Soft Union Weak-interior Ideals of Semigroups

Abstract

     It has shown to be interesting and beneficial for mathematicians to generalize the ideals of an algebraic structure. In this context, the concept of weak-interior ideal was presented as a generalization of quasi-ideal, interior ideal and (left/right) ideal of semigroup. In this paper, we transfer this concept to soft set theory and introduce a novel type of soft union (S-uni) ideal called "soft union (S-uni) weak-interior ideal”. The main goal of this study is to obtain the relations between S-uni weak-interior ideals and other certain types of S-uni ideals of a semigroup. Our findings indicate that S-uni weak-interior ideal is a generalization of S-uni ideal and interior ideal; however, the converses are true under certain conditions. Furthermore, we demonstrate that S-uni bi-ideals and S-uni quasi-ideals coincide with weak-interior ideals of a group. Our key theorem, which shows that if a subsemigroup of a semigroup is a weak-interior ideal, then its soft characteristic function is an S-uni weak-interior ideal, and vice versa, allows us to build a bridge between semigroup and soft set theory. Besides, we provide some conceptual analysis of the concept in terms of soft set operations, soft (inverse) image by backing up our claims with informative examples.