A comparative study of the MAX and SUM machine-learning algorithms using virtual fuzzy sets

Abstract

This paper presents an adaptive fuzzy learning algorithm for non-linear system identification. The algorithm is based on a concept called a “virtual fuzzy set”. The concept provides a new representation for the consequent part of a fuzzy production rule. A virtual fuzzy set, which consists of two consecutive fuzzy sets with different degrees of membership, is an imaginary fuzzy set located at a location most appropriate for a numerical training data point. The aim of virtual fuzzy set is to increase the system accuracy, at minimum expense in terms of computer resources. The concept is incorporated into a one-pass build-up adaptive algorithm for non-linear system identification. The results show that better performance can be achieved, compared with traditional fuzzy sets. Two variations of the learning algorithm, using the MAX or SUM of rule degrees, are proposed. The performance of these two approaches in identifying processes with different noise levels is evaluated.