(m, n)-Ideals in Semigroups Based on Int-Soft Sets

Abstract

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft $\left(m,n\right)$ -ideals, int-soft $\left(m,0\right)$ -ideals, and int-soft $\left(0,n\right)$ -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft $\left(m,n\right)$ -ideal, int-soft $\left(m,0\right)$ -ideal, and int-soft $\left(0,n\right)$ -ideal are studied. Also, characterizations of various types of semigroups such as $\left(m,n\right)$ -regular semigroups, $\left(m,0\right)$ -regular semigroups, and $\left(0,n\right)$ -regular semigroups in terms of their int-soft $\left(m,n\right)$ -ideals, int-soft $\left(m,0\right)$ -ideals, and int-soft $\left(0,n\right)$ -ideals are provided.