Two Differences Between Interval Type-2 and Type-1 Fuzzy Logic Controllers: Adaptiveness and Novelty

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 301)


Interval type-2 fuzzy logic controllers (IT2 FLCs) have been attracting great research interests recently. Many reported results have shown that IT2 FLCs are better able to handle uncertainties than their type-1 (T1) counterparts. A challenging question is: What are the fundamental differences between IT2 and T1 FLCs? Once the fundamental differences are clear, we can better understand the advantages of IT2 FLCs and hence better make use of them. This chapter explains two fundamental differences between IT2 and T1 FLCs: (1) Adaptiveness, meaning that the embedded T1 fuzzy sets used to compute the bounds of the type-reduced interval change as input changes; and, (2) Novelty, meaning that the upper and lower membership functions of the same IT2 fuzzy set may be used simultaneously in computing each bound of the type-reduced interval. T1 FLCs do not have these properties; thus, a T1 FLC cannot implement the complex control surface of an IT2 FLC given the same rulebase.


Fundamental differences Type-1 fuzzy set Karnik-Mendel algorithms Novelty Fuzzy logic control Example of interval type-2 fuzzy logic controller Linguistic uncertainties Interval type-2 fuzzy logic controller Switch point KM type-reducer Control surface Adaptive PI control Interval type-2 fuzzy set Adaptiveness Type-1 fuzzy logic controller Type-reduction 


  1. 1.
    Castillo, O., Melin, P.: Type-2 Fuzzy Logic Theory and Applications. Springer-Verlag, Berlin (2008)MATHGoogle Scholar
  2. 2.
    Castro, J.L.: Fuzzy logic controllers are universal approximators. IEEE Trans. Syst. Man Cybern. 25(4), 629–635 (1995)Google Scholar
  3. 3.
    Du, X., Ying, H.: Derivation and analysis of the analytical structures of the interval type-2 fuzzy-PI and PD controllers. IEEE Trans. Fuzzy Syst. 18(4), 802–814 (2010)CrossRefGoogle Scholar
  4. 4.
    Hagras, H.: A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans. Fuzzy Syst. 12, 524–539 (2004)CrossRefGoogle Scholar
  5. 5.
    Hagras, H.: Type-2 FLCs: a new generation of fuzzy controllers. IEEE Comput. Intell. Mag. 2(1), 30–43 (2007)CrossRefGoogle Scholar
  6. 6.
    Jammeh, E.A., Fleury, M., Wagner, C., Hagras, H., Ghanbari, M.: Interval type-2 fuzzy logic congestion control for video streaming across IP networks. IEEE Trans. Fuzzy Syst. 17(5), 1123–1142 (2009)CrossRefGoogle Scholar
  7. 7.
    Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132, 195–220 (2001)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)CrossRefGoogle Scholar
  9. 9.
    Kosko, B.: Fuzzy systems as universal approximators. IEEE Trans. Comput. 43(11), 1329–1333 (1994)MATHCrossRefGoogle Scholar
  10. 10.
    Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper Saddle River (2001)Google Scholar
  11. 11.
    Mendel, J.M.: Computing with words: Zadeh, Turing, Popper and Occam. IEEE Comput. Intell. Mag. 2, 10–17 (2007)CrossRefGoogle Scholar
  12. 12.
    Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)CrossRefGoogle Scholar
  13. 13.
    Mendel, J.M., Wu, D.: Perceptual Computing: Aiding People in Making Subjective Judgments. Wiley-IEEE Press, Hoboken (2010)Google Scholar
  14. 14.
    Nie, M., Tan, W.: Analytical structure and characteristics of symmetric centroid type-reduced interval type-2 fuzzy PI and PD controllers. IEEE Trans. Fuzzy Syst. 20(3), 416–430 (2012)CrossRefGoogle Scholar
  15. 15.
    Wallsten, T.S., Budescu, D.V.: A review of human linguistic probability processing: general principles and empirical evidence. Knowl. Eng. Rev. 10(1), 43–62 (1995)CrossRefGoogle Scholar
  16. 16.
    Wu, D.: An interval type-2 fuzzy logic system cannot be implemented by traditional type-1 fuzzy logic systems. In: Proceedings of World Conference on Soft Computing, San Francisco (2011)Google Scholar
  17. 17.
    Wu, D.: On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Trans. Fuzzy Syst. 20(5), 832–848 (2012)Google Scholar
  18. 18.
    Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel algorithms. IEEE Trans. Fuzzy Syst. 17(4), 923–934 (2009)CrossRefGoogle Scholar
  19. 19.
    Wu, D., Nie, M.: Comparison and practical implementation of type-reduction algorithms for type-2 fuzzy sets and systems. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 2131–2138. Taipei, Taiwan (2011)Google Scholar
  20. 20.
    Wu, D., Tan, W.W.: A type-2 fuzzy logic controller for the liquid-level process. In: Proceedings of IEEE International Conference on Fuzzy Systems, vol. 2, pp. 953–958. Budapest, Hungary (2004)Google Scholar
  21. 21.
    Wu, D., Tan, W.W.: Type-2 FLS modeling capability analysis. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 242–247. Reno, NV (2005)Google Scholar
  22. 22.
    Wu, D., Tan, W.W.: Genetic learning and performance evaluation of type-2 fuzzy logic controllers. Eng. Appl. Artif. Intell. 19(8), 829–841 (2006)CrossRefGoogle Scholar
  23. 23.
    Wu, D., Tan, W.W.: A simplified type-2 fuzzy controller for real-time control. ISA Trans. 15(4), 503–516 (2006)Google Scholar
  24. 24.
    Wu, D., Tan, W.W.: Interval type-2 fuzzy PI controllers: why they are more robust. In: Proceedings of IEEE International Conference on Granular Computing, pp. 802–807. San Jose, CA (2010)Google Scholar
  25. 25.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-1. Inf. Sci. 8, 199–249 (1975)MathSciNetMATHCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Machine Learning Lab, GE Global ResearchNiskayunaUSA

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