Skip to main content
SpringerLink
Log in

Neural Network with Fuzzy Weights Using Type-1 and Type-2 Fuzzy Learning with Gaussian Membership Functions

  • Chapter
  • First Online:
Recent Advances on Hybrid Approaches for Designing Intelligent Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 547))

  • 1405 Accesses

Abstract

In this chapter type-1 and type-2 fuzzy inferences systems are used to obtain the type-1 or type-2 fuzzy weights in the connection between the layers of a neural network. We used two type-1 or type-2 fuzzy systems that work in the backpropagation learning method with the type-1 or type-2 fuzzy weight adjustment. The mathematical analysis of the proposed learning method architecture and the adaptation of type-1 or type-2 fuzzy weights are presented. The proposed method is based on recent methods that handle weight adaptation and especially fuzzy weights. In this work neural networks with type-1 fuzzy weights or type-2 fuzzy weights are presented. The proposed approach is applied to the case of Mackey–Glass time series prediction.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abiyev, R.: A type-2 fuzzy wavelet neural network for time series prediction. Lect. Notes Comput. Sci. 6098, 518–527 (2010)

    Article  Google Scholar 

  2. Barbounis, T.G., Theocharis, J.B.: Locally recurrent neural networks for wind speed prediction using spatial correlation. Inf. Sci. 177(24), 5775–5797 (2007)

    Article  Google Scholar 

  3. Beale, E.M.L.: A derivation of conjugate gradients. In: Lootsma, F.A. (ed.) Numerical Methods for Nonlinear Optimization, pp. 39–43. Academic Press, London (1972)

    Google Scholar 

  4. Casasent, D., Natarajan, S.: A classifier neural net with complex-valued weights and square-law nonlinearities. Neural Networks 8(6), 989–998 (1995)

    Article  Google Scholar 

  5. Castillo, O., Melin, P.: A review on the design and optimization of interval type-2 fuzzy controllers. Appl. Soft Comput. 12(4), 1267–1278 (2012)

    Article  Google Scholar 

  6. Castro, J., Castillo, O., Melin, P., Rodríguez-Díaz, A.: A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks. Inf. Sci. 179(13), 2175–2193 (2009)

    Article  MATH  Google Scholar 

  7. Castro J., Castillo O., Melin P., Mendoza O., Rodríguez-Díaz A.: An interval type-2 fuzzy neural network for chaotic time series prediction with cross-validation and akaike test. In: Soft Computing for Intelligent Control and Mobile Robotics, pp. 269–285. Springer, Berlin (2011)

    Google Scholar 

  8. Cazorla, M., Escolano, F.: Two bayesian methods for junction detection. IEEE Trans. Image Process. 12(3), 317–327 (2003)

    Article  MathSciNet  Google Scholar 

  9. De Wilde, O.: The magnitude of the diagonal elements in neural networks. Neural Networks 10(3), 499–504 (1997)

    Article  Google Scholar 

  10. Draghici, S.: On the capabilities of neural networks using limited precision weights. Neural Networks 15(3), 395–414 (2002)

    Article  Google Scholar 

  11. Feuring T.: Learning in fuzzy neural networks. In: IEEE International Conference on Neural Networks, vol. 2, pp. 1061–1066 (1996)

    Google Scholar 

  12. Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. Comput. J. 7, 149–154 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gaxiola, F., Melin, P., Valdez, F., Castillo, O.: Neural network with type-2 fuzzy weights adjustment for pattern recognition of the human iris biometrics. In: MICAI’12 Proceedings of the 11th Mexican International Conference on Advances in Computational Intelligence, vol. 2, pp. 259–270 (2012)

    Google Scholar 

  14. Gaxiola, F., Melin, P., Valdez, F., Castillo, O.: Optimization of type-2 fuzzy weight for neural network using genetic algorithm and particle swarm optimization. In: 5th World Congress on Nature and Biologically Inspired Computing, pp. 22–28 (2013)

    Google Scholar 

  15. Gaxiola, F., Melin P., Valdez F.: Backpropagation method with type-2 fuzzy weight adjustment for neural network learning. In: Fuzzy Information Processing Society (NAFIPS), Annual Meeting of the North American, pp. 1–6 (2012)

    Google Scholar 

  16. Gaxiola, F., Melin, P., Valdez, F.: Genetic optimization of type-2 fuzzy weight adjustment for backpropagation ensemble neural network. In: Recent Advances on Hybrid Intelligent Systems, pp. 159–171 (2013)

    Google Scholar 

  17. Gaxiola, F., Melin, P., Valdez, F.: Neural network with lower and upper type-2 fuzzy weights using the backpropagation learning method. In: IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 637–642 (2013)

    Google Scholar 

  18. Gedeon, T.: Additive neural networks and periodic patterns. Neural Networks 12(4–5), 617–626 (1999)

    Article  Google Scholar 

  19. Hagan, M.T., Demuth, H.B., Beale, M.H.: Neural Network Design, p. 736. PWS Publishing, Boston (1996)

    Google Scholar 

  20. Hagras, H.: Type-2 fuzzy logic controllers: a way forward for fuzzy systems in real world environments. In: IEEE World Congress on Computational Intelligence, pp. 181–200 (2008)

    Google Scholar 

  21. Ishibuchi, H., Morioka, K., Tanaka, H.: A fuzzy neural network with trapezoid fuzzy weights, fuzzy systems. In: IEEE World Congress on Computational Intelligence, vol. 1, pp. 228–233 (1994)

    Google Scholar 

  22. Ishibuchi, H., Tanaka, H., Okada, H.: Fuzzy neural networks with fuzzy weights and fuzzy biases. In: IEEE International Conference on Neural Networks, vol. 3, pp. 1650-1655 (1993)

    Google Scholar 

  23. Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, p. 614. Prentice Hall, Englewood Cliffs (1997)

    Google Scholar 

  24. Kamarthi, S., Pittner, S.: Accelerating neural network training using weight extrapolations. Neural Networks 12(9), 1285–1299 (1999)

    Article  Google Scholar 

  25. Karnik, N., Mendel, J.: Applications of type-2 fuzzy logic systems to forecasting of time-series. Inf. Sci. 120(1–4), 89–111 (1999)

    Article  MATH  Google Scholar 

  26. Martinez, G., Melin, P., Bravo, D., Gonzalez, F., Gonzalez, M.: Modular neural networks and fuzzy sugeno integral for face and fingerprint recognition. Adv. Soft Comput. 34, 603–618 (2006)

    Google Scholar 

  27. Melin, P.: Modular Neural Networks and Type-2 Fuzzy Systems for Pattern Recognition, pp. 1–204. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  28. Meltser, M., Shoham, M., Manevitz, L.: Approximating functions by neural networks: a constructive solution in the uniform norm. Neural Networks 9(6), 965–978 (1996)

    Article  Google Scholar 

  29. Moller, M.F.: A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks 6, 525–533 (1993)

    Article  Google Scholar 

  30. Monirul Islam, M.D., Murase, K.: A new algorithm to design compact two-hidden-layer artificial neural networks. Neural Networks 14(9), 1265–1278 (2001)

    Article  Google Scholar 

  31. Neville, R.S., Eldridge, S.: Transformations of sigma–pi nets: obtaining reflected functions by reflecting weight matrices. Neural Networks 15(3), 375–393 (2002)

    Article  Google Scholar 

  32. Phansalkar, V.V., Sastry, P.S.: Analysis of the back-propagation algorithm with momentum. IEEE Trans. Neural Networks 5(3), 505–506 (1994)

    Article  Google Scholar 

  33. Powell, M.J.D.: Restart procedures for the conjugate gradient method. Math. Program. 12, 241–254 (1977)

    Article  MATH  Google Scholar 

  34. Salazar, P.A., Melin, P., Castillo, O.: A new biometric recognition technique based on hand geometry and voice using neural networks and fuzzy logic. In: Soft Computing for Hybrid Intelligent Systems, pp. 171–186 (2008)

    Google Scholar 

  35. Sepúlveda, R., Castillo, O., Melin, P. Montiel, O.: An efficient computational method to implement type-2 fuzzy logic in control applications. In: Analysis and Design of Intelligent Systems using Soft Computing Techniques, pp. 45–52 (2007)

    Google Scholar 

  36. Yam, J., Chow, T.: A weight initialization method for improving training speed in feedforward neural network. Neurocomputing 30(1–4), 219–232 (2000)

    Article  Google Scholar 

  37. Yeung, D., Chan, P., Ng, W.: Radial basis function network learning using localized generalization error bound. Inf. Sci. 179(19), 3199–3217 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tijuana Institute of Technology, Tijuana, Mexico

    Fernando Gaxiola, Patricia Melin & Fevrier Valdez

Authors
  1. Fernando Gaxiola
    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

  3. Fevrier Valdez
    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, Mexico

    Oscar Castillo

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

    Patricia Melin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Witold Pedrycz

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

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Gaxiola, F., Melin, P., Valdez, F. (2014). Neural Network with Fuzzy Weights Using Type-1 and Type-2 Fuzzy Learning with Gaussian Membership Functions. In: Castillo, O., Melin, P., Pedrycz, W., Kacprzyk, J. (eds) Recent Advances on Hybrid Approaches for Designing Intelligent Systems. Studies in Computational Intelligence, vol 547. Springer, Cham. https://doi.org/10.1007/978-3-319-05170-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-05170-3_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05169-7

  • Online ISBN: 978-3-319-05170-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation