Abstract
There are many papers in the literature that deal with the problem of the design of a fuzzy system from a set of given training examples. Those who get the best approximation accuracy are based on TSK fuzzy rules, which have the problem of not being as interpretable as Mamdany-type Fuzzy Systems. A question now is posed: How can the interpretability of the generated fuzzy rule-table base be increased? A possible response is to try to reduce the rule-base size by generalizing fuzzy-rules consequents which are symbolic functions instead of fixed scalar values or polynomials, and apply symbolic interpolations techniques in fuzzy system generation. A first approximation to this idea is presented in this paper for 1-D functions.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Funabashi, M., Maeda, A.: Fuzzy and neural hybrid expert systems: synergetic AI. IEEE Expert, 32–40 (1995)
Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and soft computing. Prentice-Hall, Englewood Cliffs (1997) ISBN 0-13-261066-3
Kosko, B.: Neural Networks and Fuzzy Systems. Prentice-Hall, Englewood Cliffs (1992)
Pomares, H., Rojas, I., Ortega, J., Gonzalez, J., Prieto, A.: A Systematic Approach to a Self-Generating Fuzzy Rule-Table for Function Approximation. IEEE Trans. on Syst. Man. and Cyber. 30(3) (June 2000)
Rojas, I., Merelo, J.J., Bernier, J.L., Prieto, A.: A new approach to fuzzy controller designing and coding via genetic algorithms. In: IEEE International Conference on Fuzzy Systems, Barcelona, pp. 1505–1510 (July 1997)
Rovatti, R., Guerrieri, R.: Fuzzy sets of rules for system identification. IEEE Trans. on Fuzzy Systems 4(2), 89–102 (1996)
Sudkamp, T., Hammell, R.J.: Interpolation, Completion, and Learning Fuzzy Rules. IEEE Trans. on Syst. Man and Cyber. 24(2), 332–342 (1994)
Wang, L.X., Mendel, J.M.: Generating fuzzy rules by learning from examples. IEEE Trans. On Syst. Man and Cyber 22(6), 1414–1427 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rubio, G., Pomares, H. (2005). A Basic Approach to Reduce the Complexity of a Self-generated Fuzzy Rule-Table for Function Approximation by Use of Symbolic Interpolation. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_5
Download citation
DOI: https://doi.org/10.1007/11494669_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26208-4
Online ISBN: 978-3-540-32106-4
eBook Packages: Computer ScienceComputer Science (R0)