A new notion in frame theory has been introduced recently under the name wovenweaving frames by Bemrose et al. In the study of frames, some operators like analysis,
synthesis, Gram and frame operators play the central role. In this paper, for the first
time, we introduce and define these operators for woven-weaving frames and review
some of their properties. In continuation, we investigate the effect of different types of
operators on the woven frames and their bounds. Also, we provide some conditions that
shows sum of woven frames are also woven frames. Finally, we apply these properties
with an example.