Approximation properties of fuzzy transforms

Abstract

We enlarge the class of fuzzy transforms (F-transforms) by considering different types of fuzzy partitions. New types of F-transforms are constructed based on B-splines, Shepard kernels, Bernstein basis polynomials and Favard–Szász–Mirakjan type operators. We study approximation properties of F-transforms. Particular cases of the classical Korovkin's theorems are presented, together with new error estimates for different types of fuzzy transforms. It turns out that F-transforms can be studied in the framework of classical approximation theory.