Fuzzy approximation by fuzzy convolution type operators

Authors:
G. A. Anastassiou
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2004

Citing 4
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Abstract

Here we introduce and study four sequences of naturally arising fuzzy integral operatorsof convolution type that are integral analogs of known fuzzy wavelet type operators, defined via a scaling function. Their fuzzy convergence with rates to the fuzzy unit operator is established through fuzzy inequalities involving the fuzzy modulus of continuity. Also, their high-order fuzzy approximation is given similarly by involving the fuzzy modulus of continuity of the N^t^h order (N = 1) H-fuzzy derivative of the engaged fuzzy number valued function. The fuzzy global smoothness preservation property of these operators is demonstrated also.