The structures of the families of fuzzy sets that arise out of various notions of openness and closeness in a double fuzzy topological space are explored. This research is to present a new portion of space (Double-connected intuitionistic space) in Double intuitionistic topological spaces. Through these concepts, we advance some of their characteristics and relate to themselves.

The aim of this paper is to introduce a new classis of Double intuitionistic continuous function, Double intuitionistic (open and closed) functions in Double intuitionistic topological spaces, we investigate the properties of the relationships among these types.