20092901),the Natural Science Foundation of Hubei Province(2009CDB340)
文摘With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.
基金Supported by the National Natural Science Foundation of China (60875034)the Natural Science Foundationof Education Committee of Hubei Province (D20092901+3 种基金Q20092907D20082903B200529001)the NaturalScience Foundation of Hubei Province (2008CDB341)
文摘The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.
基金Supported by National Natural Science Foundation of China(11461025,61175055)
文摘In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.
