Approximation properties of fuzzy transforms

Authors:
Barnabás Bede;Imre J. Rudas
Affiliations:
Department of Mathematics, The University of Texas Pan American, 1201 West University, Edinburg, TX 78539, USA;Óbuda University, Bécsi út 96/B, H-1034 Budapest, Hungary
Venue:
Fuzzy Sets and Systems
Year:
2011

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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-Szasz-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.