Generalized fuzzy interior ideals of semigroups

The concept of $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy interior ideals of semigroups is introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy interior ideals, (∈, ∈ ∨ q)-fuzzy interior ideals and $$(\overline{\in},\overline{\in} \vee \overline{q})$$-fuzzy interior ideals of semigroups. Finally, we give some characterization of [F]t by means of (∈, ∈ ∨ q)-fuzzy interior ideals.