Fuzzy complexity estimation of a nonlinear learning machine

Abstract

Theories for a complexity estimation of different learning machines use the Vapnik Chervonenkis dimension, or various approximations to it, to predict optimal structure of a learning machine. This approach has some deficiencies that stems from Aristotelian logic foundation behind the Vapnik Chervonenkis dimension. An alternative fuzzy logic approach is introduced that brings a concise definition of errors and complexity estimation of a learning machine. In contradiction to the statistical learning theory where errors are actually counted in the fuzzy logic approach errors are measured. It is necessary to include information about the distances of violations about the quality of prediction. Some experiments are presented to evaluate a quality of propose algorithm.