Stability Conditions of Fuzzy Filter Type III

DOI: 10.4236/jsip.2011.23034   PDF   HTML     4,852 Downloads   7,147 Views  


A digital fuzzy logic filter of type III interacts with a real model signal reference to obtain the best answer in the sense of minimum mean square error of the output. The key part of the filter is a fuzzy mechanism that adaptively selects and emits answer according to the changes of the external reference signal. Based on input signal level, this fuzzy filter selects the best parameter values from a set of membership in the knowledge base (KB), and the filter weights are updated according to the reference signal in a natural form. With this fuzzy structure the filter reduces error. The simulation result shows the stability of the filter. The states of the filtering process require that all of its answers are bounded by the error criteria probabilistically.

Share and Cite:

J. Juárez, J. Infante and J. García, "Stability Conditions of Fuzzy Filter Type III," Journal of Signal and Information Processing, Vol. 2 No. 3, 2011, pp. 245-251. doi: 10.4236/jsip.2011.23034.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. H. Sayed, “Fundamentals of Adaptive Filters,” Wiley-IEEE, Hoboken, 2003.
[2] J. Smith and A. Eiben, “Introduction to Evolutionary Computing,” Springer, Dordrecht, 2003.
[3] T. Amble, “Logic Programming and Knowledge Engineering,” Addison Wesley, Boston, 1987.
[4] J. J. Medel, J. C. García and J. C. Sánchez, “Real-time Fuzzy Digital Filters (RTFDF) Properties for SISO Systems,” Automatic Control and Computer Sciences, Vol. 41, No. 1, 2008, pp. 26-34.
[5] F. Yamakawa, “Fuzzy Neurons and Fuzzy Neural Networks,” 1989.
[6] D. Marcek, “Stock Price Forecasting: Statistical, Classical and Fuzzy Neural Networks,” Modeling Decisions for Artificial Intelligence, Springer Verlag, Berlin, 2004, pp. 41-48.
[7] V. Kharitonov, “Robust stability analysis of time delay systems: A survey,” Annual Reviews in Control, Vol. 23, 1999, pp 185-196. doi.10.1016/S1367-5788(99)90087-1
[8] L. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-XU
[9] C. L. Chen, G. Feng and X. P. Guan, “Delay Dependent Stability Analysis and Controller Synthesis for Discrete Time TS Fuzzy Systems with Time Delays,” IEEE Transactions on Fuzzy Systems, Vol. 13, No. 5, 2005, pp. 630-643. doi:10.1109/TFUZZ.2005.856562U
[10] E. Onieva,V. Milanés, J. Pérez and T. Pedro, “Estimación de un Control Lateral Difuso de Vehículos,” RIAII, Vol. 7, No. 2, 2010, pp. 91-98. doi:10.4995/RIAI.2010.02.09U
[11] C. W. Tao and J. S. Taur, “Robust Fuzzy Control for a Plant with Fuzzy Lineal Model,” IEEE Transactions on Fuzzy Systems, Vol. 13, No. 1, 2005, pp. 30-41. doi:10.1109/TFUZZ.2004.839653U
[12] E. Mamdani, “Applications of Fuzzy Algorithms for Control of Simple Dynamic Plant,” Proceedings of the IEEE, Vol. 121, No. 12, 1974, pp. 1585-1588.
[13] F. Gustafsson, “Adaptive Filtering and Change Detection,” John Wiley and Sons Ltd, Hoboken, 2000.
[14] K. M. Passino, “Fuzzy Control,” Addison Wesley, Boston, 1998.
[15] Ash, “Real Analysis and Probability,” Academic Press USA, 1970.
[16] T. Takagiand M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modelling and Control,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 15, No. 1, 1986, pp. 116-132.
[17] L. Zadeh, “Maximizing Sets and Fuzzy Markoff Algorithms,” IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, Vol. 28, No. 1, 1998, pp. 9-15. doi:10.1109/5326.661086U
[18] J. García,J. Medel andL. Guevara, “Filtrado Difuso en Tiempo Real,” Computación y Sistemas, Vol. 11, No. 4, 2008, pp. 390-401.
[19] J. García, J. Medel and J. Sánchez, “Evolutive Neural Net Fuzzy Filtering: Basic Description,” Journal of Intelligent Learning Systems and Applications, Vol. 2, No. 1, 2010, pp. 12-18.
[20] S. Haykin, “Adaptive Filtering,” Prentice Hall, UpperSaddle River, 2001.
[21] M. Margaliot and G. Langholz, “New Approaches to Fuzzy Modeling and Control Design and Analysis,” World Scientific, 2000. doi:10.1142/9789812792716U
[22] B. Rajen and M. Gopal, “Neuro-Fuzzy Decision Trees,” International Journal of Neural Filters, Vol. 16, No. 1, 2006, pp. 63-68. doi:10.1142/S0129065706000470U
[23] M. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical Journal, Vol. 27, 1948, pp. 379-423&623-656.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.