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Book ChapterDOI

On \((\in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras

20 Jul 2017-pp 91-110
TL;DR: A new concept of the descending (ascending) chain conditions of the ideals of KU-algebras is introduced and is studied using the properties of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals.
Abstract: First, new concepts of pointwise \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals and generalized fuzzy ideals of KU-algebras are defined. By using inequalities, level sets and characteristic functions, some equivalent characterizations of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are studied, a richer hierarchical structure of this fuzzy ideal is presented, and some properties are discussed using the partial order of KU-algebras. Second, it is proven that the intersections, unions (under certain conditions), homomorphic image and homomorphic preimage of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals. Then, the direct product and projection of the \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also investigated. Finally, a new concept of the descending (ascending) chain conditions of the ideals of KU-algebras is introduced and is studied using the properties of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals.
References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal ArticleDOI
TL;DR: The definition of an (ϵ, ϵ v q)-fuzzy subgroup is slightly modified and some of the fundamental properties of such fuzzy subgroups are obtained.

324 citations

Journal ArticleDOI
Nobuaki Kuroki1
TL;DR: In this article, the authors give some properties of fuzzy ideals and fuzzy bi-ideals of semigroups, and characterize semiigroups that are (left) duo, simple and semilattices of subsemigroups in terms of fuzzy notions and fuzzy ideals.

279 citations

Book
10 Dec 1998
TL;DR: L-subsets and L-subgroups of Abelian groups as discussed by the authors, which are a generalization of group L -subalgebras, and are the basis of the L-ideals structure.
Abstract: L-subsets and L-subgroups L-subgroups of Abelian groups L-submodules L-subrings and L-ideals L-subfields structure of L-subrings and L-ideals algebraic L-varieties and intersection equations L-subspaces Galois theory and group L-subalgebras.

235 citations