It is known that the category of sober topological spaces is the epireflective hull of the Sierpiński space in the category of \(T_0\) spaces. By identifying two cogenerators in the category of \(T_0\) bitopological spaces, E. Giuli and S. Salbany [\(2T_0\) spaces and closure operators, Seminarberichte aus dem Fachbereich Mathematik und Informatik, Fernuniversität Hagen 29, 11-40 (1988)] introduced two epireflective subcategories of \(T_0\) bitopological spaces, the category of absolutely \(2T_0\) closed spaces and that of sober bitopological spaces. In this paper, a perfect analogous programme was carried out within the category of \(2T_0\) fuzzy bitopological spaces. Results similar to those in that paper of Giuli and Salbany were proved in the fuzzy setting.