A Singular-Value-QR Decomposition Based Method for Training Fuzzy Logic Systems in Uncertain Environments

Abstract

We extend the theory of nonsingleton fuzzy logic systems (NSFLSs) by presenting an algorithm to design and train such systems. Since NSFLSs are a generalization of singleton fuzzy logic systems, the algorithm is equally applicable to both types of systems. The proposed SVD-QR method selects subsets of independent basis functions which are sufficient to represent a given system, through operations on a nonsingleton fuzzy basis function matrix. In addition, it provides an estimate of the number of necessary basis functions. We present several examples to illustrate the ability of the SVD-QR method to operate in uncertain environments.