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On the Identifiability of TSK Additive Fuzzy Rule-Based Models

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Part of the book series: Advances in Soft Computing ((AINSC,volume 37))

Abstract

Fuzzy Set Theory has been developed during the second half of last century, with a starting point in L.A. Zadeh seminal paper [14]. From that moment on, there has been a harsh debate between scientifics supporting it and others believing that it was an unnecesary mathematical construct, generally opposing it to Probability Theory. Those researchers usually complained about the alleged lack of mathematical soundness of Fuzzy Logic and its applications. For a succint review on this debate, see Section 1 of [2].

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References

  1. J.L. Aznarte M., J.M. Benítez, and J.L. Castro. Equivalence relationships between fuzzy additive systems for time series analysis and smooth transition models. IFSA 2005 World Conference, Beijing, China, 2005.

    Google Scholar 

  2. M-T. Gan, M. Hanmandlu, and A.H. Tan. From a gaussian mixture model to additive fuzzy systems. IEEE Transactions on Fuzzy Systems, 13(3):303–316, 2005.

    Article  Google Scholar 

  3. J.T.G. Hwang and A.A. Ding. Prediction intervals for artificial neural networks. Journal of the American Statistical Association, 92:109–125, 1997.

    Article  MathSciNet  Google Scholar 

  4. G.J. Klir and B. Yuan Fuzzy sets and fuzzy logic. Prentice-Hall, 1995.

    Google Scholar 

  5. E.H. Mamdani. Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Transactions on Computers, 26(12):1182–1191, 1977.

    Article  MATH  Google Scholar 

  6. M.C. Medeiros, T. Teräsvirta, and G. Rech. Building neural network models for time series: A statistical approach. Journal of Forecasting, 25(1):49–75, 2006.

    Article  MathSciNet  Google Scholar 

  7. M.C. Medeiros and A. Veiga. A hybrid linear-neural model for time series forecasting. IEEE Transactions on Neural Networks, 11(6):1402–1412, 2000.

    Article  Google Scholar 

  8. M.C. Medeiros and A. Veiga. A flexible coefficient smooth transition time series model. IEEE Transactions on Neural Networks, 16(1):97–113, January 2005.

    Article  Google Scholar 

  9. M. Suarez-Fariñas, C.E. Pedreira, and M.C. Medeiros. Local global neural networks: a new approach for nonlinear time series modelling. Journal of the American Statistical Association, 2004.

    Google Scholar 

  10. H.J. Sussman. Uniqueness of the weights for minimal feedforward nets with a given input-output map. Neural Networks, 5:589–593, 1992.

    Article  Google Scholar 

  11. 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, 1985.

    MATH  Google Scholar 

  12. T. Teräsvirta. Specification, estimation and evaluation of smooth transition autoregresive models. Journal of the American Statistical Association, 89:208–218, 1994.

    Article  Google Scholar 

  13. S.J. Yakowitz and J.D. Spragins. On the identifiability of finite mixtures. The Annals of Mathematical Statistics, 38(1):209–214, 1968.

    MathSciNet  Google Scholar 

  14. L.A. Zadeh. Fuzzy sets. Information and control, 3(8):338–353, 1965.

    Article  MathSciNet  Google Scholar 

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M., J., Benítez, J. (2006). On the Identifiability of TSK Additive Fuzzy Rule-Based Models. In: Lawry, J., et al. Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34777-1_11

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  • DOI: https://doi.org/10.1007/3-540-34777-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34776-7

  • Online ISBN: 978-3-540-34777-4

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