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Fuzzy approximation by fuzzy convolution type operators. (English) Zbl 1102.41305
Summary: Here we introduce and study four sequences of naturally arising fuzzy integral operators of 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 Nth order (N1) H-fuzzy derivative of the engaged fuzzy number valued function. The fuzzy global smoothness preservation property of these operators is demonstrated also.
MSC:
41A35Approximation by operators (in particular, by integral operators)
26E50Fuzzy real analysis
41A30Approximation by other special function classes