F-transform versus Takagi-Sugeno models

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 F¹-transform components. The inverse F^m-transform, m ges 0, is defined in the same way as the ordinary F-transform. Finally, difference between F^m-transforms, m ges 0, and TS fuzzy models is discussed.