The aim of this paper is to introduce the notion of hyper fuzzy AT-ideals on hyper AT-algebra. Also, hyper fuzzy AT-subalgebras and fuzzy hyper AT-ideal of hyper AT-algebras are studied. We study on the fuzzy theory of hyper AT-subalgebras and hyper AT-ideal of hyper AT-algebras. Furthermore, the fuzzy set theory of the (weak, strong, s-weak) hyper fuzzy ATideals in hyper AT-algebras are applied and the relations among them are obtained.
In this paper is to introduce the concept of hyper AT-algebras is a generalization of AT-algebras and study a hyper structure AT-algebra and investigate some of its properties. “Also, hyper AT-subalgebras and hyper AT-ideal of hyper AT-algebras are studied. We study on the fuzzy theory of hyper AT-ideal of hyper AT-algebras hyper AT-algebra”. “We study homomorphism of hyper AT-algebras which are a common generalization of AT-algebras.
The aim of this work is to a connection between two concepts which are an interval value fuzzy set and a hyper AT-algebra. Also, some properties of these concepts are found. The notions of IVF hyper AT-subalgebras, IVF hyper ideals and IVF hyper AT-ideals are defined. Then IVF (weak, strong) hyper ideals and IVF (weak, strong) hyper AT-ideals are discussed. After that, some relations among these ideals are presented and some interesting theorems are proved.
We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T-ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied. Abstract We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T- ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied.
We present the notion of bipolar fuzzy k-ideals with thresholds (
It is known that, the concept of hyper KU-algebras is a generalization of KU-algebras. In this paper, we define cubic (strong, weak,s-weak) hyper KU-ideals of hyper KU-algebras and related properties are investigated.
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.
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 threshol
... Show MoreIn this work, we study of the concept of a cubic set of a semigroup in KU-algebra. Firstly, we study a cubic sub KU-semigroup and achieve some results in this notion. And then, we get a relation between a cubic sub KU-semi group and a level set of a cubic set. Moreover, we define some cubic ideals of this structure and we found relationships between these ideals.
2010 AMS Classification. 08A72, 03G25, 06F35
Let R be a commutative ring with identity. A proper ideal I of R is called semimaximal if I is a finite intersection of maximal ideals of R. In this paper we fuzzify this concept to fuzzy ideals of R, where a fuzzy ideal A of R is called semimaximal if A is a finite intersection of fuzzy maximal ideals. Various basic properties are given. Moreover some examples are given to illustrate this concept.
Zadah in [1] introduced the notion of a fuzzy subset A of a nonempty set S as a mapping from S into [0,1], Liu in [2] introduced the concept of a fuzzy ring, Martines [3] introduced the notion of a fuzzy ideal of a fuzzy ring. A non zero proper ideal I of a ring R is called an essential ideal if I  J  (0), for any non zero ideal J of R, [4]. Inaam in [5] fuzzified this concept to essential fuzzy ideal of fuzzy ring and gave its basic properties. Nada in [6] introduced and studied notion of semiessential ideal in a ring R, where a non zero i
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