The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-262

“Non-Singleton Fuzzy Logic Systems: Theory and Application”

by George C. Mouzouris and Jerry M. Mendel

May 1994

In this paper we present a formal derivation of general nonsingleton fuzzy logic systems (NSFLSs), and show how they can be efficiently computed. We give examples for special cases of membership functions and inference. We show how a NSFLS can be expressed as a nonsingleton fuzzy basis function expansion, and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations. We prove that a NSFLS can uniformly approximate any given continuous function on a compact set, and show that our NSFLS does a much better job of predicting a noisy chaotic time series than does a singleton FLS.

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