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Continuous and discrete higher-degree \(F\)-transforms based on B-splines. (English) Zbl 1384.65094

A fuzzy transform with polynomial components of degree \(m\geq 0\) is denoted as \(F^m\)-transform. The authors show that continuous and discrete \(F^m\)-transforms based generalized fuzzy partition by B-splines of degree \(2k-1\) are precise for polynomials of degree \(r \leq \min \{2m+1,\,2k-1\}\). Then they present error estimates for the approximation of a transformed function and its derivatives by continuous and discrete \(F^m\)-transforms.

MSC:

65R10 Numerical methods for integral transforms
41A35 Approximation by operators (in particular, by integral operators)
65D07 Numerical computation using splines
44A99 Integral transforms, operational calculus
26E50 Fuzzy real analysis

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References:

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