Properties of Hybrid Bi-Interior Ideals of Semigroups

The fuzzy set is an excellent tool for dealing with indeterminacy that can be clearly and effectively analysed from the decision-maker’s viewpoint, and it is extremely helpful for showing people’s hesitations in their everyday interactions. In order to deal with practical problems, soft set theory has recently been created. By combining the fuzzy and soft sets, Jun et al. [Hybrid structures and applications, Annals of Communications in Mathematics 1(1) (2018) 11–25] created hybrid structures. Hybrid structures are a combination of soft-set and fuzzy-set theories. The concepts of hybrid bi-interior ideals of semigroups are addressed in this paper. We also characterize regular semigroups in terms of hybrid bi-interior ideals of semigroups.