Continuous and discrete higher-degree \(F\)-transforms based on B-splines (Q1701845)

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.