A Genetic-Programming-Based Approach for the Learning of Compact Fuzzy Rule-Based Classification Systems

  • F. J. Berlanga
  • M. J. del Jesus
  • M. J. Gacto
  • F. Herrera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


In the design of an interpretable fuzzy rule-based classification system (FRBCS) the precision as much as the simplicity of the extracted knowledge must be considered as objectives. In any inductive learning algorithm, when we deal with problems with a large number of features, the exponential growth of the fuzzy rule search space makes the learning process more difficult. Moreover it leads to an FRBCS with a rule base with a high cardinality. In this paper, we propose a genetic-programming-based method for the learning of an FRBCS, where disjunctive normal form (DNF) rules compete and cooperate among themselves in order to obtain an understandable and compact set of fuzzy rules, which presents a good classification performance with high dimensionality problems. This proposal uses a token competition mechanism to maintain the diversity of the population. The good results obtained with several classification problems support our proposal.


Fuzzy Rule Rule Base Disjunctive Normal Form Feature Selection Process Redundant Rule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Interpretability Issues in Fuzzy Modeling. Series Studies in Fuzziness and Soft Computing, vol. 128. Springer, Heidelberg (2003)MATHGoogle Scholar
  2. 2.
    Chi, Z., Wu, J., Yan, H.: Handwritten numeral recognition using self-organizing maps and fuzzy rules. Pattern Recognition 28(1), 59–66 (1995)CrossRefGoogle Scholar
  3. 3.
    Cordón, O., del Jesus, M.J., Herrera, F.: A Proposal on Reasoning Methods in Fuzzy Rule-Based Classification Systems. International Journal of Approximate Reasoning 20, 21–45 (1999)Google Scholar
  4. 4.
    Cordón, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems. In: Evolutionary tuning and learning of fuzzy knowledge bases, World Scientific, Singapore (2001)Google Scholar
  5. 5.
    García, S., González, F., Sánchez, L.: Evolving fuzzy based classifiers with GA-P: A grammatical approach. In: Langdon, W.B., Fogarty, T.C., Nordin, P., Poli, R. (eds.) EuroGP 1999. LNCS, vol. 1598, pp. 203–210. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Geyer-Schulz, A.: Fuzzy rule-based expert systems and genetic machine learning. Physica-Verlag, Heidelberg (1995)Google Scholar
  7. 7.
    González, A., Pérez, R.: Selection of relevant features in a fuzzy genetic learning algorithm. IEEE Transactions on Systems, Man and Cybernetics Part B 31(3), 417–425 (2001)CrossRefGoogle Scholar
  8. 8.
    González, A., Pérez, R.: SLAVE: A genetic learning system based on an iterative approach. IEEE Transactions on Fuzzy Systems 27, 176–191 (1999)CrossRefGoogle Scholar
  9. 9.
    Ishibuchi, H., Nozaki, K., Tanaka, H.: Distributed representation of fuzzy rules and its application to pattern classification. Fuzzy Sets and Systems 52, 21–32 (1992)CrossRefGoogle Scholar
  10. 10.
    Ishibuchi, H., Nozaki, K., Yamamoto, N., Tanaka, N.: Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Trans. Fuzzy Systems 3(3), 260–270 (1995)CrossRefGoogle Scholar
  11. 11.
    Kovacs, T.: Strength or Accuracy: Credit Assignment in Learning Classifier Systems. Springer, Heidelberg (2004)MATHGoogle Scholar
  12. 12.
    Koza, J.R.: Genetic programming on the programming of computers by means of natural selection. The MIT Press, Cambridge (1992)MATHGoogle Scholar
  13. 13.
    Krone, A., Krause, P., Slawinski, T.: A new rule reduction method for finding interpretable and small rule bases in high dimensional search spaces. In: Proc. of the 9th IEEE International Conference on Fuzzy Systems, vol. 2, pp. 694–699 (2000)Google Scholar
  14. 14.
    Mendes, R.R.F., Voznika, F., de, B., Freitas, A.A., Nievola, J.C.: Discovering Fuzzy Classification Rules with Genetic Programming and Co-evolution. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, p. 314. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
  16. 16.
    Ravi, V., Reddy, P.J., Zimmermann, H.J.: Pattern classification with principal component analysis and fuzzy rule bases. European Journal of Operational Research 126(3), 526–533 (2000)MATHCrossRefGoogle Scholar
  17. 17.
    Ravi, V., Zimmermann, H.J.: Fuzzy rule based classification with FeatureSelector and modified threshold accepting. European Journal of Operational Research x 126(1), 16–28 (2000)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Sánchez, L., Couso, I., Corrales, J.A.: Combining GP operators with SA search to evolve fuzzy rule based classifiers. Information Sciences 136(1–4), 175–191 (2001)MATHCrossRefGoogle Scholar
  19. 19.
    Tsakonas, A., Dounias, G., Jantzen, J., Axer, H., Bjerregaard, B., von Keyserlingk, D.G.: Evolving rule-based systems in two medical domains using genetic programming. Artificial Intelligence in Medicine 32(3), 195–216 (2004)CrossRefGoogle Scholar
  20. 20.
    Wang, L.X., Mendel, J.M.: Generating fuzzy rules by learning from examples. IEEE Transactions on Systems, Man, and Cybernetics 22(6), 1414–1427 (1992)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Wong, M.L., Leung, K.S.: Data Mining using grammar based genetic programming and applications. Kluwer Academic Publishers, Dordrecht (2000)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • F. J. Berlanga
    • 1
  • M. J. del Jesus
    • 1
  • M. J. Gacto
    • 2
  • F. Herrera
    • 2
  1. 1.Dept. of Computer ScienceUniversity of JaénJaénSpain
  2. 2.Dept. of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain

Personalised recommendations