Skip to main content
Springer Nature Link
Log in

Optimization of the Interval Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction: Case of the Mexican Stock Exchange

  • Chapter
  • First Online:
Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 601))

Abstract

This paper describes the optimization of the fuzzy integrators in Ensembles of ANFIS model for time series prediction: case of the Mexican Stock Exchange. The Mexican stock exchange that is used corresponds to the period of 11/09/2005 to 01/15/2009 to simulate the performance of the proposed architecture. We used interval type-2 fuzzy systems to integrate the outputs (forecast) of each of the ANFIS models in the Ensemble. Genetic Algorithms (GAs) are used for the optimization of memberships function “MFs” for the 2 MFs (used linguistic labels “Small and Large”) and for the 3 MFs (used linguistic labels “Small, Middle and Large”) parameters of the fuzzy integrators. In the experiments the genetic algorithms optimized the Gaussian, Generalized Bell and Triangular membership functions for each of the fuzzy integrators; in the interval type-2 fuzzy integrator there are more parameters, thereby increasing the complexity of the training for the fuzzy integrators. Simulation results show the effectiveness of the proposed approach in comparison with other researchers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

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

    Google Scholar 

  3. Cervantes, M., Montoya, M. Cueto, D.C.: Momentum Effect on the Mexican Stock Exchange, pp. 1–20. Social Science Electronic Publishing (2014)

    Google Scholar 

  4. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

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

    Article  Google Scholar 

  6. Goldberg, D.E., Kalyanmoy, D.: A comparative analysis of selection schemes used in genetic algorithms. In: Gregory, J.E.R. (ed.) Foundations of Genetic Algorithms, pp. 69–93. Morgan Kaufmann Publishers, San Mateo, California (1991)

    Google Scholar 

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

    MATH  Google Scholar 

  8. Lawrence, D.M.: Handbook of Genetic Algorithms. Van Nostrand Reinhold (1991)

    Google Scholar 

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

    Article  Google Scholar 

  10. Pulido, M., Melin, P., Castillo, O.: Particle swarm optimization of ensemble neural networks with fuzzy aggregation for time series prediction of the Mexican Stock Exchange. Inf. Sci. 280(1), 188–204 (2014)

    Article  MathSciNet  Google Scholar 

  11. Jang, J.S.R.: ANFIS: Adaptive-network-based fuzzy inference systems. In: IEEE Transaction on Systems, Man, and Cybernetics, vol. 23, pp. 665–685 (1992)

    Google Scholar 

  12. Jang, J.S.R.: Rule extraction using generalized neural networks. In: Proceedings of the 4th IFSA Wolrd Congress, pp. 82–86 (1991)

    Google Scholar 

  13. 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 

  14. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. In: IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, pp. 116–132 (1985)

    Google Scholar 

  15. Sharkey, A.: Combining Artificial Neural Nets: Ensemble and Modular Multi-net Systems. Springer, London (1999)

    Book  MATH  Google Scholar 

  16. Sollich, P., Krogh, A.: Learning with ensembles: how over-fitting can be useful. In: Touretzky, D.S., Mozer, M.C., Hasselmo, M.E. (eds.) Advances in Neural Information Processing Systems, pp. 190–196. MIT Press, Cambridge, MA (1996)

    Google Scholar 

  17. 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  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  20. 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, Heidelberg (2008)

    Google Scholar 

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

    Google Scholar 

  22. 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)

    Google Scholar 

  23. 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 

  24. Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems. Springer, Heidelberg (2001)

    Google Scholar 

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

    Google Scholar 

  26. Castro, J.R., Castillo, O., Melin, P. Rodríguez, A.: Hybrid Learning Algorithm for Interval Type-2 Fuzzy Neural Networks, pp. 157–162. GrC (2007)

    Google Scholar 

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

    Google Scholar 

  28. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, pp. 25–200. Prentice Hall, New Jersey (2000)

    Google Scholar 

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

    Article  Google Scholar 

  30. 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)

    Google Scholar 

  31. 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)

    Google Scholar 

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

    Book  Google Scholar 

  33. 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 

  34. Eason, G., Noble, B., Sneddon, I.N.: On certain integrals of Lipschitz-Hankel type involving products of Bessel functions. Phil. Trans. Roy. Soc. London A247, 529–551 (1955)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  37. Mexico Bank Database: http://www.banxico.org.mx (2011)

  38. Pulido, M., Mancilla, A., Melin, P.: An ensemble neural network architecture with fuzzy response integration for complex time series prediction. In: Evolutionary Design of Intelligent Systems in Modeling, Simulation and Control, pp. 85–110 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tijuana Institute of Technology, Tijuana, Mexico

    Jesus Soto & Patricia Melin

Authors
  1. Jesus Soto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patricia Melin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patricia Melin .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Soto, J., Melin, P. (2015). Optimization of the Interval Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction: Case of the Mexican Stock Exchange. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Studies in Computational Intelligence, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-17747-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-17747-2_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17746-5

  • Online ISBN: 978-3-319-17747-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics