Abstract
Redundancy may be present in fuzzy models which are acquired from data by using techniques like fuzzy clustering and gradient learning. The redundancy may manifest itself in the form of a larger number of rules than necessary, or in the form of fuzzy sets that are very similar to one another. By reducing this redundancy, transparent fuzzy models with appropriate number of rules and distinct fuzzy sets are obtained. This chapter considers cluster validity and cluster merging techniques for determining the relevant number of rules for a given application when fuzzy clustering is used for modeling. Similarity based rule base simplification is then applied for reducing the number of fuzzy sets in the model. The techniques lead to transparent fuzzy models with low redundancy.
This is a preview of subscription content, log in via an institution to check access.
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
Babuška, R. and Kaymak, U. (1995). Application of compatible cluster merging to fuzzy modeling of multivariable systems. In Proc. Third European Congress on Intelligent Techniques and Soft Computing 2, 565–569, Aachen, Germany.
Babuška, R., Setnes, M., Kaymak, U., and van Nauta Lemke, H.R. (1996). Rule base simplification with similarity measures. In Proc. Fifth IEEE Int. Con f. on Fuzzy Systems 3, 1642–1647, New Orleans, USA.
Babuška, R. and Verbruggen, H. B. (1994). Applied fuzzy modeling. In IFAC Symposium on Artificial Intelligence in Real Time Control, 61–66, Valencia, Spain.
Babuška, R. and Verbruggen, H.B. (1995). Identification of composite linear models via fuzzy clustering. In Proc. of the European Control Conference, 1207–1212, Rome, Italy.
Backer, E. (1995). Computer-Assisted Reasoning in Cluster Analysis. Prentice Hall, New York.
Bezdek, J. (1981). Pattern Recognition with Fuzzy Objective Function. Plenum Press, New York.
Gath, I. and Geva, A. B. (1989). Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:7, 773–781.
Gustafson, D. and Kessel, W. (1979). Fuzzy clustering with a fuzzy covariance matrix. In Proc. IEEE CDC, 761–766, San Diego, USA.
Kaymak, U. (1994). Application of fuzzy methodologies to a washing process. Chartered designer thesis, Delft University of Technology, Control Lab., Faculty of El. Eng., Delft. (TWAIO 94.054).
Kaymak, U. and Babuška, R. (1995). Compatible cluster merging for fuzzy modelling. In Proc. Fourth IEEE Int. Conf. on Fuzzy Systems 2, 897–904, Yokohama, Japan.
Krishnapuram, R. and Freg, C.-P. (1992). Fitting an unknown number of lines and planes to image data through compatible cluster merging. Pattern Recognition 25:4, 385–400.
Mamdani, E. (1974). Applications of fuzzy algorithms for control of simple dynamic plant. In Proc. IEE 121 1585–1588.
Setnes, M. (1995). Fuzzy rule-base simplification using similarity measures. M.Sc. thesis, Delft University of Technology, Control Lab., Faculty of El. Eng., Delft. (A.95.023).
Setnes, M., Babuska, R., Kaymak, U., and van Nauta Lemke, H.R. (1997). Similarity measures in fuzzy rule base simplification. To appear in IEEE Transactions on Systems,Man and Cybernetics.
Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modelling and control. IEEE Transactions on Systems,Man and Cybernetics 15:1, 116–132.
Yang, M.-S. (1993). A survey of fuzzy clustering. Mathematical and Computer Modelling 18:11, 1–16.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kaymak, U., Babuška, R., Setnes, M., Verbruggen, H.B., van Nauta Lemke, H.R. (1997). Methods for Simplification of Fuzzy Models. In: Ruan, D. (eds) Intelligent Hybrid Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6191-0_4
Download citation
DOI: https://doi.org/10.1007/978-1-4615-6191-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7838-9
Online ISBN: 978-1-4615-6191-0
eBook Packages: Springer Book Archive