In this paper, we introduce the concepts of -fuzzy ideals, -fuzzy left (right) ideals and -fuzzy interior ideals of semigroups, where  and    These concepts are more general forms of the paper by Shabir and Ali [15]. Special attention is paid to -fuzzy (left, right, interior) ideals of semigroups and related properties  are investigated. Regular, intra-regular and semisimple semigroups   are characterized in terms of their -fuzzy ideals, -fuzzy left (right) ideals and -fuzzy interior ideals.

-fuzzy ideals, -fuzzy ideals, regular semigroups, intra-regular semigroups, semisimple semigroups