On (α, β)-fuzzy KU-ideals of KU-algebras

Afrika Matematika, 2014

In current paper we have defined (α, β)-fuzzy KU-ideals of KU-algebras and then some useful characterizations have provided. Finally we have introduced the concept of (α, β)-fuzzy KU-relation and then by the use of this notion we have proved some more interesting results.

International Journal of Pure and Apllied Mathematics, 2014

In this paper, we introduced the notion of interval-valued (θ, δ)fuzzy KU-ideals of KU-algebras and some related properties are investigated. We proved that U (η; t) is a KU-ideal if and only if the interval-valued fuzzy subset η is an interval-valued (θ, δ)-fuzzy KU-ideal of a KU-algebra for θ ≺ t δ.

In this paper, we apply the notion of a bipolar fuzzy n-fold KU-ideal of KU-algebras. We introduce the concept of a bipolar fuzzy n-fold KU-ideal and investigate several properties. Also, we give relations between a bipolar fuzzy n-fold KU-ideal and n-fold KU-ideal. The image and the pre-image of bipolar fuzzy n-fold KU-ideals in KU-algebras are defined and how the image and the pre-image of bipolar fuzzy n-fold KU-ideals in KU-algebras become bipolar fuzzy n-fold KU-ideals are studied. Moreover, the product of bipolar fuzzy n-fold KU-ideals in Cartesian product KU-algebras is given. Key words: KU-algebra, fuzzy KU-ideal, (bipolar fuzzy) KU-ideal, (bipolar fuzzy) n-fold KU-ideal.

In this manuscript, we introduce a new concept, which is called fuzzy left (right) derivations KU- ideals in KU-algebras. We state and prove some theorems about fundamental properties of it. Moreover, we give the concepts of theimage and the pre-image of fuzzy left (right) derivations KU-ideals under homomorphism of KU- algebras and investigated some its properties. Further, we have proved that every the image and the pre-image of fuzzy left (right) derivations KU-ideals under homomorphism of KU- algebras are fuzzy left (right) derivations KU-ideals. Furthermore, we give the concept of the Cartesian product of fuzzy left (right) derivations KU - ideals in Cartesian product of KU – algebras.

In this paper, we introduce the concept of fuzzy n-fold KU-ideal in KU-algebras, which is a generalization of fuzzy KU-ideal of KU-algebras and we obtain a few properties that is similar to the properties of fuzzy KU-ideal in KU-algebras, see [8]. Furthermore, we construct some algorithms for folding theory applied to KU-ideals in KU-algebras.-ideal, fuzzy n-fold KU-ideal, image and the pre image of fuzzy n-fold KU-ideal, product of fuzzy n-fold KU-ideals.

In this paper, we will introduce the concept of interval value fuzzy n-fold KU-ideal in KU-algebras, which is a generalization of interval value fuzzy KU-ideal of KU-algebras and we will obtain few properties that is similar to the properties of interval value fuzzy KU-ideal in KU-algebras, see [8]. Also, we construct some algorithms for folding theory applied to KU-ideals in KU-algebras.

2019

We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.

Ibn Al-Haitham Journal For Pure And Applied Science, 2022

In this paper, we introduce the concept of cubic bipolar-fuzzy ideals with thresholds (α,β),(ω,ϑ) of a semigroup in KU-algebra as a generalization of sets and in short (CBF). Firstly, a (CBF) sub-KU-semigroup with a threshold (α,β),(ω,ϑ) and some results in this notion are achieved. Also, (cubic bipolar fuzzy ideals and cubic bipolar fuzzy k-ideals) with thresholds (α,β),(ω ,ϑ) are defined and some properties of these ideals are given. Relations between a (CBF).sub algebra and-a (CBF) ideal are proved. A few characterizations of a (CBF) k-ideal with thresholds (α, β), (ω,ϑ) are discussed. Finally, we proved that a (CBF) k-ideal and a (CBF) ideal with thresholds (α, β), (ω,ϑ) of a KU-semi group are equivalent relations.

Complexity ( Hindawi), 2021

e concept of KM-algebras has been originated in 2019. KM-algebra is a generalization of some of the B-algebras such as BCK, BCI, BCH, BE, and BV and also d-algebras. KM-algebra serves two purposes in mathematics and computer science as follows: a tool for application in both fields and a strategy for creating the foundations. On the fuzziness of KM-algebras, an innovative perspective on fuzzy product KM-algebras as well as some related features is offered. Moreover, the notion of KMM-ideals is described and also initiated the concept of the KM-Cartesian product of fuzzy KM-algebras, and related outcomes are examined. Some of the innovative results in fuzzy KMM-ideals and KM-Cartesian product of fuzzy KM-subalgebras are analyzed, and some are as follows: arbitrary intersection of fuzzy KMM-ideals is again a fuzzy KMM-ideal, order reversing holds true in every KMMideal, every fuzzy KM-subalgebra is a fuzzy KMM-ideal, and KM-Cartesian product of two fuzzy KM-subalgebras is again a fuzzy KM-subalgebra.