In this paper a new class of fuzzy sets, namely r-(τi, τj)-θ-generalized fuzzy closed sets is introduced for smooth bitopological spaces. This class falls strictly in between the class of r-(τj, τi)fuzzy θ-closed sets and the class of r-(τi, τj)generalized fuzzy closed sets. Furthermore, by using the class of r-(τi, τj)-θgeneralized fuzzy closed sets we establish a new fuzzy closure operator wh...