Fuzzy transform as an additive normal form

In this paper, we recall a class of approximating formulas. Since they arose as a generalization of classical normal forms we denote them by the same term. Moreover, we will show that the fuzzy transform (F-transform) introduced in [Perfilieva, I., Fuzzy approach to solution of differential equations with imprecise data: application to reef growth problem, in: R.V. Demicco, G.J. Klir (Eds.), Fuzzy Logic in Geology, Academic Press, Amsterdam, 2003, pp. 275–300 (Chapter 9), Perfilieva, I., Fuzzy transforms, in: J.F. Peters, A. Skowron (Eds.), Transactions on Rough Sets II. Rough Sets and Fuzzy Sets, Lecture Notes in Computer Science, vol. 3135, 2004, pp. 63–81] as an approximation method for continuous functions can be viewed as a particular case of normal form. Therefore, the results valid for normal forms may be applied to F-transforms as well.