Approximation by multivariate higher degree \(F\)-transform based on B-splines (Q1701844)

A fuzzy transform with multivariate polynomial components of total degree \(m\) is a multivariate \(F^m\)-transform. This paper deals with the approximation by integral and discrete versions of multivariate \(F^m\)-transforms. The authors generalize results for univariate \(F^m\)-transforms to the multivariate case. Using multivariate B-splines as generating functions of multidimensional fuzzy partition, the authors improve the approximation of multivariate functions and their derivatives.