Designing fuzzy logic systems for uncertain environments using a singular-value-QR decomposition method

Nonsingleton fuzzy logic systems (NSFLSs) are generalizations of singleton fuzzy logic systems (FLSs), that are capable of handling set-valued input. In this paper, we extend the theory of NSFLSs by presenting an algorithm to design and train such systems. Since they generalize singleton FLSs, 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 examples to illustrate the ability of the SVD-QR method to operate in uncertain environments.