Construction of a Neurofuzzy Network Capable of Extrapolating (and Interpolating) With Respect to the Convex Hull of a Set of Input Samples in ${{\bb R}}^n$

The problem of regression estimation is considered with a specific regard for the distinction between interpolation and extrapolation. A neurofuzzy network named NFECH is proposed that is capable of extrapolating (and interpolating) with respect to the convex hull of a finite set of input samples X sub Ropfⁿ. The geometrical construction of the proposed network is explained both mathematically and graphically. The illustrations explain how the particular parts of the construction work, and also show the final surfaces of the obtained models. The method is tested on artificial datasets generated from mathematical functions according to various statistical distributions. Also, comparisons to the commonly used radial basis function (RBF), multilayered perceptron (MLP) neural networks, and to fuzzy rule interpretation (FRI)/fuzzy rule extrapolation (FRE) approach are presented.