The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-alge...The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.展开更多
This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we ...This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.展开更多
Some properties of nil ideals in BCI-algebras are discussed. The notion of k-associative BCI-algebras which is a generalization of associative and quasi-associative BCI-algebras is introduced. Moreover,several charact...Some properties of nil ideals in BCI-algebras are discussed. The notion of k-associative BCI-algebras which is a generalization of associative and quasi-associative BCI-algebras is introduced. Moreover,several characterizations of k-associative BCI-algebras are given.展开更多
In this paper, we firstly introduce the concept of（α, β）-soft ideals of Weak-BCIalgebras after endowing a parameter set as a Weak-BCI-algebra. When U = [0, 1], α = U,β = ？, it becomes the hesitant fuzzy ideals ...In this paper, we firstly introduce the concept of（α, β）-soft ideals of Weak-BCIalgebras after endowing a parameter set as a Weak-BCI-algebra. When U = [0, 1], α = U,β = ？, it becomes the hesitant fuzzy ideals of Weak-BCI-algebras. Then important properties of（α, β）-soft ideals of Weak-BCI-algebras are given. Finally, we investigate the properties of the homomorphism image and inverse image of（α, β）-soft ideals of Weak-BCI-algebras.展开更多
基金Supported by the Special Item of Key Laboratory of Education Bureau of Sichuan Province(2006ZD050)Supported by Natural Science Foundation of China(11071178)
文摘The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.
文摘This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.
文摘Some properties of nil ideals in BCI-algebras are discussed. The notion of k-associative BCI-algebras which is a generalization of associative and quasi-associative BCI-algebras is introduced. Moreover,several characterizations of k-associative BCI-algebras are given.
基金Supported by the National Natural Science Foundation of China(Grant No.61170121)the Natural Science Foundation of Jiangsu Province(Grant No.BK20151117)the Natural Science Foundation of Wuxi Taihu University(Grant No.16WUNS006)
文摘In this paper, we firstly introduce the concept of（α, β）-soft ideals of Weak-BCIalgebras after endowing a parameter set as a Weak-BCI-algebra. When U = [0, 1], α = U,β = ？, it becomes the hesitant fuzzy ideals of Weak-BCI-algebras. Then important properties of（α, β）-soft ideals of Weak-BCI-algebras are given. Finally, we investigate the properties of the homomorphism image and inverse image of（α, β）-soft ideals of Weak-BCI-algebras.
