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Soft intersection bi-ideal is a generalization of soft intersection quasi-ideals; and soft intersection quasi-ideal is a generalization of soft intersection left (right) ideal. In this study, as a generalization of nonnull soft intersection bi-ideals of semigroups, we introduced the concept of soft intersection almost bi-ideals and studied its basic properties in detail. By obtaining that if a nonempty set is almost bi-ideal, then its soft characteristic function is soft intersection almost bi-ideal and vice versa, we acquire many interesting relationships between almost bi-ideals and soft intersection almost bi-ideals concerning minimality, primeness, semiprimeness, and strongly primeness.
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