This paper introduces the concepts and properties of complex fuzzy ideals (generalized biideals, bi-ideals, interior ideals, quasi-ideals, and (1, 2)-ideals) in semigroups, with proofs.Furthermore, we investigate the essential conditions for coincidence in the regular, intraregular, semisimple, weakly regular, or quasi-regular manner, in semigroups.
Khamrot et al. (Tue,) studied this question.