Advertisement

Learning of Type-2 Fuzzy Logic Systems by Simulated Annealing with Adaptive Step Size

  • Majid Almaraashi
  • Robert John
  • Samad Ahmadi
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 130)

Abstract

In this paper, a combination of an interval type-2 fuzzy logic system (IT2FLS) models and simulated annealing is used to predict the Mackey–Glass time series by searching for the best configuration of the IT2FLS. Simulated annealing is used to learn the parameters of the antecedent and the consequent parts of the rules for a Mamdani model. Simulated annealing is combined with a method to reduce the computations associated with it using adaptive step sizes. The results of the proposed methods are compared to results of a type-1 fuzzy logic system (T1FLS).

Keywords

Root Mean Square Error Membership Function Simulated Annealing Fuzzy System Fuzzy Logic System 
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.

References

  1. 1.
    Aarts E, Lenstra JK (2003) Local search in combinatorial optimization. Princeton University Press, Princeton, NJMATHGoogle Scholar
  2. 2.
    Aarts EHL, Eikelder HMM Ten (2002) Handbook of applied optimization, chapter Simulated Annealing. Oxford University Press, NY, pp 209–220Google Scholar
  3. 3.
    Majid A, Robert J (2010) Tuning fuzzy systems by simulated annealing to predict time series with added noise. In: Proceedings of UKCI, EssexGoogle Scholar
  4. 4.
    Majid A, Robert J (2011) Tuning of type-2 fuzzy systems by simulated annealing to predict time series. Lecture notes in engineering and computer science: proceedings of the world congress on engineering 2011, WCE 2011, vol 2. U.K. Newswood Limited, London, pp 976–980Google Scholar
  5. 5.
    Majid A, Robert J, Simon C, Adrian H (2010) Time series forecasting using a tsk fuzzy system tuned with simulated annealing. In: Proceedings of FUZZ-IEEE2010 world congress on computational intelligence, BarcelonaGoogle Scholar
  6. 6.
    Cordon O, Gomide F, Herrera F, Hoffmann F, Magdalena L (2004) Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Syst 141(1):5–32MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Dadone P (2001) Design optimization of fuzzy logic systems. PhD thesis, Virginia Polytechnic Institute and State UniversityGoogle Scholar
  8. 8.
    Drack L, Zadeh HS (2006) Soft computing in engineering design optimisation. J Int Fuzzy Syst 17(4):353–365Google Scholar
  9. 9.
    Garibaldi JM, Ifeachor EC (1999) Application of simulated annealing fuzzy model tuning to umbilical cord acid-base interpretation. IEEE Trans Fuzzy Syst 7(1):72–84CrossRefGoogle Scholar
  10. 10.
    Goonatilake S, Khebbal S (1995) Intelligent hybrid systems. Wiley, New York, NYGoogle Scholar
  11. 11.
    Hagras H (2007) Type-2 flcs: a new generation of fuzzy controllers. Comput Intel Mag IEEE 2(1):30–43CrossRefGoogle Scholar
  12. 12.
    Hoffmann F (2001) Evolutionary algorithms for fuzzy control system design. Proc IEEE 89(9):1318–1333CrossRefGoogle Scholar
  13. 13.
    Jang JSR (1993) Anfis: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybernet 23(3):665–685CrossRefGoogle Scholar
  14. 14.
    John R, Coupland S (2007) Type-2 fuzzy logic: a historical view. Comput Intel Mag IEEE 2:57–62CrossRefGoogle Scholar
  15. 15.
    Chia-Feng J, Chin-Teng L (1998) An online self-constructing neural fuzzy inference network and its applications. IEEE Trans Fuzzy Syst 6(1):12–32CrossRefGoogle Scholar
  16. 16.
    Karnik NN, Mendel JM (2001) Centroid of a type-2 fuzzy set. Inform Sci 132(1):195–220MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Karnik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7(6):643–658CrossRefGoogle Scholar
  18. 18.
    Kim D, Kim C (2002) Forecasting time series with genetic fuzzy predictor ensemble. IEEE Trans Fuzzy Syst 5(4):523–535Google Scholar
  19. 19.
    Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing, 1983. Science 220:671–680MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Dragan K (2002) Design of adaptive takagi-sugeno-kang fuzzy models. Appl Soft Comput 2(2):89–103CrossRefGoogle Scholar
  21. 21.
    Cheng-Jian L, Chin-Teng L (1997) An art-based fuzzy adaptive learning control network. IEEE Trans Fuzzy Syst 5(4):477–496CrossRefGoogle Scholar
  22. 22.
    Liu G, Yang W (2000) Learning and tuning of fuzzy membership functions by simulated annealing algorithm. In: The 2000 IEEE Asia-Pacific conference on circuits and systems, 2000. IEEE APCCAS 2000, pp 367–370Google Scholar
  23. 23.
    Ji-Chang L, Chien-Hsing Y (1999) A heuristic error-feedback learning algorithm for fuzzy modeling. IEEE Trans Syst Man Cybernet Part A: Syst Humans 29(6):686–691Google Scholar
  24. 24.
    Locatelli M (2002) Simulated annealing algorithms for continuous global optimization. Handbook Global Opt 2:179–229MathSciNetCrossRefGoogle Scholar
  25. 25.
    Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197(4300):287–289CrossRefGoogle Scholar
  26. 26.
    Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice Hall, Englewood Cliffs, NJMATHGoogle Scholar
  27. 27.
    Mendel JM (2007) Advances in type-2 fuzzy sets and systems. Inform Sci 177(1):84–110MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  29. 29.
    Miki M, Hiroyasu T, Ono K (2002) Simulated annealing with advanced adaptive neighborhood. In: Second international workshop on intelligent systems design and application, Dynamic Publishers, pp 113–118Google Scholar
  30. 30.
    Nolle L, Goodyear A, Hopgood A, Picton P, Braithwaite N (2001) On step width adaptation in simulated annealing for continuous parameter optimisation. Computational intelligence. Theory and applications. Springer, Heidelberg, pp 589–598Google Scholar
  31. 31.
    Timothy JR (2004) Fuzzy logic with engineering applications. Wiley, New York, NYMATHGoogle Scholar
  32. 32.
    Russo M (2000) Genetic fuzzy learning. IEEE Trans Evol Comput 4(3):259–273CrossRefGoogle Scholar
  33. 33.
    White SR (1984) Concepts of scale in simulated annealing. In: American institute of physics conference series, vol 122, pp 261–270Google Scholar
  34. 34.
    Zadeh LA (1994) Soft computing and fuzzy logic. IEEE Software 11(6):48–56CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.The Centre for Computational IntelligenceDe Montfort UniversityLeicesterUK

Personalised recommendations