Neuro-fuzzy Kolmogorov's network with a modified perceptron learning rule for classification problems

Abstract

A novel Neuro-Fuzzy Kolmogorov's Network (NFKN) is considered. The NFKN is based on the famous Kolmogorov's superposition theorem (KST) and is the development of the previously proposed Fuzzy Kolmogorov's Network (FKN). Modifications of the FKN architecture include multiple outputs as required for classification problems with more than two classes, as well as the possibility of defining different number of membership functions at each input. A new learning algorithm, based on the modified perceptron learning rule and designed for classification problems, is proposed. The validity of theoretical results and the advantages of the new NFKN are confirmed by experiments in data classification and visualization.