Differentiating adaptive Neuro-Fuzzy Inference System for accurate function derivative approximation

Function and its partial derivative approximation based upon a set of discrete dataset are important issues in soft computing. Several function approximators have been presented most of them fits a model to the dataset so that the Mean Squared Error is minimized. In this paper, we propose to calculate the derivative of the Neuro-Fuzzy function approximator directly according to the parametric structure of the system and the available dataset. A criterion for derivative approximation is defined based on a combination of MSE and Approximate Entropy. According to this criterion, the superiority of the Neuro-Fuzzy model is demonstrated in comparison with some other types of Artificial Neural Networks and Polynomial models.

[1]  Reza Langari,et al.  Complex systems modeling via fuzzy logic , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[2]  Detlef Nauck,et al.  A Neuro-Fuzzy Development Tool for Fuzzy Controllers under MATLAB/SIMULINK , 2000 .

[3]  Wen-Pai Wang,et al.  A neuro-fuzzy based forecasting approach for rush order control applications , 2008, Expert Syst. Appl..

[4]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[5]  H. Joel Trussell,et al.  Fuzzy inference systems implemented on neural architectures for motor fault detection and diagnosis , 1999, IEEE Trans. Ind. Electron..

[6]  Kazuo Tanaka,et al.  Successive identification of a fuzzy model and its applications to prediction of a complex system , 1991 .

[7]  Simon Parsons,et al.  Soft computing: fuzzy logic, neural networks and distributed artificial intelligence by F. Aminzadeh and M. Jamshidi (Eds.), PTR Prentice Hall, Englewood Cliffs, NJ, pp 301, ISBN 0-13-146234-2 , 1996, Knowl. Eng. Rev..

[8]  Elif Derya Übeyli,et al.  Adaptive neuro-fuzzy inference system for classification of EEG signals using wavelet coefficients , 2005, Journal of Neuroscience Methods.

[9]  Jyh-Shing Roger Jang,et al.  Self-learning fuzzy controllers based on temporal backpropagation , 1992, IEEE Trans. Neural Networks.

[10]  M Aliakcayol.  Application of adaptive neuro-fuzzy controller for SRM , 2004 .

[11]  Oliver Vornberger,et al.  Sales forecasting using neural networks , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[12]  Francesco Masulli,et al.  Building a neuro-fuzzy system to efficiently forecast chaotic time series , 1997 .

[13]  Junfei Qiao,et al.  A self-organizing fuzzy neural network and its applications to function approximation and forecast modeling , 2008, Neurocomputing.

[14]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Derek A. Linkens,et al.  A systematic neuro-fuzzy modeling framework with application to material property prediction , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[16]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .