In this paper, a new type of fuzzy generalized closed set is defined via fuzzy α-open sets, called fgα^θ-closed set. Complements of fgα^θ -closed sets, called fgα^θ -open sets form a family that is not a topology. Using this new type of generalized closed sets, the corresponding open functions and closed function are introduced and studied. A new separation property generalizing the T₂-property of fuzzy topological space is shown to be invariant to bijective fgα^θ -open functions. Many examples are given, to illustrate the new concepts and to distinguish these from known related concepts.