Skip to main content
SpringerLink
Log in

Triple-I FMP algorithm for double hierarchical fuzzy system based on manifold learning

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

As is well known, Zadeh presented the compositional rule of inference to discuss complex inference modes. After that other researchers also investigated this problem. However, the classic fuzzy control systems in the application often encounter the curse of dimensionality. To overcome these difficulties in the classic fuzzy control systems with high-dimensional input variables, the entire triple-I algorithm for double fuzzy control systems and manifold learning of dimensionality reduction will be discussed in this paper. Specifically, triple-I FMP algorithm is presented for double hierarchical fuzzy control system based on Guojun Wang’s implication operator and its reversibility is proved. Using manifold learning, dimension reduction SNE algorithm is given for double-layer hierarchical fuzzy control systems to keep the distribution of peak possibly point, so as to minimize the control stability impact due to reducing dimension. Since any type of multi-layer fuzzy control system is regarded as multiple fusion of double-layer hierarchical fuzzy system, the proposed algorithms and their reversibility are universal.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Chen CS, Chen WL (1998) Robust adaptive sliding-mode control using fuzzy modeling for an inverted pendulum system. IEEE Trans Ind Electron 45(2):297–306

    Article  Google Scholar 

  2. Chen CLP, Liu ZL (2018) Broad learning system: an effective and efficient incremental learning system without the need for deep architecture. IEEE Trans Neural Netw Learn Syst 29(1):10–24

    Article  MathSciNet  Google Scholar 

  3. Gong M, Zhao J, Liu J, Miao Q, Jiao L (2016) Change detection in synthetic aperture radar images based on deep neural networks. IEEE Trans Neural Netw Learn Syst 27(1):125–138

    Article  MathSciNet  Google Scholar 

  4. Hinton G, Roweis S (2002) Stochastic neighbor embedding. Adv Neural Inf Process Syst 41(4):833–840

    Google Scholar 

  5. Joo MG, Lee JS (2005) A class of hierarchical fuzzy systems with constraints on the fuzzy rules. IEEE Trans Fuzzy Syst 13(2):194–203

    Article  MathSciNet  Google Scholar 

  6. Li HL, Liu DR, Wang D (2018) Manifold regularized reinforcement learning. IEEE Trans Neural Netw Learn Syst 29(4):932–943

    Article  Google Scholar 

  7. Li JH, Mei CL, Lv YJ (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165

    Article  MathSciNet  MATH  Google Scholar 

  8. Li HX, Miao ZH, Wang JY (2002) Variable universe adaptive fuzzy control on the quadruple inverted pendulum. Sci China Ser E (Technol Sci 45(2):213–224

    Article  MathSciNet  MATH  Google Scholar 

  9. Li KW, Shao MW, Wu WZ (2017) A data reduction method in formal fuzzy contexts. Int J Mach Learn Cybern 8(4):1145–1155

    Article  Google Scholar 

  10. Liu PY, Li HX (2005) Approximation of stochastic processes by TCS fuzzy systems. Fuzzy Sets Syst 155(2):215–235

    Article  Google Scholar 

  11. Mamdani EH (1977) Application of fuzzy logic to approximate reasoning using linguistic systems. IEEE Trans Comput 26(12):1182–1191

    Article  MATH  Google Scholar 

  12. Pei DW (2008) Unified full implication algorithms of fuzzy reasoning. Inf Sci 178(2):520–530

    Article  MathSciNet  MATH  Google Scholar 

  13. Raju GVS, Jun Z (1993) Adaptive hierarchical fuzzy controller. IEEE Trans Syst Man Cybern 23(4):973–980

    Article  Google Scholar 

  14. Shao MW, Li KW (2017) Attribute reduction in generalized one-sided formal contexts. Inf Sci 378:317–327

    Article  MathSciNet  Google Scholar 

  15. Song SJ, Feng CB, Lee ES (2002) Triple I method of fuzzy reasoning. Comput Math Appl 44(12):1567–1579

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang CZ, Hu QH, Wang XZ, Chen DG, Qian YH, Dong Z (2018) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst 29(7):2986–2999

    MathSciNet  Google Scholar 

  17. Wang GJ (1999) Full implication triple I algorithm for fuzzy reasoning. Sci China Ser E (Technol Sci) 29(1):43–53 (in Chinese)

    Google Scholar 

  18. Wang GJ (2000) Triple I method and interval value for fuzzy reasoning. Sci China Ser E (Technol Sci) 40(3):242–253 (in Chinese)

    Article  MATH  Google Scholar 

  19. Wang GJ, Duan CX (2012) Generalized hierarchical hybrid fuzzy system and its universal approximation. Control Theory Appl 29(5):673–680 (in Chinese)

    Google Scholar 

  20. Wang LX (1998) Universal approximation by hierarchical fuzzy system. Fuzzy Sets Syst 93(2):223–230

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang LX (1999) Analysis and design of hierarchical fuzzy systems. IEEE Int Trans Fuzzy Syst 7(5):617–624

    Article  Google Scholar 

  22. Xiang SM, Nie FP, Zhang CS, Zhang CX (2009) Nonlinear dimensionality reduction with local spline embedding. IEEE Trans Knowl Data Eng 21(9):1285–1298

    Article  Google Scholar 

  23. Yin JS, Xiao J, Zhou ZT, Hu DW (2007) Method of nonliner manifold learning and its application. Progress Nat Sci 17(8):1015–1025

    Google Scholar 

  24. Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern 3(1):28–33

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang JP, Chen DW, Kruger U (2008) Adaptive constraint K-segment principal curves for intelligent transportation system. IEEE Trans Intell Transp Syst 9(4):666–677

    Article  Google Scholar 

  26. Zhang J, Ding SF, Zhang N, Shi ZZ (2016) Incremental extreme learning machine based on deep feature embedded. Int J Mach Learn Cybern 7(1):111–120

    Article  Google Scholar 

  27. Zhang X, Mei CL, Chen DG, Li JH (2016) Feature selection in mixed data: a method using a novel fuzzy rough set-based information entropy. Pattern Recognit 56:1–15

    Article  MATH  Google Scholar 

  28. Zhao YX, Li JH, Liu WQ, Xu WH (2017) Cognitive concept learning from incomplete information. Int J Mach Learn Cybern 8(1):159–170

    Article  Google Scholar 

  29. Zhao SY, Chen H, Li CP, Du XY, Sun H (2015) A novel approach to building a robust fuzzy rough classifier. IEEE Trans Fuzzy Syst 23(4):769–786

    Article  Google Scholar 

  30. Zhao Z, Feng GC, Zhu JH, Shen Q (2016) Manifold learning: dimensionality reduction and high dimensional data reconstruction via dictionary learning. Neurocomputing 216:268–285

    Article  Google Scholar 

  31. Zhu XD, Wang J (2013) A new type of hierarchical fuzzy system and its approximation performance. Control Decis 28(10):1559–1563, 1567 (in Chinese)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (nos. 61573173 and 61562050).

Author information

Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Meng Li & Wenqi Liu

  2. Data Science Research Center, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Meng Li & Wenqi Liu

Authors
  1. Meng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenqi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenqi Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, M., Liu, W. Triple-I FMP algorithm for double hierarchical fuzzy system based on manifold learning. Int. J. Mach. Learn. & Cyber. 10, 2459–2466 (2019). https://doi.org/10.1007/s13042-018-0882-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-018-0882-x

Keywords

Search

Navigation