F-transform; Fm-transform; fuzzy partition; orthogonal basis; TS model

The aim of this contribution is to provide a deeper analysis of fuzzy modeling and its contribution to general mathematics. We show how the F-transform technique can be generalized and considered as a special integral transform in a functional space with inner product. We apply a technique of numeric integration in order to simplify computation of F1- transform components. The inverse Fm-transform, m>0, is defined in the same way as the ordinary F-transform. Finally, difference between Fm-transforms, m > 0, and TS fuzzy models is discussed.