Construction of Fuzzy Classes by Fuzzy Partitioning

  • Christophe Marsala
  • Bernadette Bouchon-Meunier
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 7)


In this paper, we propose a new algorithm to infer automatically a fuzzy partition for the universe of a set of fuzzy values, when each of these values is associated with a class. This algorithm can be used in a fuzzy decision tree system to extract knowledge from a database and to construct a set of fuzzy rules.


Membership Function Fuzzy Rule Membership Degree Fuzzy Subset Numerical Attribute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    N. Aladenise and B. Bouchon-Meunier. Acquisition de connaissances imparfaites: mise en évidence d’une fonction d’appartenance. Revue Internationale de Systémique, 11 (1): 109–127, 1997.Google Scholar
  2. 2.
    T. Bilgiç and I. B. Türk§en. Measurement of memberchip functions: Theoretical and empirical work. In D. Dubois and H. Prade, editors, Fundamentals of fuzzy Sets, volume 7 of Handbook of Fuzzy Sets. Kluwer, 2000.Google Scholar
  3. 3.
    I. Bloch and H. Maitre. Constructing a fuzzy mathematical morphology: Alternative ways. In Proceedings of the Second IEEE International Conference on Fuzzy Systems, San Francisco, USA, April 1993.Google Scholar
  4. 4.
    S. Bothorel, B. Bouchon-Meunier, and S. Muller. A fuzzy logic based approach for semiological analysis of microcalcifications in mammographic images. International Journal of Intelligent Systems, 12: 819–843, 1997.CrossRefGoogle Scholar
  5. 5.
    B. Bouchon-Meunier and C. Marsala. Learning fuzzy decision rules. In D. D. J. Bezdek and H. Prade, editors, Fuzzy Sets in Approximate Reasoning and Information Systems, volume 3 of Handbook of Fuzzy Sets, chapter 4. Kluwer Academic Publisher, 1999.Google Scholar
  6. 6.
    B. Bouchon-Meunier, C. Marsala, and M. Ramdani. Learning from imperfect data. In D. Dubois, H. Prade, and R. R. Yager, editors, Fuzzy Information Engineering: a Guided Tour of Applications, pages 139–148. John Wileys and Sons, 1997.Google Scholar
  7. 7.
    L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone. Classification And Regression Trees. Chapman and Hall, New York, 1984.MATHGoogle Scholar
  8. 8.
    C. Carter and J. Catlett. Assessing credit card applications using machine learning. IEEE Expert, Fall Issues: 71–79, 1987.Google Scholar
  9. 9.
    K. J. Cios, W. Pedrycz, and R. W. Swiniarski. Data Mining - Methods for Knowledge discovery. Engineering and Computer Science. Kluwer Academic Publishers, 1998.MATHCrossRefGoogle Scholar
  10. 10.
    U. M. Fayyad and K. B. Irani. Multi-interval discretization of continuous-valued attributes for classification learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, volume 2, pages 1022–1027, 1993.Google Scholar
  11. 11.
    T.-P. Hong and J.-B. Chen. Finding relevant attributes and membership functions. Fuzzy Sets and Systems, 103 (3): 389–404, May 1999.Google Scholar
  12. 12.
    T.-P. Hong and C.-Y. Lee. Induction of fuzzy rules and membership functions from training examples. Fuzzy Sets and Systems, 84: 33–47, 1996.MathSciNetMATHGoogle Scholar
  13. 13.
    J.-S. R. Jang. Structure determination in fuzzy modeling: a fuzzy CART approach. In Proceedings of the 3rd IEEE Int. Conf. on Fuzzy Systems,volume 1, pages 480–485, Orlando, 6 1994. IEEE.Google Scholar
  14. 14.
    R. Kerber. ChiMerge: Discretization of numeric attributes. In Proceedings of the 10th National Conference on Artificial Intelligence, pages 123–128. AAAI, 1992.Google Scholar
  15. 15.
    R. Krishnapuram. Generation of membership functions via possibilistic clustering. In Proceedings of the 3rd IEEE Int. Conf. on Fuzzy Systems, volume 2, pages 902–908, Orlando, Florida, June 1994.Google Scholar
  16. 16.
    C. Marsala. Arbres de décision et sous-ensembles flous. Rapport 94/21, LAFORIA-IBP, Université Pierre et Marie Curie, Paris, France, Novembre 1994.Google Scholar
  17. 17.
    C. Marsala and B. Bouchon-Meunier. Fuzzy partioning using mathematical morphology in a learning scheme. In Proceedings of the 5th IEEE Int. Conf. on Fuzzy Systems, volume 2, pages 1512–1517, New Orleans, USA, September 1996.Google Scholar
  18. 18.
    C. Marsala and B. Bouchon-Meunier. An adaptable system to construct fuzzy decision trees. In Proc. of the NAFIPS’99 (North American Fuzzy Information Processing Society), pages 223–227, New York (USA), June 1999.Google Scholar
  19. 19.
    H. Narazaki and A. L. Ralescu. An alternative method for inducing a membership function of a category. International Journal of Approximate Reasoning, 11(41–28, july 1994.Google Scholar
  20. 20.
    J. R. Quinlan. Induction of decision trees. Machine Learning, 1 (1): 86–106, 1986.Google Scholar
  21. 21.
    M. Ramdani. Système d’Induction Formelle à Base de Connaissances Imprécises. PhD thesis, Université P. et M. Curie, Paris, France, Février 1994.Google Scholar
  22. 22.
    M. Rifqi. Mesures de comparaison, typicalité et classification d’objets flous: théorie et pratique. PhD thesis, Université P. et M. Curie, Paris, France, Décembre 1996.Google Scholar
  23. 23.
    J.-P. Serra. Image Analysis and Mathematical Morphology. Academic Press, New York, 1982.MATHGoogle Scholar
  24. 24.
    T. Van de Merckt. Decision trees in numerical attribute spaces. In IJCA I-93 Proceedings of the 13th International Joint Conference on Artificial Intelligence, volume 2, pages 1016–1021, 1993.Google Scholar
  25. 25.
    L. Wehenkel. Discretization of continuous attributes for supervised learning. variance evaluation and variance reduction. In M. Mareg, R. Mesiar, V. Novak, J. Ramik, and A. Stupíianova, editors, Proceedings of the Seventh International Fuzzy Systems Association World Congress, volume 1, pages 381–388, Prague, Czech Republic, June 1997.Google Scholar
  26. 26.
    T.-P. Wu and S.-M. Chen. A new method for constructing membership functions and fuzzy rules from training examples. IEEE Transactions on Systems, Man, and Cybernetics, 29 (1): 25–40, February 1999.Google Scholar
  27. 27.
    Y. Yuan and M. J. Shaw. Induction of fuzzy decision trees. Fuzzy Sets and systems, 69: 125–139, 1995.MathSciNetGoogle Scholar
  28. 28.
    J. Zeidler and M. Schlosser. Continuous-valued attributes in fuzzy decision trees. In Proceedings of the 6th International Conference IPM U, volume 1, pages 395–400, Granada, Spain, july 1996.Google Scholar
  29. 29.
    D. A. Zighed, R. Rakotomalala, and S. Rabaséda. A discretization method of continuous attributes in induction graphs. In R. Trappl, editor, Cybernetics and systems’96, volume 2, pages 997–1002. Austrian Society for Cybernetics Studies, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christophe Marsala
    • 1
  • Bernadette Bouchon-Meunier
    • 1
  1. 1.Université Pierre et Marie CurieParis cedex 05France

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