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Just as the concept of interior ideal of semigroups is a generalization of ideal in semigroups, the notion of soft intersection (soft-int) interior ideal is a generalization of soft-int ideal. In this paper, we propose the concepts of soft-int (weakly) almost interior ideal of a semigroup as a generalization of the nonnull soft-int interior ideals. We explore their algebraic properties in detail. We also show that an idempotent soft-int almost interior ideal is a soft-int almost subsemigroup. We additionally derive several intriguing relations related to semiprimeness, minimality, and (strongly) primeness between almost interior ideals and soft-int almost interior ideals.
Sezgin et al. (Tue,) studied this question.