In data fusion, we have several approximations to the desired objects, and we need to fuse them into a single -- more accurate -- approximation. In the traditional approach to data fusion, we usually assume that all the given approximations were obtained by minimizing the same distance function -- most frequently, the Euclidean (L2) distance. In practice, however, we sometimes need to use approximations corresponding to different distance functions. To handle such situations, a new more general approach to data processing and data fusion is needed. In this paper, we show that the simplest cases of such new situations lead to F-transform. Thus, F-transform can be viewed as a first step to such a general approach. From this viewpoint, we explain the formulas for the inverse F-transform, formulas which are empirically successful but which look somewhat strange from the viewpoint of the traditional approximation theory.