In this paper, we extend the four notions of connectedness introduced by Ajmal and Kohli [1] to pairwise connectedness for an arbitrary fuzzy set in fuzzy bitopological spaces (X, τ1, τ2) and discuss the implications that exist between them. These conditions are called сk- pairwise connectedness (k = 1, 2, 3, 4). We establish that the union of an arbitrary family of сk- pairwise connected (k = 1, 2) fuzzy set which are pairwise intersecting is сk- pairwise connected (k = 1, 2). Also the union of arbitrary family of сk- pairwise connected (k = 3, 4) fuzzy set which are overlapping is сk- pairwise connected (k = 3, 4). It is also shown that (τi, τj)- closure of a с1- pairwise connected fuzzy set. We also discuss the preservation of  сk- pairwise connectedness (k = 1, 2, 3, 4) under fuzzy pairwise continuous mapping and fuzzy pairwise open mapping.