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-softm,n-ideals, int-softm,0-ideals, and int-soft0,n-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-softm,n-ideal, int-softm,0-ideal, and int-soft0,n-ideal are studied. Also, characterizations of various types of semigroups such asm,n-regular semigroups,m,0-regular semigroups, and0,n-regular semigroups in terms of their int-softm,n-ideals, int-softm,0-ideals, and int-soft0,n-ideals are provided.
Highlights
Soft set theory of Molodtsov [1] is an important mathematical tool to dealing with uncertainties and fuzzy or vague objects and has huge applications in real-life situations
The problems of uncertainties deal with enough numbers of parameters which make it more accurate than other mathematical tools. us, the soft sets are better than the other mathematical tools to describe the uncertainties
In [4], Maji et al investigated several operations on soft sets. e notions of soft sets introduced in different algebraic structures had been applied and studied by several authors, for example, Aktas and Çaǧman [2] for soft groups, Feng et al [5] for soft semirings, and Naz and Shabir [6, 7] for soft semi-hypergroups
Summary
Soft set theory of Molodtsov [1] is an important mathematical tool to dealing with uncertainties and fuzzy or vague objects and has huge applications in real-life situations. We prove that a soft set (K , S) over U is an int-soft (m, n)-ideal over U if and only if (K m°χS°K n, S) ⊆ (K , S). We characterize (m, n) regular semigroups in terms of int-soft (m, n)-ideals over U.
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