Abstract
In this paper, we use IVI-octahedron ideals and IVI-octahedron bi-ideals to discuss some characterizations of special semigroups, e.g., an intra-regular semigroup, a semigroup which is semilattice of left [respectively, right] simple semigroups or simple left groups and a semigroup which is a semilattice of groups and a [respectively, left and right] simple semigroups. Finally, we define an IVIO-simple [IVIOL-simple and IVI) R-simple] semigroup and study some of its properties and we give a characterization of a semisimple semigroup by IVIOIs.