(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we displayed and characterized a novel class of fuzzy open sets (F-open sets) in double fuzzy topological spaces (DFTSs) based on Šostak^,s sense, called (r,s)-fuzzy b-open sets ((r,s)-F-b-open sets). This class is contained in the class of (r,s)-F-β-open sets and contains all (r,s)-F-α-open sets, (r,s)-F-pre-open sets, and (r,s)-F-semi-open sets. Next, we explored and studied the notion of DF-b-continuity between DFTSs (G, , ^*) and (Z, , ^*). We also defined and discussed the notions of DF-almost b-continuity and DF-weakly b-continuity, which are weaker forms of DF-b-continuity. Thereafter, we presented and investigated novel DF-mappings via (r,s)-F-b-open and (r,s)-F-b-closed sets. Finally, we introduced some novel types of DF-separation axioms, called (r,s)-F-b-regular and (r,s)-F-b-normal spaces, and studied some properties of them.