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Abstract

The importance of semigroups and their fuzzy subsystems is evident from their applications and significant role in several applied disciplines like computer sciences, control engineering, error-correcting codes and fuzzy automata theory. In this paper, we give generalizations of intuitionistic fuzzy interior ideals of semigroups and introduced the notions of intuitionistic fuzzy interior ideals of type \((\overline{∈}, \overline{∈} ∨ \overline{q}_{k})\) and \((\overline{∈}, \overline{∈})\) of semigroups. The important mile stone of the present paper is to link ordinary intuitionistic fuzzy interior ideals, \((\overline{∈}, \overline{∈})\)-intuitionistic fuzzy interior ideals and \((\overline{∈}, \overline{∈} ∨ \overline{q}_{k})\)-intuitionistic fuzzy interior ideals. Moreover semigroups are characterized by the properties of these notions.