Abstract
The theory of bipolar fuzzy sets introduced by Lee [9] has been applied to many branches of mathematics. In this paper, we initiate a study on bipolar fuzzy sets in Gamma-semihypergroups. We define bipolar fuzzy left (right, bi-, interior, (1, 2)-) Gamma-hyperideals and explore some related properties. We use these bipolar fuzzy Gamma-hyperideals to characterize some classes of Gamma-semihypergroups. We consider the Gamma-semihypergroup (H) under bar of the bipolar fuzzy points of a Gamma-semihypergroup H to discuss the relation between the bipolar fuzzy sub Gamma-semihypergroup (left, right, bi-, interior, (1, 2)-) Gamma-hyperideal and the subsets of (H) under bar in a (regular) Gamma-semihypergroup. In the end, we discuss in detail a number of results on homomorphic images and preimages of bipolar fuzzy Gamma-hyperideals.