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Genetic Optimization of Type-1 and Interval Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction

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Recent Developments and New Direction in Soft-Computing Foundations and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 342))

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Abstract

This paper describes the Mackey-Glass time series prediction using genetic optimization of type-1 and interval type-2 fuzzy integrators in Ensembles of adaptive neuro-fuzzy inferences systems (ANFIS) models, with emphasis on its application to the prediction of chaotic time series. The considered chaotic problem is the Mackey-Glass time series that is generated from the differential equations, so this benchmark time series is used to the test of performance of the proposed Ensemble architecture. We used the interval type-2 and type-1 fuzzy systems to integrate the outputs (forecasts) of each of the ANFIS models in the Ensemble. Genetic algorithms (GAs) were used for the optimization of memberships function (with linguistic labels “Small, Middle, and Large”) parameters of the fuzzy integrators. In the experiments, the GAs optimized the Gaussians, generalized bell and triangular membership functions for each of the fuzzy integrators, thereby increasing the complexity of the training. Simulation results show the effectiveness of the proposed approach.

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References

  1. Brocklebank, J.C., Dickey, D.A.: SAS for Forecasting Series, pp. 6–140. SAS Institute Inc., Cary (2003)

    MATH  Google Scholar 

  2. Holland, J.H.: Outline for a logical theory of adaptive systems. J. Assoc. Comput. Mach. 3, 297–314 (1962)

    Article  MATH  Google Scholar 

  3. Holland, J.H.: Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  4. Goldberg, D.E., Kalyanmoy, D.: A comparative analysis of selection schemes used in genetic algorithms. In: G.J.E. Rawlins (eds.) Foundations of Genetic Algorithms, pp. 69–93. Morgan Kaufmann Publishers, San Mateo (1991)

    Google Scholar 

  5. Goldberg, D.E., Korb, B., Kalyanmoy, D.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3, 493–530 (1989)

    MathSciNet  MATH  Google Scholar 

  6. Lawrence, D.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)

    Google Scholar 

  7. Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1997)

    Article  Google Scholar 

  8. Mackey, M.C.: “Mackey-Glass”. McGill University, Canada, http://www.sholarpedia.org/-article/ Mackey-Glass_equation, 5 Sept 2009

  9. Brockwell, P.D., Richard, A.D.: Introduction to Time Series and Forecasting. Springer, New York, pp 1–219 (2002)

    Google Scholar 

  10. Jang, J.S.R.: ANFIS: Adaptive-network-based fuzzy inference systems. IEEE Trans. Syst Man Cybern. 23, 665–685 (1992)

    Google Scholar 

  11. Melin, P., Soto, J., Castillo, O., Soria, J.: A new approach for time series prediction using ensembles of ANFIS models. Experts Syst Appl, El-Sevier 39(3), 3494–3506 (2012)

    Article  Google Scholar 

  12. Wang, C., Zhang, J.P.: Time series prediction based on ensemble ANFIS. In: Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18–21 Aug 2005

    Google Scholar 

  13. Werbos, P.: Beyond regression: new tools for prediction and analysis in the behavioral sciences. Ph.D. thesis, Harvard University (1974)

    Google Scholar 

  14. Castro, J.R., Castillo, O., Melin, P., Rodríguez, A.: Hybrid learning algorithm for interval type-2 fuzzy neural networks. GrC, pp. 157–162 (2007)

    Google Scholar 

  15. Castro, J.R., Castillo, O., Melin, P., Rodriguez, A.: A hybrid learning algorithm for interval type-2 fuzzy neural networks: the case of time series prediction, vol. 15a, pp. 363–386. Springer, Berlin (2008)

    Google Scholar 

  16. Pulido, M., Mancilla, A., Melin, P.: Redes ensemble con integración Difusa para Pronosticar Series de Tiempo Complejas. Tijuana Institute of Technology, Mexico, 21 Sept 2009

    Google Scholar 

  17. Jang, J.S.R.: Rule extraction using generalized neural networks. En Proceedings of te 4th IFSA World Congress, pp. 82–86 (1991)

    Google Scholar 

  18. Takagi, T., Sugeno, M.: Derivation of fuzzy control rules from human operation control actions. In: Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, pp. 55–60 (1983)

    Google Scholar 

  19. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. 1, pp. 318–362. MIT Press, Cambridge (1986)

    Google Scholar 

  20. Takagi, T., Sugeno, M.: Derivation of fuzzy control rules from human operation control actions. In: Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, pp. 55-60 (1983)

    Google Scholar 

  21. Zhou, Z.H., Wu, J., Tang, W.: Ensembling neural networks: many could be better than all. Artif. Intell. 137(1–2), 239–263 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zadeh, L.A.: Fuzzy logic. Computer 1(4), 83–93 (1988)

    Article  MathSciNet  Google Scholar 

  23. Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103 (1996)

    Article  MathSciNet  Google Scholar 

  24. Jang, J.S.R.: Fuzzy modeling using generalized neural networks and Kalman fliter algorithm. In: Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI-91), pp. 762–767 (1991)

    Google Scholar 

  25. Melin, P., Mendoza, O., Castillo, O.: An improved method for edge detection based on interval type-2 fuzzy logic. Expert Syst Appl. 37(12), 8527–8535 (2010)

    Article  Google Scholar 

  26. Mendel, J.M.: Why we need type-2 fuzzy logic systems. Article is provided courtesy of Prentice Hall, By Jerry Mendel, 11 May 2001

    Google Scholar 

  27. Mendel, J.M.: Uncertain rule-based fuzzy logic systems: introduction and new, directions, pp. 25–200. Prentice Hall, USA (2000) (Ed)

    Google Scholar 

  28. Mendel, J.M., Mouzouris, G.C.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)

    Article  Google Scholar 

  29. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Publishing Company, Boston (1989)

    Google Scholar 

  30. Castillo, O., Melin, P.: Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Appl. Soft Comput. 12(4), 1267–1278 (2012)

    Article  Google Scholar 

  31. Castro, J.R., Castillo, O., Martínez, L.G.: Interval type-2 fuzzy logic toolbox. Eng. Lett. 15(1), 89–98 (2007)

    Google Scholar 

  32. Chua, T.W., Tan, W.W.: Genetically evolved fuzzy rule-based classifiers and application to automotive classification. Lect. Notes Comput. Sci. 5361, 101–110 (2008)

    Article  Google Scholar 

  33. Cordon, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Syst. 141, 5–31 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  34. Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L.: “Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy”, Knowledge Bases. World Scientific, Singapore (2001)

    Book  MATH  Google Scholar 

  35. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computation, pp. 37–69. Springer, Berlin (2003)

    MATH  Google Scholar 

  36. Cordon, O., Herrera, F., Villar, P.: Analysis and guidelines to obtain a good uniform fuzzy partition granularity for fuzzy rule-based systems using simulated annealing. Int. J. Approximate Reasoning 25, 187–215 (2000)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Division of Graduates Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Jesus Soto, Patricia Melin & Oscar Castillo

Authors
  1. Jesus Soto
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  2. Patricia Melin
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  3. Oscar Castillo
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Corresponding author

Correspondence to Jesus Soto .

Editor information

Editors and Affiliations

  1. University of California, Berkeley, USA

    Lotfi A. Zadeh

  2. Tech. of the Republic of Azerbaijan, Ministry of Communications Info., Baku, Azerbaijan

    Ali M. Abbasov

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

    Ronald R. Yager

  4. Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

  5. University of Alberta, Edmonton, Alberta, Canada

    Marek Z. Reformat

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Soto, J., Melin, P., Castillo, O. (2016). Genetic Optimization of Type-1 and Interval Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction. In: Zadeh, L., Abbasov, A., Yager, R., Shahbazova, S., Reformat, M. (eds) Recent Developments and New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing, vol 342. Springer, Cham. https://doi.org/10.1007/978-3-319-32229-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-32229-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32227-8

  • Online ISBN: 978-3-319-32229-2

  • eBook Packages: EngineeringEngineering (R0)

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