Abstract
A novel learning algorithm for recurrent neurofuzzy networks is introduced in this paper. The learning algorithm uses the gradient projection method to update the network weights. Moreover, the core of the learning algorithm uses equality index as the performance measure to be optimized. Equality index is especially important because its properties reflect the fuzzy set-based structure of the neural network and nature of learning. The neural network topology is built with fuzzy neuron units and performs neural processing consistent with fuzzy system methodology. Therefore neural processing and learning are fully embodied within fuzzy set theory. The performance recurrent neurofuzzy network is verified via examples of nonlinear system modeling and time series prediction. The results confirm the effectiveness of the neurofuzzy network.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Santos, E. P., Von Zuben, F. J.: Efficient Second-Order Learning Algorithms for Discrete-Time Recurrent Neural Networks. In: Medsker, L. R., Jain, L. C. (eds.): Recurrent Neural Networks: Design and Applications, CRC Press (1999) 47–75.
Lin, F. J., HwangChang, W. J., Wai, R. J.: A supervisory fuzzy neural network control system for tracking periodic inputs. IEEE Trans. on Fuzzy Systems, Vol. 7 (1999) 41–52.
Wang, L. X.: Adaptive Fuzzy Systems and Control, Prentice-Hall (1997).
Lee, C. H., Teng, C. C.: Identification and control of dynamic systems using recurrent fuzzy neural networks. IEEE Trans. on Fuzzy Systems, Vol. 8(4) (2000) 349–366.
Blanco, A., Delgado, M. Pegalajar, M. C.: Identification of fuzzy dynamic systems using Max-Min recurrent neural networks. IEEE Trans. On Systems, Man and Cybernetics, Vol 26(1) (2001) 451–467.
Ballini, R., Soares, S., Gomide, F.: A recurrent neurofuzzy network structure and learning algorithm. In 10th IEEE Int. Conference on Fuzzy Systems, Vol. 3 (2001) 1408–1411.
Rosen, J. B.: The gradient projection method for nonlinear programming, Part I, Linear Constraints. SIAM J. Applied Mathematics, Vol. 8 (1960) 514–553.
Pedrycz, W.: Neurocomputations in relational systems. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 13(3) (1991) 289–297.
Pedrycz, W., Gomide, F.: An Introduction to Fuzzy Sets: Analysis and Design. MIT Press, Cambridge, (1998).
Pedrycz, W., Rocha, A.: Fuzzy-set based models of neuron and knowledge based networks. IEEE Trans. on Fuzzy Systems, Vol. 4(1) (1998) 254–266.
Ballini, R., Gomide, F.: Learning in recurrent, hybrid neurofuzzy networks. In 11th IEEE Int. Conference on Fuzzy Systems, (2002) 785–790.
Caminhas, W., Tavares, H., Gomide, F. Pedrycz, W.: Fuzzy set based neural networks: structure, learning ands applications. Journal of Advanced Computational Intelligence, Vol. 3(3) (1999) 151–157.
Bazaraa, A. S., Shetty, M.: Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York (1979).
Narendra, K. S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Networks, Vol. 1(1) (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ballini, R., Gomide, F. (2003). Gradient Projection Method and Equality Index in Recurrent Neural Fuzzy Network. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_70
Download citation
DOI: https://doi.org/10.1007/3-540-44967-1_70
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40383-8
Online ISBN: 978-3-540-44967-6
eBook Packages: Springer Book Archive