The Learning Algorithm for a Novel Fuzzy Neural Network

  • Puyin Liu
  • Qiang Luo
  • Wenqiang Yang
  • Dongyun Yi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4113)


Symmetric polygonal fuzzy numbers are employed to construct a class of novel feedforward fuzzy neural networks (FNN’s)—the polygonal FNN’s. Their input–output (I/O) relationships are built upon a novel fuzzy arithmetic and extension principle for the polygonal fuzzy numbers. We build the topological architecture of a three layer polygonal FNN, and present its I/O relationship representation. Also the fuzzy BP learning algorithm for the polygonal fuzzy number connection weights and thresholds is developed based on calculus of max–min (∨– ∧) functions. At last some simulation examples are compared to show that our model possess strong I/O ability and generalization capability.


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  1. 1.
    Aliev, R.A., Fazlollahi, B., Vahidov, R.M.: Genetic Algorithm-Based Learning of Fuzzy Neural Networks. Part I: Feed-Forward Fuzzy Neural Networks. Fuzzy Sets and Systems 118, 351–358 (2001)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Blanco, A., Delgado, M., Requena, I.: Identification of Fuzzy Relational Equations by Fuzzy Neural Networks. Fuzzy Sets and Systems 71, 215–226 (1995)CrossRefGoogle Scholar
  3. 3.
    Blanco, A., Delgado, M., Requena, I.: Improved Fuzzy Neural Networks for Solving Fuzzy Relational Equations. Fuzzy Sets and Systems 72, 311–322 (1995)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Buckley, J.J., Hayashi, Y.: Can Neural Nets Be Universal Approximators for Fuzzy Functions. Fuzzy Sets and Systems 101, 323–330 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Buckley, J.J., Hayashi, Y.: Fuzzy Neural Networks: A Survey. Fuzzy Sets and Systems 66, 1–13 (1994)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Buckley, J.J., Hayashi, Y.: Direct Fuzzification of Neural Networks. In: Proc. of 1st Asian Fuzzy Sys. Symp., Singapore, vol. 1, pp. 560–567 (1993)Google Scholar
  7. 7.
    Dunyak, J., Wunsch, D.: Fuzzy Number Neural Networks. Fuzzy Sets and Systems 108, 49–58 (1999)CrossRefGoogle Scholar
  8. 8.
    Feuring, T., Lippe, W.M.: The Fuzzy Neural Network Approximation Lemma. Fuzzy Sets and Systems 102, 227–236 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ishibuchi, H., Fujioka, R., Tanaka, H.: Neural Networks that Learn from Fuzzy If–Then Rules. IEEE Trans. on Fuzzy Systems 1, 85–97 (1993)CrossRefGoogle Scholar
  10. 10.
    Ishibuchi, H., Kwon, K., Tanaka, H.A.: Learning Algorithm of Fuzzy Neural Networks with Triangular Fuzzy Weights. Fuzzy sets and Systems 71, 277–293 (1995)CrossRefGoogle Scholar
  11. 11.
    Ishibuchi, H., Nii, M.: Numerical Analysis of the Learning of Fuzzified Neural Networks from Fuzzy If–Then Rules. Fuzzy Sets and Systems 120, 281–307 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Li, Z., Kecman, V., Ichikawa, A.: Fuzzified Neural Network Based on Fuzzy Number Operations. Fuzzy Sets and Systems 130, 291–304 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Liu, P.: Analyses of Regular Fuzzy Neural Networks for Approximation Capability. Fuzzy Sets and Systems 114, 329–338 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Liu, P.: On the Approximation Realization of Fuzzy Closure Mapping by Multilayer Regular Fuzzy Neural Networks. Multiple Valued Logic 5(11), 463–480 (2000)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Liu, P.: A Novel Fuzzy Neural Network and Its Approximation Property. Science in China (Series F) 44(3), 184–194 (2001)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Liu, P.: Representation of Digital Image by Fuzzy Neural Networks. Fuzzy Sets and Systems 130, 109–123 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Nguyen, H.T.: A Note on the Extension Principle for Fuzzy Set. J. Math. Anal. Appl. 64, 369–380 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Liu, P., Li, H.: Fuzzy Neural Network Theory and Application. World Scientific Publishing, Singapore (2004)zbMATHCrossRefGoogle Scholar
  19. 19.
    Zhang, X.H., Tan, S.H., Huang, C.C., et al.: An Efficient Computational Algorithm for Min-Max Operations. Fuzzy Sets and Systems 104, 297–304 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Zhang, X.H., Huang, C.C., Tan, S.H., et al.: The Min-Max Function Differentiation and Training of Fuzzy Neural Networks. IEEE Trans. on Neural Networks 7, 1139–1150 (1996)CrossRefGoogle Scholar
  21. 21.
    Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets. World Scientific Publishing, Singapore (1994)zbMATHGoogle Scholar
  22. 22.
    Liu, P., Li, H.: Symmetric Polygonal Fuzzy Numbers. In: The 9th International Conference on Fuzzy Theory and Technology, NC, USA, pp. 26–30 (2003)Google Scholar
  23. 23.
    Park, S., Han, T.: Iterative Inversion of Fuzzified Neural Networks. IEEE Trans. on Fuzzy Systems 8, 268–280 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Puyin Liu
    • 1
  • Qiang Luo
    • 1
  • Wenqiang Yang
    • 1
  • Dongyun Yi
    • 1
  1. 1.Department of MathematicsNational University of Defense TechnologyChangshaP.R. China

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