Fuzzy Control

  • Rudolf Kruse
  • Christian Borgelt
  • Frank Klawonn
  • Christian Moewes
  • Matthias Steinbrecher
  • Pascal Held
Part of the Texts in Computer Science book series (TCS)


The biggest success of fuzzy systems in the field of industrial and commercial applications has been achieved with fuzzy controllers. Fuzzy control is a way of defining a nonlinear table-based controller whereas its nonlinear transition function can be defined without specifying every single entry of the table individually. Fuzzy control does not result from classical control engineering approaches. In fact, its roots can be found in the area of rule-based systems. Fuzzy controllers simply comprise a set of vague rules that can be used for knowledge-based interpolation of a vaguely defined function.


Fuzzy Rule Rule Base Fuzzy Controller Membership Degree Fuzzy Relation 
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.


  1. A.G. Barto, R.S. Sutton, and C.W. Anderson. Neuronlike Adaptive Elements that Can Solve Difficult Learning Control Problems. IEEE Transactions on Systems, Man and Cybernetics, 13(5):834–846. IEEE Press, Piscataway, NJ, USA, 1983 CrossRefGoogle Scholar
  2. H.R. Berenji and P. Khedkar. Learning and Tuning Fuzzy Logic Controllers Through Reinforcements. IEEE Transactions on Neural Networks, 3(5):724–740. IEEE Press, Piscataway, NJ, USA, 1992 CrossRefGoogle Scholar
  3. S.K. Halgamuge and M. Glesner. Neural Networks in Designing Fuzzy Systems for Real World Applications. Fuzzy Sets and Systems, 65(1):1–12. Elsevier, Amsterdam, Netherlands, 1994 CrossRefGoogle Scholar
  4. J. Hopf and F. Klawonn. Learning the Rule Base of a Fuzzy Controller by a Genetic Algorithm. In: R. Kruse, J. Gebhardt and R. Palm (eds.). Fuzzy Systems in Computer Science, 63–74. Vieweg, Braunschweig, Germany, 1994 CrossRefGoogle Scholar
  5. J.-S.R. Jang. ANFIS: Adaptive-Network-Based Fuzzy Inference System. IEEE Transactions on Systems, Man and Cybernetics, 23(3):665–685. IEEE Press, Piscataway, NJ, USA, 1993 CrossRefGoogle Scholar
  6. L.P. Kaelbling, M.H. Littman, and A.W. Moore. Reinforcement Learning: A Survey. Journal of Artificial Intelligence Research, 4:237–285. AI Access Foundation and Morgan Kaufman Publishers, El Segundo/San Francisco, CA, USA, 1996 Google Scholar
  7. J. Kahlert and H. Frank. Fuzzy-Logik und Fuzzy-Control, 2nd edition (in German). Vieweg, Braunschweig, Germany, 1994 MATHGoogle Scholar
  8. J. Kinzel, F. Klawonn, and R. Kruse. Modifications of Genetic Algorithms for Designing and Optimizing Fuzzy Controllers. In: Proc. IEEE Conf. on Evolutionary Computation (ICEC’94, Orlando, FL), 28–33. IEEE Press, Piscataway, NJ, USA, 1994 Google Scholar
  9. F. Klawonn. On a Lukasiewicz Logic Based Controller. In: Proc. Int. Seminar on Fuzzy Control Through Neural Interpretations of Fuzzy Sets (MEPP’92), 53–56. Åbo Akademi, Turku, Finland, 1992 Google Scholar
  10. F. Klawonn and J.L. Castro. Similarity in Fuzzy Reasoning. Mathware and Soft Computing, 2:197–228. University of Granada, Granada, Spain, 1995 MathSciNetMATHGoogle Scholar
  11. F. Klawonn and R. Kruse. The Inherent Indistinguishability in Fuzzy Systems. In: W. Lenski (ed.) Logic Versus Approximation: Essays Dedicated to Michael M. Richter on the Occasion of His 65th Birthday, 6–17. Springer-Verlag, Berlin, Germany, 2004 Google Scholar
  12. F. Klawonn and V. Novák. The Relation Between Inference and Interpolation in the Framework of Fuzzy Systems. Fuzzy Sets and Systems, 81:331–354. Elsevier, Amsterdam, Netherlands, 1996 MathSciNetMATHCrossRefGoogle Scholar
  13. B. Kosko (ed.). Neural Networks for Signal Processing. Prentice Hall, Englewood Cliffs, NJ, USA, 1992 Google Scholar
  14. M. Lee and H. Takagi. Integrating Design Stages of Fuzzy Systems Using Genetic Algorithms. In: Proc. IEEE Int. Conf. on Fuzzy Systems (San Francisco, CA), 612–617. IEEE Press, Piscataway, NJ, USA, 1993 Google Scholar
  15. E.H. Mamdani and S. Assilian. An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. International Journal of Man-Machine Studies 7:1–13. Academic Press, Waltham, MA, USA, 1975 MATHCrossRefGoogle Scholar
  16. K. Michels, F. Klawonn, R. Kruse, and A. Nürnberger. Fuzzy Control: Fundamentals, Stability and Design of Fuzzy Controllers. Studies in Fuzziness and Soft Computing, vol. 200. Springer-Verlag, Berlin/Heidelberg, Germany, 2006 MATHGoogle Scholar
  17. C. Moewes and R. Kruse. On the Usefulness of Fuzzy SVMs and the Extraction of Fuzzy Rules from SVMs. In: S. Galichet, J. Montero, and G. Mauris (eds.) Proc. 7th Conf. of Europ. Soc. for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011, 943–948. Advances in Intelligent Systems Research, vol. 17. Atlantis Press, Amsterdam/Paris, Netherlands/France, 2011 Google Scholar
  18. C. Moewes and R. Kruse. Fuzzy Control for Knowledge-Based Interpolation. In: E. Trillas, P.P. Bonissone, L. Magdalena, and J. Kacprzyk (eds.) Combining Experimentation and Theory: A Hommage to Abe Mamdani, 91–101. Springer-Verlag, Berlin/Heidelberg, Germany, 2012 CrossRefGoogle Scholar
  19. C. Moewes and R. Kruse. Evolutionary Fuzzy Rules for Ordinal Binary Classification with Monotonicity Constraints. In: R.R. Yager, A.M. Abbasov, M.Z. Reformat, and S.N. Shahbazova (eds.) Soft Computing: State of the Art Theory and Novel Applications, 105–112. Studies in Fuzziness and Soft Computing, vol. 291. Springer-Verlag, Berlin/Heidelberg, Germany, 2013 CrossRefGoogle Scholar
  20. D. Nauck and R. Kruse. A Fuzzy Neural Network Learning Fuzzy Control Rules and Membership Functions by Fuzzy Error Backpropagation. In: Proc. IEEE Int. Conf. on Neural Networks (ICNN’93, 1993, San Francisco, CA), 1022–1027. IEEE Press, Piscataway, NJ, USA, 1993 Google Scholar
  21. D.D. Nauck and A. Nürnberger. Neuro-Fuzzy Systems: A Short Historical Review. In: C. Moewes and A. Nürnberger (eds.) Computational Intelligence in Intelligent Data Analysis, 91–109. Studies in Computational Intelligence, vol. 445. Springer-Verlag, Berlin/Heidelberg, Germany, 2012 CrossRefGoogle Scholar
  22. D.D. Nauck, F. Klawonn, and R. Kruse. Foundations of Neuro-Fuzzy Systems. Wiley, Chichester, 1997 Google Scholar
  23. H. Nomura, I. Hayashi, and N. Wakami. A Learning Method of Fuzzy Inference Rules by Descent Method. In: Proc. IEEE Int. Conf. on Fuzzy Systems 1992, 203–210. San Diego, CA, USA, 1992 CrossRefGoogle Scholar
  24. A. Nürnberger, D.D. Nauck, and R. Kruse. Neuro-Fuzzy Control Based on the NEFCON-Model: Recent Developments. Soft Computing, 2(4):168–182. Springer-Verlag, Berlin/Heidelberg, Germany, 1999 CrossRefGoogle Scholar
  25. M. Riedmiller, M. Spott, and J. Weisbrod. FYNESSE: A Hybrid Architecture for Selflearning Control. In: I. Cloete and J. Zurada (eds.) Knowledge-Based Neurocomputing, 291–323. MIT Press, Cambridge, MA, USA, 1999 Google Scholar
  26. T.A. Runkler. Kernel Based Defuzzification. In: C. Moewes and A. Nürnberger (eds.) Computational Intelligence in Intelligent Data Analysis, 61–72. Springer-Verlag, Berlin/Heidelberg, Germany, 2012 Google Scholar
  27. T.A. Runkler and M. Glesner. A Set of Axioms for Defuzzification Strategies—Towards a Theory of Rational Defuzzification Operators. In: Proc. 2nd IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE’93, San Francisco, CA), 1161–1166. IEEE Press, Piscataway, NJ, USA, 1993 Google Scholar
  28. M. Sugeno. An Introductory Survey of Fuzzy Control. Information Sciences, 36:59–83. Elsevier, New York, NY, USA, 1985 MathSciNetMATHCrossRefGoogle Scholar
  29. R.S. Sutton and A.G. Barto. Reinforcement Learning: An Introduction. MIT Press, Cambridge, MA, USA, 1998 Google Scholar
  30. T. Takagi and M. Sugeno. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems, Man and Cybernetics 15:116–132. IEEE Press, Piscataway, NJ, USA, 1985 MATHCrossRefGoogle Scholar
  31. L.A. Zadeh. Towards a Theory of Fuzzy Systems. In: R.E. Kalman and N. de Claris (eds.) Aspects of Networks and System Theory, 469–490. Rinehart and Winston, New York, USA, 1971 Google Scholar
  32. L.A. Zadeh. A Rationale for Fuzzy Control. Journal of Dynamic Systems, Measurement, and Control, 94(1):3–4. American Society of Mechanical Engineers (ASME), New York, NY, USA, 1972 MathSciNetCrossRefGoogle Scholar
  33. L.A. Zadeh. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man and Cybernetics, 3:28–44. IEEE Press, Piscataway, NJ, USA, 1973 MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rudolf Kruse
    • 1
  • Christian Borgelt
    • 2
  • Frank Klawonn
    • 3
  • Christian Moewes
    • 1
  • Matthias Steinbrecher
    • 4
  • Pascal Held
    • 1
  1. 1.Faculty of Computer ScienceOtto-von-Guericke University MagdeburgMagdeburgGermany
  2. 2.Intelligent Data Analysis & Graphical Models Research UnitEuropean Centre for Soft ComputingMieresSpain
  3. 3.FB InformatikOstfalia University of Applied SciencesWolfenbüttelGermany
  4. 4.SAP Innovation CenterPotsdamGermany

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