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Mathematical Problems in Engineering
Volume 2017, Article ID 8594738, 10 pages
Research Article

Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations

Departamento de Control Automatico, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico

Correspondence should be addressed to Wen Yu; xm.vatsevnic.lrtc@wuy

Received 19 July 2016; Revised 26 October 2016; Accepted 21 December 2016; Published 22 January 2017

Academic Editor: Rosana Rodriguez-Lopez

Copyright © 2017 Raheleh Jafari and Wen Yu. 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.


The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.