Skip to main content
SpringerLink
Log in

Study on Weighted-Based Discrete Noniterative Algorithms for Computing the Centroids of General Type-2 Fuzzy Sets

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Since the α-planes expression theory of general type-2 fuzzy sets (GT2 FSs) was put forward, the computational complexity of general type-2 fuzzy logic systems (GT2 FLSs) has been greatly reduced. Calculating the centroids of GT2 FSs is an important block for theoretical research of GT2 FLSs. Noniterative algorithms can overcome the disadvantages of being computationally intensive and time consuming. The paper discovers the relations between discrete types of noniterative algorithms and continuous types of noniterative algorithms. In terms of the Newton–Cotes quadrature formulas, three types of weighted-based noniterative algorithms are proposed to compute the centroids. In case of choosing the same sampling rate of primary variable, four computer simulation instances illustrate that, the proposed weighted-based noniterative algorithms have higher calculation accuracies and faster convergence speeds in contrast to the original noniterative algorithms.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput. Intell. Mag. 2(1), 20–29 (2007)

    Article  Google Scholar 

  2. Chen, Y., Wang, D.Z., Tong, S.C.: Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: with the combination of BP algorithms and KM algorithms. Neurocomputing 174(b), 1133–1146 (2016)

    Article  Google Scholar 

  3. Mendel, J.M.: General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans. Fuzzy Syst. 22(5), 1162–1182 (2014)

    Article  Google Scholar 

  4. Liu, F.L.: An efficient centroid type-reduction strategy for general type-2 fuzzy logic system. Inf. Sci. 178(1), 2224–2236 (2008)

    Article  MathSciNet  Google Scholar 

  5. Mendel, J.M., Liu, F.L., Zhai, D.Y.: Alpha-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans. Fuzzy Syst. 17(5), 1189–1207 (2009)

    Article  Google Scholar 

  6. Wagner, C., Hagras, H.: Toward general type-2 fuzzy logic systems based on zSlices. IEEE Trans. Fuzzy Syst. 18(4), 637–660 (2010)

    Article  Google Scholar 

  7. Gonzalez, C., Melin, P., Castro, J.R., et al.: An edge detection method based on generalized type-2 fuzzy logic. Soft Comput. 20(2), 773–784 (2016)

    Article  Google Scholar 

  8. Melin, P., Gonzalez, C.I., Castro, J.R., Mendoza, O., Castillo, O.: Edge-detection method for image processing based on generalized type-2 fuzzy logic. IEEE Trans. Fuzzy Syst. 22(6), 1515–1525 (2014)

    Article  Google Scholar 

  9. Chen, Y., Wang, D.Z., Ning, W.: Forecasting by TSK general type-2 fuzzy logic systems optimized with genetic algorithms. Optim. Control Appl. Methods 39(1), 393–409 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, Y., Wang, D.Z.: Forecasting by general type-2 fuzzy logic systems optimized with QPSO algorithms. Int. J. Control Autom. Syst. 15(6), 2950–2958 (2017)

    Article  Google Scholar 

  11. Chen, Y., Wang, D.Z.: Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms. Trans. Inst. Meas. Control 41(10), 2886–2896 (2019)

    Article  MathSciNet  Google Scholar 

  12. Mendel, J.M.: On KM algorithms for solving type-2 fuzzy set problems. IEEE Trans. Fuzzy Syst. 21(3), 426–446 (2013)

    Article  Google Scholar 

  13. Mendel, J.M., Liu, F.L.: Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set. IEEE Trans. Fuzzy Syst. 15(2), 309–320 (2007)

    Article  Google Scholar 

  14. Wu, D.R., Mendel, J.M.: Enhanced Karnik-Mendel algorithms. IEEE Trans. Fuzzy Syst. 17(4), 923–934 (2009)

    Article  Google Scholar 

  15. Liu, X.W., Mendel, J.M., Wu, D.R.: Study on enhanced Karnik-Mendel algorithms: initialization explanations and computation improvements. Inf. Sci. 184(1), 75–91 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen, Y., Wang, D.Z.: Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted enhanced Karnik-Mendel algorithms. Soft Comput. 22(4), 1361–1380 (2018)

    Article  MATH  Google Scholar 

  17. Chen, Y.: Study on centroid type-reduction of interval type-2 fuzzy logic systems based on noniterative algorithms. Complexity. 2019, 1–12 (2019)

  18. EI-Nagar, A.M., EI-Bardini, M.: Simplified interval type-2 fuzzy logic system based on new type-reduction. J. Intell. Fuzzy Syst. 27(4), 1999–2010 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, J.W., John, R., Coupland, S., Kendall, G.: On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 26(2), 1036–1039 (2018)

    Article  Google Scholar 

  20. Chen, Y.: Study on sampling based discrete Nie-Tan algorithms for computing the centroids of general type-2 fuzzy sets. IEEE Access 7(1), 156984–156992 (2019)

    Article  Google Scholar 

  21. Biglarbegian, M., Melek, W.W., Mendel, J.M.: On the stability of interval type-2 TSK fuzzy logic systems. IEEE Trans. Syst. Man Cybern. B 40(3), 798–818 (2010)

    Article  Google Scholar 

  22. Biglarbegian, M., Melek, W.W., Mendel, J.M.: On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. Inf. Sci. 181(7), 1325–1347 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wu, H.W., Mendel, J.M.: Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 10(5), 622–639 (2002)

    Article  Google Scholar 

  24. Greenfield, S., Chiclana, F., Coupland, S., John, R.: The collapsing method of defuzzification for discretised interval type-2 fuzzy sets. Inf. Sci. 179(13), 2055–2069 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Greenfield, S., Chiclana, F.: Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. Int. J. Approx. Reason. 54(8), 1013–1033 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu, X.W., Mendel, J.M.: Connect Karnik-Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set. IEEE Trans. Fuzzy Syst. 19(4), 652–665 (2011)

    Article  Google Scholar 

  27. Wu, D.R.: Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans. Fuzzy Syst. 21(1), 80–99 (2013)

    Article  Google Scholar 

  28. Hu, H.Z., Wang, Y., Cai, Y.L.: Advantages of the enhanced opposite direction searching algorithm for computing the centroid of an interval type-2 fuzzy set. Asian J. Control 14(5), 1422–1430 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Greenfield, S., Chiclana, F.: Defuzzification of the discretised generalised type-2 fuzzy set: experimental evaluation. Inf. Sci. 244(7), 1–25 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mathews, J.H., Fink, K.K.: Numerical Methods Using MATLAB. Prentice-Hall, Inc., Upper Saddle River (2004)

    Google Scholar 

  31. Chen, Y.: Study on weighted Nagar-Bardini algorithms for centroid type-reduction of interval type-2 fuzzy logic systems. J. Intell. Fuzzy Syst. 34(4), 2417–2428 (2018)

    Article  Google Scholar 

  32. Mendel, J.M., Liu, X.W.: Simplified interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 21(6), 1056–1069 (2013)

    Article  Google Scholar 

  33. Khanesar, M.A., Jalalian, A., Kaynak, O.: Improving the speed of center of set type-reduction in interval type-2 fuzzy systems by eliminating the need for sorting. IEEE Trans. Fuzzy Syst. 25(5), 1193–1206 (2017)

    Article  Google Scholar 

  34. Wu, D.R., Mendel, J.M.: Recommendations on designing practical interval type-2 fuzzy systems. Eng. Appl. Artif. Intell. 85, 182–193 (2019)

    Article  Google Scholar 

  35. Gaxiola, F., Melin, P., Valdez, F., Castro, J.R., Castillo, O.: Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO. Appl. Soft Comput. 38, 860–871 (2016)

    Article  Google Scholar 

  36. Tao, C.W., Taur, J.S., Chang, C.W., Chang, Y.H.: Simplified type-2 fuzzy sliding controller for wing rocket system. Fuzzy Sets Syst. 207(16), 111–129 (2012)

    Article  MATH  Google Scholar 

  37. Sanchez, M.A., Castillo, O., Castro, J.R.: Generalized type-2 fuzzy systems for controlling a mobile robot and a performance comparison with interval type-2 and type-1 fuzzy systems. Expert Syst. Appl. 42(14), 5904–5914 (2015)

    Article  Google Scholar 

  38. Hsu, C.H., Juang, C.F.: Evolutionary robot wall-following control using type-2 fuzzy controller with species-de-activated continuous ACO. IEEE Trans. Fuzzy Syst. 21(1), 100–112 (2013)

    Article  Google Scholar 

  39. Ontiveros-Robles, E., Melin, P., Castillo, O.: New methodology to approximate type-reduction based on a continuous root-finding Karnik Mendel algorithm. Algorithms 10(3), 77–96 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  40. Castillo, O., Amador-Angulo, L., Castro, J.R., et al.: A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf. Sci. 354(c), 257–274 (2016)

    Article  Google Scholar 

  41. Castillo, O., Melin, P., Ontiveros, E., et al.: A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics. Eng. Appl. Artif. Intell. 85, 666–680 (2019)

    Article  Google Scholar 

  42. Cervantes, L., Castillo, O.: Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control. Inf. Sci. 324, 247–256 (2015)

    Article  Google Scholar 

  43. Ontiveros-Robles, E., Melin, P., Castillo, O.: Comparative analysis of noise robustness of type 2 fuzzy logic controllers. Kybernetika 54(1), 175–201 (2018)

    MathSciNet  MATH  Google Scholar 

  44. Chen, Y.: Study on sampling-based discrete noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems. Soft Comput. 24(15), 11819–11828 (2020)

    Article  Google Scholar 

  45. Tong, S.C., Li, Y.M.: Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci. China Inf. Sci. 53(2), 307–324 (2010)

    Article  MathSciNet  Google Scholar 

  46. Tong, S.C., Li, Y.M.: Observer-based adaptive fuzzy backstepping control of uncertain pure-feedback systems. Sci. China Inf. Sci. 57(1), 1–14 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  47. Fan, Q.F., Wang, T., Chen, Y., et al.: Design and application of interval type-2 fuzzy logic system based on QPSO algorithm. Int. J. Fuzzy Syst. 20(3), 835–846 (2018)

    Article  Google Scholar 

  48. Mendel, J.M., John, R.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Article  Google Scholar 

  49. Mendel, J.M., John, R., Liu, F.L.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2007)

    Article  Google Scholar 

  50. Mo, H., Wang, F.Y., Zhou, M., et al.: Footprint of uncertainty for type-2 fuzzy sets. Inf. Sci. 272, 96–110 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  51. Wang, F.Y., Mo, H.: Some fundamental issues on type-2 fuzzy sets. Acta Autom. Sin. 43(7), 1114–1141 (2017)

    MATH  Google Scholar 

Download references

Acknowledgements

The paper is sponsored by the National Natural Science Foundation of China (Nos. 61973146 and No. 61903167), the Liaoning Province Natural Science Foundation (No. 20180550056), the Doctoral Scientific Research Foundation of Liaoning Province (No. 2021-BS-258), and the Talent Fund Project of Liaoning University of Technology (No. xr2020002). The author is very thankful to Professor Jerry Mendel, who has provided the author some valuable suggestions.

Author information

Authors and Affiliations

  1. College of Science, Liaoning University of Technology, Jinzhou, 121001, China

    Yang Chen

Authors
  1. Yang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Y. Study on Weighted-Based Discrete Noniterative Algorithms for Computing the Centroids of General Type-2 Fuzzy Sets. Int. J. Fuzzy Syst. 24, 587–606 (2022). https://doi.org/10.1007/s40815-021-01166-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01166-y

Keywords

Search

Navigation