In this paper, a new type of generalized version of the notion of fuzzy closed set, viz., fs^θg-closed set, is introduced and studied. Using this concept as a basic tool, here we introduce and study fs^θg -open and fs^θg -closed functions, the class of which are strictly larger than that of fuzzy open and fuzzy closed functions respectively. Afterwards, we introduce and study fs^θg -continuous and fs^θg -irresolute functions. Next, we introduce fs^θg -regular, fs^θg -normal, fs^θg -compact and fs^θg -T₂-spaces and the applications of the functions defined in this paper on these spaces are discussed here.