We present a novel color video compression method using the greatest solution of a system of bilinear fuzzy relation equations to assess the similarity between frames. The frames in each band are treated separately and each frame is classified as an Intra frame or a Predictive frame. A frame is labelled as Predictive frame, and compressed more than an Intra-frame, if the similarity value with the previous Intra frame is higher than a selected threshold; A pre-processing activity is performed to select the optimal threshold value of the similarity between frames. The proposed method allows to supply a high quality of the reconstructed frames and has the advantage of not requiring high CPU time and memory storage for its execution; it was tested on color videos of the Fast-Moving Objects dataset; the results show that it produces better performances than the Lukasiewicz similarity-based video compression method and comparable with those achieved by MPEG-4 and the deep learning video compression method DVC_pro. The results show that the quality of the reconstructed frames obtained with BFRE is comparable with that of DVC Pro, but has a lower computational complexity, providing better performances in terms of video encoding speed.