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Motivated by studying partial order and lattice of bipolar fuzzy sets, and algebraic framework of bipolar fuzzy sets, in this paper, we introduce the notion of a bipolar fuzzy abundant semigroup by developing a new technique for constructing fuzzy semigroups. After obtaining some properties of bipolar fuzzy abundant semigroups, we give necessary and sufficient conditions of a bipolar fuzzy subset of an abundant semigroup to be bipolar fuzzy abundant. As an application, we extend our results to the case of regular semigroup. 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