Abstract
This paper proposes a new fuzzy modeling method, which involves the Minimum Cluster Volume clustering algorithm. The cluster centers founded are naturally considered to be the centers of Gaussian membership functions. Covariance matrix obtained from the result of cluster method is made use to estimate the parameters σ for Gaussian membership functions. A direct result of this method are compared in our simulations with published methods, which indicate that our method is powerful so that it solves the multi-dimension problems more accurately even with less complexity of our fuzzy model structure.
The Project Supported by Zhejiang Provincial Natural Science Foundation of China. No.601112.
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References
Bezdek, J.C.: Pattern recognition with fuzzy objective function. Plenum Press, New York (1981)
Gustafson, D.E., Kessel, W.C.: Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE CDC, San Diego, CA, USA, pp. 761–766 (1979)
Krishnapuram, R., Kim, J.: Clustering Algorithms on Volume Criteria. IEEE Trans. Fuzzy Systems 8(2), 228–236 (2000)
Yager, R., Filev, D.: Generation of Fuzzy Rules by Mountain Clustering. Journal of Intelligent & Fuzzy Systems 2(3), 209–219 (1994)
Chiu, S.: Fuzzy Model Identification Based on Cluster Estimation. Journal of Intelligent & Fuzzy Systems 2(3) (September 1994)
Babuska, R.: Fuzzy Modeling for Control. Kluwer Academic Publishers, Boston (1998)
Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal of Optimization 9(1), 112–147 (1998)
Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and Soft computing. Prentice-Hall, Englewood Cliffs (1997)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Llikelihood From Incomplete Data via the EM Algorithm. J. Roy. Statist. Soc. B(39), 1–38 (1977)
Glodberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Michigan (1975)
Zadeh, L.A.: Fuzzy Logic Toolbox User’s Guide Version 2.1.1. MathWorks Inc., Berkeley (2001)
Xie, X.L., Beni, G.: A Validity Measure for Fuzzy Clustering. IEEE Trans. Pattern Anal. 13, 841–847 (1991)
Mackey, M., Glass, L.: Oscillation and Chaos in Physiological Control Systems. Science 197, 287–289
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© 2005 Springer-Verlag Berlin Heidelberg
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Yang, C., Meng, J. (2005). Optimal Fuzzy Modeling Based on Minimum Cluster Volume. In: Li, X., Wang, S., Dong, Z.Y. (eds) Advanced Data Mining and Applications. ADMA 2005. Lecture Notes in Computer Science(), vol 3584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527503_28
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DOI: https://doi.org/10.1007/11527503_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27894-8
Online ISBN: 978-3-540-31877-4
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