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Advances in Fuzzy Systems
Volume 2013 (2013), Article ID 136214, 16 pages
http://dx.doi.org/10.1155/2013/136214
Research Article

Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification

1Tijuana Institute of Technology, 22379 Tijuana, BCN, Mexico
2Baja California Autonomous University (UABC), 22379 Tijuana, BCN, Mexico

Received 15 January 2013; Revised 20 June 2013; Accepted 20 June 2013

Academic Editor: F. Herrera

Copyright © 2013 Oscar Castillo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.