Combining Experimentation and Theory pp 91-101

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 271) | Cite as

Fuzzy Control for Knowledge-Based Interpolation

Chapter

Abstract

Fuzzy control accounts for the biggest industrial success of fuzzy logic. We review an interpretation of Mamdani’s heuristic control approach. It can be seen as knowledge-based interpolation based on input-output points of a vaguely known function.We reexamine two real-world control problems that have been fortunately solved based on this interpretation.

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References

  1. 1.
    Boixader, D., Jacas, J.: Extensionality based approximate reasoning. International Journal of Approximate Reasoning 19(3-4), 221–230 (1998); doi:10.1016/S0888-613X(98)00018-8CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    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(1), 21–45 (1999); doi:10.1016/S0888-613X(00)88942-2Google Scholar
  3. 3.
    Gabbay, D.M., Kruse, R. (eds.): Abductive Reasoning and Uncertainty Management Systems, Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 4. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  4. 4.
    Klawonn, F., Castro, J.L.: Similarity in fuzzy reasoning. Mathware & Soft Computing 2(3), 197–228 (1995)MATHMathSciNetGoogle Scholar
  5. 5.
    Klawonn, F., Gebhardt, J., Kruse, R.: Fuzzy control on the basis of equality relations with an example from idle speed control. IEEE Transactions on Fuzzy Systems 3(3), 336–350 (1995), doi:10.1109/91.413237CrossRefGoogle Scholar
  6. 6.
    Klawonn, F., Kruse, R.: Equality relations as a basis for fuzzy control. Fuzzy Sets and Systems 54(2), 147–156 (1993), doi:10.1016/0165-0114(93)90272-JCrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Klawonn, F., Kruse, R.: The Inherent Indistinguishability in Fuzzy Systems. In: Lenski, W. (ed.) Logic versus Approximation. LNCS, vol. 3075, pp. 6–17. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Klawonn, F., Novák, V.: The relation between inference and interpolation in the framework of fuzzy systems. Fuzzy Sets and Systems 81(3), 331–354 (1996), doi:10.1016/0165-0114(96)83710-9CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Kruse, R., Gebhardt, J., Klawonn, F.: Foundations of Fuzzy Systems. John Wiley & Sons Ltd., Chichester (1994)Google Scholar
  10. 10.
    Kruse, R., Gebhardt, J., Palm, R. (eds.): Fuzzy Systems in Computer Science. Vieweg-Verlag, Braunschweig/Wiesbaden, Germany (1994)Google Scholar
  11. 11.
    Kruse, R., Siegel, P. (eds.): ECSQAU 1991 and ECSQARU 1991. LNCS, vol. 548. Springer, Heidelberg (1991)Google Scholar
  12. 12.
    Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7(1), 1–13 (1975), doi:10.1016/S0020-7373(75)80002-2CrossRefMATHGoogle Scholar
  13. 13.
    Schröder, M., Petersen, R., Klawonn, F., Kruse, R.: Two Paradigms of Automotive Fuzzy Logic Applications. In: Jamshidi, M., Titli, A., Zadeh, L., Boverie, S. (eds.) Applications of Fuzzy Logic: Towards High Machine Intelligence Quotient Systems. Environmental and Intelligent Manufacturing Systems Series, vol. 9, pp. 153–174. Prentice-Hall Inc, Upper Saddle River (1997)Google Scholar
  14. 14.
    Sudkamp, T.: Similarity, interpolation, and fuzzy rule construction. Fuzzy Sets and Systems 58(1), 73–86 (1993), doi:10.1016/0165-0114(93)90323-ACrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculty of Computer ScienceOtto-von-Guericke University of MagdeburgMagdeburgGermany

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