Fuzzy transforms, korovkin theorems and the durrmeyer operator
Barnabás Bede, Imre J. Rudas · European Society for Fuzzy Logic and Technology Conference · 2009
In the present paper a Korovkin-type theorem is pro- posed for the approximation operators defined by the inverse F- transforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform's framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions are shown to include, for example the Bernstein ba- sis polynomials. The F-transform considered with the Bernstein basis polynomials as atoms of a fuzzy partition, is shown to be the classical Durrmeyer operator.