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Developing Fuzzy State Models as Markov Chain Models with Fuzzy Encoding

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Fifty Years of Fuzzy Logic and its Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

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Abstract

This paper examines the relationship and establishes the equivalence between a class of dynamic fuzzy models, called Fuzzy State Models (FSM), and recently introduced Markov Chain models with fuzzy encoding. The equivalence between the two models leads to a methodology for learning FSMs from data and a systematic way for model based design of rule-based fuzzy controllers. The proposed approach is demonstrated on a case study of vehicle adaptive cruise control system in which an FSM is identified from simulation data and a fuzzy feedback controller is generated by exploiting the Stochastic Dynamic Programming (SDP).

The research of Ilya Kolmanovsky was supported in part by the National Science Foundation Award Number ECCS 1404814 to the University of Michigan.

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References

  1. Mamdani, E.H.: Applications of fuzzy set theory to control systems: a survey. In: Gupta, M.M., Saridis, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 77–88. North-Holland: Amsterdam (1977)

    Google Scholar 

  2. Mamdani, E., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7, 1–13 (1975)

    Article  MATH  Google Scholar 

  3. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  4. Filev, D.: Fuzzy modeling of complex systems. Int. J. Approx. Reason. 5(3), 281–290 (1991)

    Article  MATH  Google Scholar 

  5. Gain scheduling based control of a class of TSK systems. In: Farinwata, S., Filev, D., Langari, R. (eds.) Fuzzy Control: Synthesis and Analysis, pp. 321–334. Wiley, London (2000)

    Google Scholar 

  6. Tanaka, K., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, London (2004)

    Google Scholar 

  7. Filev, D., Kolmanovsky, I.V.: Markov chain modelling approaches for on-board applications. In: Proceedings of 2010 American Control Conference, pp. 4139–4145 (2010)

    Google Scholar 

  8. McDonough, K., Kolmanovsky, I.V., Filev, D., Szwabowski, S., Yanakiev, D., Michelini, J.: Stochastic fuel efficient optimal control of vehicle speed. In: Del Rey, L. et al. (eds.) Lecture Notes in Control and Information Sciences, vol. 455, pp. 147–162. Springer International Publishing Switzerland (2014)

    Google Scholar 

  9. Filev, D., Kolmanovsky, I.V.: Generalized Markov Models for real time modeling of continuous systems. IEEE Trans. Fuzzy Syst. 22(4), 983–998 (2014)

    Article  Google Scholar 

  10. Bellman, R., Zadeh, L.: Decision making in a fuzzy environment. Manage. Sci. 17, B-141–B-164 (1970)

    Google Scholar 

  11. Kolmanovsky, I.V., Siverguina, I., Lygoe, B.: Optimization of powertrain operation policy for feasibility assessment and calibration: Stochastic Dynamic Programming approach. In: Proceedings of American Control Conference, Anchorage, Alaska, pp. 1425–1430 (2002)

    Google Scholar 

  12. Di Cairano, S., Bernardini, D., Bemporad, A., Kolmanovsky, I.V.: Stochastic MPC with learning for driver-predictive vehicle control and its application to HEV energy management. IEEE Trans. Control Syst. Technol. 22(3), 1018–1031 (2014)

    Article  Google Scholar 

  13. Bemporad, A., Di Cairano, S.: Model-Predictive Control of discrete hybrid stochastic automata. IEEE Trans. Autom. Control 56(6), 1307–1321 (2011)

    Article  Google Scholar 

  14. Kolmanovsky, I.V., Filev, D.: Stochastic optimal control of systems with soft constraints and opportunities for automotive applications. In: Proceedings of IEEE Multi-Conference on Systems and Control, St. Petersburg, Russia, pp. 1265–1270 (2009)

    Google Scholar 

  15. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  16. Yager, R.R., Liu, L.: (Dempster, A.P., Shafer, G. Advisory Editors) Classic Works of the Dempster-Shafer Theory of Belief Functions. Springer: Heidelberg (2008)

    Google Scholar 

  17. Dynkin, E.B., Yushkevich, A.A.: Markov Processes: Theorems and Problems. Nauka, Moscow, in Russian. English translation published by Plenum, New York (1969)

    Google Scholar 

  18. Yager, R.R., Filev, D.: Essentials of Fuzzy Modeling and Control. Wiley, New York (1994)

    Google Scholar 

  19. Athans, M.: Presentation at the 1998 IEEE Conference on Decision and Control debate between Professors Lotfi Zadeh and Michael Athans on fuzzy versus conventional control,Tampa, FL (1998)

    Google Scholar 

  20. Kloeden, P.E.: Fuzzy dynamical systems. Fuzzy Sets Syst. 7, 275–296 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  21. Filev, D., Ying, H.: The look-up table controllers and a particular class of Mamdani fuzzy controllers are equivalent—implications to real-world applications. In: Proceeding of Joint IFSA World Congress & NAFIPS Annual Meeting, Alberta, Canada, pp. 902–907 (2013)

    Google Scholar 

  22. Pedrycz, W.: Fuzzy Control and Fuzzy Systems. Research Studies Press (1993)

    Google Scholar 

  23. Wang, L.: A Course in Fuzzy systems and Control. Prentice-Hall International, Inc

    Google Scholar 

  24. Passino, K.M., Yurkovich, S.: Fuzzy Control. Addison Wesley Longman, Inc. (1998)

    Google Scholar 

  25. Kosko, B.: Fuzzy Engineering. Prentice-Hall, Inc., Upper Saddle River (1996)

    Google Scholar 

  26. Zadeh, L.: Probability Measures of Fuzzy Events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  27. Yager, R., Filev, D.: Using Dempster-Shafer structures to provide probabilistic outputs in fuzzy systems modeling. In: Trillas, E., et al. (eds.) Combining Experimentation and Theory, STUDFUZZ 271, pp. 301–327. Springer, Berlin (2012)

    Google Scholar 

  28. Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Inf. Sci. 41, 93–137 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  29. Pedrycz, W., Skowron, A., Kreinovich, V.: (eds.) Handbook of Granular Computing. Wiley (2008)

    Google Scholar 

  30. Filev, D., Kolmanovsky, I.V. Yager, R.: On the relationship between fuzzy state models and Markov chain models with fuzzy encoding. In: Proceeding of IEEE World Conference on Soft Computing, San Francisco, May 2011

    Google Scholar 

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Author information

Authors and Affiliations

  1. Research & Innovation Center, Ford Motor Company, Dearborn, MI, USA

    Dimitar Filev

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA

    Ilya Kolmanovsky

  3. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald Yager

Authors
  1. Dimitar Filev
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  2. Ilya Kolmanovsky
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  3. Ronald Yager
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Corresponding author

Correspondence to Dimitar Filev .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

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Filev, D., Kolmanovsky, I., Yager, R. (2015). Developing Fuzzy State Models as Markov Chain Models with Fuzzy Encoding. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19682-4

  • Online ISBN: 978-3-319-19683-1

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