In this paper, we introduce a generalization of a bipolar fuzzy subsemigroup, namely a (a1, a2; β1, β2)-bipolar fuzzy subsemigroup. The notions of (a1, a2; β1, β2)-bipolar fuzzy left (right, bi-) ideals are discussed. Some necessary and sufficient conditions of (a1, a2; β1, β2)-bipolar fuzzy left (right, bi-) ideals are obtained. Furthermore, any regular semigroup is characterized in terms of generalized bipolar fuzzy semigroups.
