Choice of Implication Functions to Reduce Uncertainty in Interval Type-2 Fuzzy Inferences

  • Sumantra Chakraborty
  • Amit Konar
  • Ramadoss Janarthanan
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 27)

Abstract

Selection of implication function is a well-known problem in Type-1 fuzzy reasoning. Several comparison of type-1 implications have been reported using set of (nine) standard axioms. This paper attempts to select the most efficient implication function that results in minimum uncertainty in the interval type-2 inference. An analysis confirms that Lukasiewicz-1/Lukasiewicz-2 membership function is most efficient in the present context.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    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. on Fuzzy Systems 17(5), 1123–1142 (2009)CrossRefGoogle Scholar
  3. 3.
    Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. on Fuzzy Systems 10, 117–127 (2002)CrossRefGoogle Scholar
  4. 4.
    Mendel, J.M.: Advances in type-2 fuzzy sets and systems. Information Sciences 177(1), 84–110 (2007)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Mendel, J.M.: Type-2 fuzzy sets and systems: An overview. IEEE Computational Intelligence (2007)Google Scholar
  6. 6.
    Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. on Fuzzy Systems 14, 808–821 (2006)CrossRefGoogle Scholar
  7. 7.
    Wu, D., Mendel, J.M.: Uncertainty measures for interval type-2 fuzzy sets. Information Sciences 177(23), 5378–5393 (2007)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Mendel, J.M., Wu, H.: Type-2 fuzzistics for nonsymmetric interval type-2 fuzzy sets: forward problems. IEEE Trans. on Fuzzy Systems 15(5), 916–930 (2007)CrossRefGoogle Scholar
  9. 9.
    Mendel, J.M., Wu, D.: Perceptual computing: Aiding people in making subjective judgments, vol. 13. Wiley-IEEE Press (2010)Google Scholar
  10. 10.
    Wu, D., Mendel, J.M.: Linguistic summarization using IF–THEN rules and interval type-2 fuzzy sets. IEEE Trans. on Fuzzy Systems 19(1), 136–151 (2011)CrossRefGoogle Scholar
  11. 11.
    Wu, D., Tan, W.: Type-2 fuzzy logic controller for liquid level process. In: Proc. IEEE Int. Conf. on Fuzzy Systems, pp. 242–247 (2005)Google Scholar
  12. 12.
    Lascio, L.D., Gisolfi, A., Nappi, A.: Medical differential diagnosis through type-2 fuzzy sets. In: Proc. IEEE Int. Conf. on Fuzzy Systems, pp. 371–376 (2005)Google Scholar
  13. 13.
    Hagras, H.: A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans. on Fuzzy Systems 12, 524–539 (2004)CrossRefGoogle Scholar
  14. 14.
    Coupland, S., John, R.: Geometric type-1 and type-2 fuzzy logic systems. IEEE Tran. on Fuzzy Systems 15(1), 3–15 (2007)CrossRefGoogle Scholar
  15. 15.
    Karnik, N.N., Mendel, J.M.: Centroid of type-2 fuzzy set. Information Sciences 132, 195–220 (2001)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Aguero, J.R., Vargas, A.: Calculating functions of interval type-2 fuzzy numbers for fault current analysis. IEEE Trans. Fuzzy Syst. 15(1), 31–40 (2007)CrossRefGoogle Scholar
  17. 17.
    Juang, C.-F., Huang, R.-B., Lin, Y.-Y.: A recurrent self-evolving interval type-2 fuzzy neural network for dynamic system processing. IEEE Trans. Fuzzy Syst. 17(5), 1092–1105 (2009)CrossRefGoogle Scholar
  18. 18.
    Mendel, J.M., Wu, H.: Type-2 fuzzistics for nonsymmetric interval type-2 fuzzy sets: forward problem. IEEE Trans. Fuzzy Systems 15(5), 916–930 (2007)CrossRefGoogle Scholar
  19. 19.
    Klir, G.J., Yuan, B.: Approximate reasoning: Fuzzy sets and fuzzy Logic (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sumantra Chakraborty
    • 1
  • Amit Konar
    • 1
  • Ramadoss Janarthanan
    • 2
  1. 1.Electronics and Tele-Communication Engineering DepartmentJadavpur UniversityKolkataIndia
  2. 2.Computer Science and Engineering DepartmentTJS Engineering CollegeChennaiIndia

Personalised recommendations