Fuzzy and Crisp Representations of Real-Valued Input for Learning Classifier Systems

  • Andrea Bonarini
  • Claudio Bonacina
  • Matteo Matteucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1813)


We discuss some issues concerning the application of learning classifier systems to real-valued applications. In particular, we focus on the possibility of classifying data by crisp and fuzzy intervals, showing the effect of their granularity on the learning performance. We introduce the concept of sensorial cluster and we discuss the difference between cluster aliasing and perceptual aliasing. We show the impact of different choices on the performance of both crisp and fuzzy learning classifier systems applied to a mobile, autonomous, robotic agent.


Membership Function Fuzzy Rule Reinforcement Function Control Step Fuzzy Interval 
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.
    A. Bonarini. Evolutionary learning of fuzzy rules: competition and cooperation. In W. Pedrycz, editor, Fuzzy modeling: paradigms and practice, pages 265–284, Norwell, MA, 1996. Kluwer Academic Press.Google Scholar
  2. 2.
    A. Bonarini. Anytime learning and adaptation of hierarchical fuzzy logic behaviors. Adaptive Behavior Journal, 5(3–4):281–315, 1997.CrossRefGoogle Scholar
  3. 3.
    A. Bonarini. Reinforcement distribution to fuzzy classifiers: a methodology to extend crisp algorithms. In IEEE International Conference on Evolutionary Computation — WCCI-ICEC’98, volume 1, pages 51–56, Piscataway, NJ, 1998. IEEE Computer Press.Google Scholar
  4. 4.
    A. Bonarini. Comparing reinforcement learning algorithms applied to crisp and fuzzy learning classifier systems. In IWLCS99, Cambridge, MA, 1999. AAAI Press.Google Scholar
  5. 5.
    A. Bonarini, C. Bonacina, and M. Matteucci. A framework to support the reinforcement function design. In preparation, 2000.Google Scholar
  6. 6.
    Andrea Bonarini. ELF: Learning incomplete fuzzy rule sets for an autonomous robot. In Hans-Jürgen Zimmermann, editor, First European Congress on Fuzzy and Intelligent Technologies — EUFIT’93, volume 1, pages 69–75, Aachen, D, 1993. Verlag der Augustinus Buchhandlung.Google Scholar
  7. 7.
    M. Dorigo and M. Colombetti. Robot shaping: an experiment in behavior engineering. MIT Press / Bradford Books, 1997.Google Scholar
  8. 8.
    G. J. Klir, B. Yuan, and U. St. Clair. Fuzzy set theory: foundations and applicatons. Prentice-Hall, Englewood Cliffs, MA, 1997.Google Scholar
  9. 9.
    Lozano-Perez. Spatial planning: A configuration space approach. IEEE Transaction on Computers, C-32(2):26–38, feb 1983.CrossRefMathSciNetGoogle Scholar
  10. 10.
    S. P. Singh and R. S. Sutton. reinforcement learning with replacing eligibility traces. Machine Learning, 22(1):123–158, 1996.zbMATHGoogle Scholar
  11. 11.
    R. S. Sutton. Learning to predict by the method of temporal differences. Machine Learning, 3(1):9–44, 1988.Google Scholar
  12. 12.
    C. Watkins and P. Dayan. Q-learning. Machine Learning, 8:279–292, 1992.zbMATHGoogle Scholar
  13. 13.
    S. D. Whitehead and D. H. Ballard. Learning to perceive and act by trial and error. Machine Learning, 7:45–83, 1991.Google Scholar
  14. 14.
    S. W. Wilson. Classifier fitness based on accuracy. Evolutionary Computation, 3(2):149–175, 1995.CrossRefGoogle Scholar
  15. 15.
    L. A. Zadeh. Fuzzy sets. Information and control, 8:338–353, 1966.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andrea Bonarini
    • 1
  • Claudio Bonacina
    • 1
  • Matteo Matteucci
    • 1
  1. 1.Politecnico di Milano AI and Robotics Project, Dipartimento di Elettronica e InformazionePolitecnico di MilanoMilanoItaly

Personalised recommendations