Soft Intersection Tri-ideals of Semigroups

In this paper, we introduce a novel type of soft intersection (S-int) ideal form called “soft intersection (S-int) tri-ideal” and obtain the relations between S-int tri-ideals and other certain types of S-int ideals of a semigroup. Our results show that the concept of S-int tri-ideal is a generalization of S-int ideal, interior ideal, bi-ideal, quasi-ideal, weak-interior ideal, bi-interior ideal, bi-quasi ideal, and quasi-interior ideal, however, the converses are valid only when the semigroup have specific conditions. Furthermore, we present conceptual characterizations and analysis of the new concept in terms of soft set operations and vital concepts of soft sets.