Abstract
The adequate analysis of bipolar information of a semigroup using a fuzzy set requires incorporation of a bipolar fuzzy set and an appropriate semigroup structure. 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. In particular, bipolar fuzzy regular semigroups are investigated.
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