Soft Intersection Almost Tri-bi-ideals of Semigroups - Aslihan Sezgin; Aleyna Ilgin; Akin Osman Atagun (Science & Technology Asia, 2024)
In this study, we introduce the notion of soft intersection almost tri-bi-ideals of semigroups as a generalization of nonnull soft intersection tri-bi-ideals and investigate its properties in depth. It is aimed to explore the relations of soft intersection almost tri-bi ideals with other certain kinds of soft intersection almost ideals of semigroups. It is shown that an idempotent soft intersection almost tri-bi-ideal coincides with the soft intersection almost bi-ideal of a semigroup. It is also illustrated that every idempotent soft intersection almost tri-bi-ideal is a soft intersection almost subsemigroup. Furthermore, we propose the concepts of soft intersection prime, semiprime and strongly prime almost ideals of a semigroup and explore the relationships regarding minimality, primeness, semiprimeness, and strong primeness between almost tri-bi-ideals and soft intersection almost tri-bi-ideals by deriving a notable result that if a nonempty subset of a semigroup is an almost tri-bi-ideal, then its soft characteristic function is a soft intersection almost tri-bi-ideal, and vice versa. This enables us to construct a bridge between classical semigroup theory and soft set theory.