r-(τi, τj)-θ-Generalized Fuzzy Closed Sets in Smooth Bitopological Spaces

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 which is generate a smooth topology. Finally, (i, j) strongly-θ-fuzzy continuous, (i, j)-θgeneralized fuzzy continuous and (i, j)-θ-generalized fuzzy irresolute mappings are introduce, we show that (i, j)-θ-generalized fuzzy continuous properly fits in between (j, i) strongly-θ-fuzzy continuous and (i, j)-generalized fuzzy continuous.