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On the Equivalence between Generalized Ellipsoidal Basis Function Neural Networks and T-S Fuzzy Systems

  • Ning Wang
  • Min Han
  • Nuo Dong
  • Meng Joo Er
  • Gangjian Liu
Conference paper
  • 3.3k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7952)

Abstract

This paper deals with the functional equivalence between Generalized Ellipsoidal Basis Function based Neural Networks (GEBF-NN) and T-S fuzzy systems. Significant contributions are summarized as follows. 1) The GEBF-NN is equivalent to a T-S fuzzy system under the condition that the GEBF unit and the local model correspond to the premise and the consequence of the T-S fuzzy system. 2) The normalized (nonnormalized) GEBF-NN is equivalent to a normalized (nonnormalized) T-S fuzzy system using dissymmetrical Gaussian functions (DGF) as univariate membership functions and local models as consequent parts. 3) The equivalence between the normalized GEBF-NN and the nonnormalized T-S fuzzy system is established by employing GEBF units as multivariate membership functions of fuzzy rules. 4) These theoretical results would not only fertilize the learning schemes for fuzzy systems but also enhance the interpretability of neural networks, and thereby contributing to innovative neuro-fuzzy paradigms. Finally, numerical examples are conducted to illustrate the main results.

Keywords

generalized ellipsoidal basis function neural network T-S fuzzy system functional equivalence 

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References

  1. 1.
    Wang, N., Er, M.J., Meng, X.: A Fast and Accurate Online Self-Organizing Scheme for Parsimonious Fuzzy Neural Networks. Neurocomput. 72, 3818–3829 (2009)CrossRefGoogle Scholar
  2. 2.
    Wang, N., Er, M.J., Meng, X.Y., Li, X.: An Online Self-Organizing Scheme for Parsimonious and Accurate Fuzzy Neural Networks. Int. J. Neural Syst. 20, 389–403 (2010)CrossRefGoogle Scholar
  3. 3.
    Jang, J.R., Sun, C.T.: Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems. IEEE Trans. Neural Netw. 4, 156–159 (1993)CrossRefGoogle Scholar
  4. 4.
    Anderson, H.C., Lotfi, A., Westphal, L.C., Jang, J.R.: Comments on ”Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems”. IEEE Trans. Neural Netw. 9, 1529–1531 (1998)CrossRefGoogle Scholar
  5. 5.
    Hunt, K.J., Haas, R., Murray-Smith, R.: Extending the Functional Equivalence of Radial Basis Function Networks and Fuzzy Inference Systems. IEEE Trans. Neural Netw. 7, 776–781 (1996)CrossRefGoogle Scholar
  6. 6.
    Azeem, M.F., Hanmandlu, M., Ahmad, N.: Generalization of Adaptive Neuro-Fuzzy Inference Systems. IEEE Trans. Neural Netw. 11, 1332–1346 (2000)CrossRefGoogle Scholar
  7. 7.
    Azeem, M.F., Hanmandlu, M., Ahmad, N.: Structure Identification of Generalized Adaptive Neuro-Fuzzy Inference Systems. IEEE Trans. Fuzzy Syst. 11, 666–681 (2003)CrossRefGoogle Scholar
  8. 8.
    Li, H.X., Chen, C.P.: The Equivalence between Fuzzy Logic Systems and Feedforward Neural Networks. IEEE Trans. Neural Netw. 11, 356–365 (2000)CrossRefGoogle Scholar
  9. 9.
    Kolman, E., Margaliot, M.: Are Artificial Neural Networks White Boxes? IEEE Trans. Neural Netw. 16, 844–852 (2005)CrossRefGoogle Scholar
  10. 10.
    Aznarte, J.L., Benitez, J.M.: Equivalences between Neural-Autoregressive Time Series Models and Fuzzy Systems. IEEE Trans. Neural Netw. 21, 1434–1444 (2010)CrossRefGoogle Scholar
  11. 11.
    Barra, A., Bernacchia, A., Santucci, E., Contucci, P.: On the Equivalence of Hopfield Networks and Boltzmann Machines. Neural Netw. 34, 1–9 (2012)zbMATHCrossRefGoogle Scholar
  12. 12.
    Wang, N.: A Generalized Ellipsoidal Basis Function Based Online Self-Constructing Fuzzy Neural Network. Neural Process. Lett. 34, 13–37 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ning Wang
    • 1
  • Min Han
    • 2
  • Nuo Dong
    • 1
  • Meng Joo Er
    • 1
    • 3
  • Gangjian Liu
    • 1
  1. 1.Marine Engineering CollegeDalian Maritime UniversityDalianChina
  2. 2.Faculty of EIEEDalian University of TechnologyDalianChina
  3. 3.School of EEENanyang Technological UniversitySingapore

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