# 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.

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