Skip to main content
Springer Nature Link
Log in

Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

By combining of the benefits of high-order network and TSK (Tagaki-Sugeno-Kang) inference system, Pi-Sigma network is capable to dispose with the nonlinear problems much more effectively, which means it has a compacter construction, and quicker computational speed. The aim of this paper is to present a gradient-based learning method for Pi-Sigma network to train TSK fuzzy inference system. Moreover, some strong convergence results are established based on the weak convergence outcomes, which indicates that the sequence of weighted fuzzy parameters gets to a fixed point. Simulation results show the modified learning algorithm is effective to support the theoretical results.

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

Access this article

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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Singh P, Borah B (2009) High-order fuzzy-neuro expert system for time series forecasting. Knowl Based Syst 46:12–21. doi:10.1016/j.knosys.2013.01.030

    Article  Google Scholar 

  2. Lin Y, Chang J, Lin C (2013) Identification and prediction of dynamic systems using an interactively recurrent self-evolving fuzzy neural network. IEEE Trans Neural Netw Learn Syst 24(2):310–321. doi:10.1109/TNNLS.2012.2231436

    Article  Google Scholar 

  3. Chen P, Fei M, Tian E (2013) Networked control for a class of T–S fuzzy systems with stochastic sensor faults. Fuzzy Sets Syst 212:62–77. doi:10.1016/j.fss.2012.09.015

    Article  MathSciNet  MATH  Google Scholar 

  4. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(2):116–132. doi:10.1109/TSMC.1985.6313399

    Article  MATH  Google Scholar 

  5. Tseng C, Chen B, Uang H (2001) Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model. IEEE Trans Fuzzy Syst 9(3):381–392. doi:10.1109/91.928735

    Article  Google Scholar 

  6. Shin Y, Ghosh J (1991) The Pi-Sigma networks: an efficient higher-order neural network for pattern classification and function approximation. Proc Int Joint Conf Neural Netw 1:13–18. doi:10.1109/IJCNN.1991.155142

    Google Scholar 

  7. Ghazali R, Hussain AJ, Nawi NM, Mohamad B (2009) Non-stationary and stationary prediction of financial time series using dynamic ridge polynomial neural network. Neurocomputing 72(10–12):2359–2367. doi:10.1016/j.neucom.2008.12.005

    Article  Google Scholar 

  8. Jin Y, Jiang J, Zhu J (2012) Neural network based fuzzy identification and its application to modeling and control of complex systems. IEEE Trans Syst Man Cybern 25(6):990–997. doi:10.1109/21.384264

    Google Scholar 

  9. Yu W, Li MQ, Luo J, Su S, Li C (2010) Prediction of the mechanical properties of the post-forged TiC6AlC4V alloy using fuzzy neural network. Mater Des 31(7):3282–3288. doi:10.1016/j.matdes.2010.02.009

    Article  Google Scholar 

  10. Zhang C, Wu W, Chen X, Xiong Y (2008) Convergence of BP algorithm for product unit neural networks with exponential weights. Neurocomputing 72(1–3):513–520. doi:10.1016/j.neucom.2007.12.004

    Article  Google Scholar 

  11. Sun Z, Au KF, Choi TM (2007) A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines. IEEE Trans Syst Man Cybern 37(5):1321–1331. doi:10.1109/TSMCB.2007.901375

    Article  Google Scholar 

  12. Campo I, Echanobe J, Bosque G, Tarela J (2008) Efficient hardware/software implementation of an adaptive neuro-fuzzy system. IEEE Trans Fuzzy Syst 16(3):761–778. doi:10.1109/TFUZZ.2007.905918

    Article  Google Scholar 

  13. Liu Y, Yang J, Yang D, Wu W (2014) A modified gradient-based neuro-fuzzy learning algorithm for pi-sigma network based on first-order takagi-sugeno system. J Math Res Appl 34(1):114–126

    MathSciNet  MATH  Google Scholar 

  14. Faria FA, Geraldo NS, Vilma AO (2013) Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions. Int J Syst Sci 44(10):1956–1969. doi:10.1080/00207721.2012.670307

    Article  MathSciNet  MATH  Google Scholar 

  15. Chen D et al (2013) Application of Takagi-Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization. Nonlinear Dyn 73(3):1495–1505. doi:10.1007/s11071-013-0880-1

    Article  MathSciNet  MATH  Google Scholar 

  16. Jang JSR (1993) ANFIS adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685. doi:10.1109/21.256541

    Article  Google Scholar 

  17. Charurved K, Pandit M, Srivastava L (2007) Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch. Appl Soft Comput 8(4):1428–1438. doi:10.1016/j.asoc.2007.10.010

    Google Scholar 

  18. Yuan YX, Sun WY (2001) Optimization theory and method. Science Press, Beijing

    Google Scholar 

  19. Wu W, Li L, Yang J, Liu Y (2010) A modified gradient-based neuro-fuzzy learning algorithm and its convergence. Inf Sci 180(9):1630–1642. doi:10.1016/j.ins.2009.12.030

    Article  MathSciNet  MATH  Google Scholar 

  20. Ampazis N, Perantonis SJ (2002) Two highly efficient second-order algorithms for training feedforward networks. IEEE Trans Neural Netw 13(5):1064–1074. doi:10.1109/TNN.2002.1031939

    Article  Google Scholar 

  21. Mackay DJC (1992) Bayesian interpolation. Neural Comput 4(3):415–447. doi:10.1162/neco.1992.4.3.415

    Article  MATH  Google Scholar 

  22. Liu Y, Yang J, Li L, Wu W (2012) Negative effects of sufficiently small initial weights on back-propagation neural networks. J of Zhejiang Univ Sci C (Comput & Electron) 13(8):585–592. doi:10.1631/jzus.C1200008

    Article  Google Scholar 

  23. Chen D, Han W (2013) Prediction of multivariate chaotic time series via radial basis function neural network. Complexity 18(4):55–66. doi:10.1002/cplx.21441

    Article  Google Scholar 

  24. Meng D, Leung Y, Xu Z (2013) The strong convergence of visual classification method and its applications. Inf Sci 249(10):85–95. doi:10.1016/j.ins.2013.06.028

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Dalian Polytechnic University, Dalian, 116034, China

    Yan Liu, Li Guo & Jianjun Zhang

  2. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, 116024, China

    Yan Liu

  3. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, 510006, China

    Dakun Yang

  4. Department of Electromechanical Engineering, Jining Polytechnic, Jining, 272037, China

    Nan Nan

Authors
  1. Yan Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Dakun Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Nan Nan
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Li Guo
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Jianjun Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yan Liu.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 61403056 and 61473059), Foundation of Liaoning Educational Committee (No. L2014218) and Foundation of major platform for National Engineering Research Center of Seafood ([2011]191).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Yang, D., Nan, N. et al. Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models. Neural Process Lett 43, 745–758 (2016). https://doi.org/10.1007/s11063-015-9445-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-015-9445-2

Keywords