A new notion in frame theory has been introduced recently under the name of woven-weaving frames by Bemros et. al. In this paper, Motivating by the concepts of fusion and weaving frames, we introduce the notion of woven-weaving fusion frames and present some of their features. It is well known that the perturbation theory is a paramount component in the study of frames. In this paper, we show that those of fusion frames that are small perturbations of each other, constitute woven-weaving fusion frames.
