On generalized interval valued fuzzy quasi-ideals of semigroups

In this paper, we give the concepts of generalized interval valued fuzzy subsemigroups, which are generalizations of the notion of interval valued fuzzy subsemigroups and of (ᾱ, β)-interval valued fuzzy subsemigroups, where ᾱ ≺ β. Also we prove some of related properties of generalized interval valued fuzzy quasi-ideals on semigroups. In the main results, we characterize regular and intra-regular semigroups in terms of generalized interval valued fuzzy ideal and quasi-ideals.Publisher's Versio

On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. We say that a proper submodule $N$ of $M$ is a weakly $2$-absorbing semi-primary submodule if $a_{1}, a_{2}\in R, m\in N$ with $0 \neq a_{1}a_{2}m \in N$, then $a_{1}a_{2}\in \sqrt{(N : M)}$ or $a_{1}m \in N$ or $a^{n}_{2}m\in N$ for some positive integer $n$. In this paper, we study weakly $2$-absorbing semi-primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of weakly $2$-absorbing semi-primary submodules and we investigate weakly $2$-absorbing semi-primary submodules of some well-known modules

On properties of generalized bipolar fuzzy semigroups

In this paper, we introduce a generalization of a bipolar fuzzy subsemigroup, namely a (1, 2; 1, 2)-bipolar fuzzy subsemigroup. The notions of (1, 2; 1, 2)-bipolar fuzzy left (right, bi-) ideals are discussed. Some necessary and sufficient conditions of (1, 2; 1, 2)-bipolar fuzzy left (right, bi-) ideals are obtained. Furthermore, any regular semigroup is characterized in terms of generalized bipolar fuzzy semigroup

On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. We say that a proper submodule $N$ of $M$ is a weakly $2$-absorbing semi-primary submodule if $a_{1}, a_{2}\in R, m\in N$ with $0 \neq a_{1}a_{2}m \in N$, then $a_{1}a_{2}\in \sqrt{(N : M)}$ or $a_{1}m \in N$ or $a^{n}_{2}m\in N$ for some positive integer $n$. In this paper, we study weakly $2$-absorbing semi-primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of weakly $2$-absorbing semi-primary submodules and we investigate weakly $2$-absorbing semi-primary submodules of some well-known modules

On rough sets induced by fuzzy relations approach in semigroups

In this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified

On fuzzy soft bi-ideals over semigroups

The aim of this paper is to study fuzzy soft bi-ideals over semigroups and give some properties of prime, strongly prime and semiprime fuzzy soft bi-ideals over semigroups. We also show that a semigroup is both regular and intra-regular if and only if every fuzzy soft bi-ideal over the semigroup is a semiprime

Some Types of Subsemigroups Characterized in Terms of Inequalities of Generalized Bipolar Fuzzy Subsemigroups

In this paper, we introduce a generalization of a bipolar fuzzy (BF) subsemigroup, namely, a ( α 1 , α 2 ; β 1 , β 2 ) -BF subsemigroup. The notions of ( α 1 , α 2 ; β 1 , β 2 ) -BF quasi(generalized bi-, bi-) ideals are discussed. Some inequalities of ( α 1 , α 2 ; β 1 , β 2 ) -BF quasi(generalized bi-, bi-) ideals are obtained. Furthermore, any regular semigroup is characterized in terms of generalized BF semigroups