Abstract
Fuzzy clustering provides a (fuzzy) classification of data into different classes. From the result of a fuzzy cluster analysis fuzzy classification rules can be derived. The most common techniques for this derivation of rules are based on projections of the clusters. The corresponding rules classify only approximately in the same way as the fuzzy clusters themselves, since a certain loss of information has to be tolerated caused by the projections. In this paper, we propose to compute the class or cluster boundaries induced by the fuzzy clusters explicitly and to build up fuzzy rules that reflect exactly these boundaries.
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References
J.C. Bezdek: Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York (1981)
O. Cordón, M. José del Jesus, F. Herrera: Analysing the reasoning mechanism in fuzzy rule based classification systems. Mathware & Soft Computing 5 (1998), 321–332
R.N. Davé: Characterisation and detection of noise in clustering. Pattern Recognition Letters 12 (1991), 657–664
R.N. Davé, R. Krishnapuram: Robust clustering methods: A unified view, IEEE Transactions on Fuzzy Systems 5 (1997), 270–293
R.A. Fisher: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7 (1936), 179–188
H. Genther, M. Glesner: Automatic generation of a fuzzy classification system using fuzzy clustering methods. Proc. ACM Symposium on Applied Computing (SAC’94), Phoenix (1994), 180–183
D. Gustafson, W. Kessel: Fuzzy clustering with a fuzzy covariance matrix. Proc. IEEE CDC, San Diego (1979), 761–766
F. Höppner, F. Klawonn, R. Kruse, T. Runkler: Fuzzy cluster analysis. Wiley, Chichester (1999)
A. Keller, F. Klawonn: Fuzzy clustering with weighting of data variables. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8 (2000), 735–746
F. Klawonn, E.P. Klement: Mathematical analysis of fuzzy classifiers. In: Mathematical analysis of fuzzy classifiers. In: X. Liu, P. Cohen, M. Berthold (eds.): Advances in intelligent data analysis. Springer, Berlin (1997), 359–370
F. Klawonn, R. Kruse: Derivation of fuzzy classification rules from multidimensional data. In: G.E. Lasker, X. Liu (eds.): Advances in intelligent data analysis. The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Ontario (1995), 90–94
R. Krishnapuram, J. Keller: A Possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems 1 (1993), 98–110
L.I. Kuncheva: How good are fuzzy if-then classifiers? IEEE Transactions on Systems, Man and Cybernetics 30, Part B (2000)a, 501–509
K.D. Meyer Gramann: Fuzzy classification: An overview. In: R. Kruse, J. Gebhardt, R. Palm (eds.): Fuzzy systems in computer science. Vieweg, Braunschweig (1994), 277–294
A. Nürnberger, A. Klose, R. Kruse: Discussing cluster shapes of fuzzy classifiers. Proc. 18th Conf. of the North American Fuzzy Information Processing Society (NAFIPS’99), New York (1999), 546–550
A. Nürnberger, A. Klose, R. Kruse: Analyzing borders between partially contradicting fuzzy classification rules. Proc. 19th Conf. of the North American Fuzzy Information Processing Society (NAFIPS’00), Atlanta (2000), 59–63
W. Pedrycz: Algorithms of fuzzy clustering with partial supervision. Pattern Recognition Letters 23 (1985), 13–20
B. von Schmidt, F. Klawonn: Fuzzy max-min classifiers decide locally on the basis of two attributes. Mathware and Soft Computing 6 (1999), 91–108
B. von Schmidt, F. Klawonn: Construction of fuzzy classification systems with the Lukasiewicz-t-norm. Proc. 19th Conf. of the North American Fuzzy Information Processing Society (NAFIPS’00), Atlanta (2000), 109–113
M. Sugeno, T. Yasukawa: A fuzzy logic-based approach to qualitative modelling. IEEE Transactions on Fuzzy Systems 1 (1993), 7–31
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von Schmidt, B., Klawonn, F. (2003). Extracting Fuzzy Classification Rules from Fuzzy Clusters on the Basis of Separating Hyperplanes. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds) Interpretability Issues in Fuzzy Modeling. Studies in Fuzziness and Soft Computing, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37057-4_27
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DOI: https://doi.org/10.1007/978-3-540-37057-4_27
Publisher Name: Springer, Berlin, Heidelberg
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