F-transform, fuzzy modeling, random set, fuzzy control

F-transform is a modern and successful technique in fuzzy modeling. It maps an original universe of functions into a universe of their ``skeleton models'' (vectors of F-transform components) where further computations are easier. By this, it is as useful in applications (image compression, image fusion, data mining, time series procession, etc.) as traditional transforms. The empirical successes of F-transform suggest that this transformation can be provided with a natural probabilistic interpretation. Such an interpretation is presented in this paper. Specifically, we show that the probabilistic interpretation of fuzzy modeling by Sanchez et al. can be modified into a natural probabilistic explanation of F-transform formulas.