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Fuzzy Interpolative Reasoning Using Interval Type-2 Fuzzy Sets

  • Li-Wei Lee
  • Shyi-Ming Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5027)

Abstract

In this paper, we present a new fuzzy interpolative reasoning method using interval type-2 fuzzy sets. We calculate the ranking values through the reference points and the heights of the upper and the lower membership functions of interval type-2 fuzzy sets. By means of calculating the ranking values of the upper and the lower membership functions of interval type-2 fuzzy sets, we can use interval type-2 fuzzy sets to handle fuzzy interpolative reasoning in sparse fuzzy rule-based system in a more flexible manner.

Keywords

Fuzzy interpolative reasoning interval type-2 fuzzy sets ranking values 

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References

  1. 1.
    Baranyi, P., Gedeon, T.D., Koczy, L.T.: A General Interpolation Technique in Fuzzy Rule Bases with Arbitrary Membership Functions. In: Proceedings of the 1996 IEEE International Conference on Systems, Man, and Cybernetics, pp. 510–515 (1996)Google Scholar
  2. 2.
    Baranyi, P., Koczy, L.T., Gedeon, T.D.: A Generalized Concept for Fuzzy Rule Interpolative. IEEE Transactions on Fuzzy Systems 12(6), 820–837 (2004)CrossRefGoogle Scholar
  3. 3.
    Baranyi, P., Tikk, D., Yam, Y., Koczy, L.T.: A New Method for Avoiding Abnormal Conclusion for α-cut Based Rule Interpolation. In: Proceedings of the 1999 IEEE International Conference on Fuzzy Systems, pp. 383–388 (1999)Google Scholar
  4. 4.
    Bouchon-Meunier, B., Marslla, C., Rifqi, M.: Interpolative Reasoning Based on Graduality. In: Proceedings of the 2000 IEEE International Conference on Fuzzy Systems, pp. 483–487 (2000)Google Scholar
  5. 5.
    Hsiao, W.H., Chen, S.M., Lee, C.H.: A New Interpolation Reasoning Method in Sparse Rule-Based Systems. Fuzzy Sets and Systems 93(1), 17–22 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Huang, Z.H., Shen, Q.: Fuzzy Interpolative Reasoning via Scale and Move Transformations. IEEE Transactions on Fuzzy Systems 14(2), 340–359 (2006)CrossRefGoogle Scholar
  7. 7.
    Koczy, L.T., Hirota, K.: Interpolative Reasoning with Insufficient Evidence in Sparse Fuzzy Rule Bases. Information Sciences 71(1), 169–201 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Koczy, L.T., Hirota, K.: Approximate Reasoning by Linear Rule Interpolation and General Approximation. International Journal of Approximate Reasoning 9(3), 197–225 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Koczy, L.T., Hirota, K.: Size Reduction by Interpolation in Fuzzy Rule Bases. IEEE Transactions on Systems, Man, and Cybernetics 27(1), 14–25 (1997)CrossRefGoogle Scholar
  10. 10.
    Li, Y.M., Huang, D.M., Tsang, E.C., Zhang, L.N.: Weighted Fuzzy Interpolative Reasoning Method. In: Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, pp. 3104–3108 (2005)Google Scholar
  11. 11.
    Mendel, J.M., John, R.I., Liu, F.L.: Interval Type-2 Fuzzy Logical Systems Made Simple. IEEE Transactions on Fuzzy Systems 14(6), 808–821 (2006)CrossRefGoogle Scholar
  12. 12.
    Qiao, W.Z., Mizumoto, M., Yan, S.Y.: An Improvement to Koczy and Hirota’s Interpolative Reasoning in Sparse Fuzzy Rule Bases. International Journal of Approximate Reasoning 15(3), 185–201 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Shi, Y., Mizumoto, M.: Some Considerations on Koczy’s Interpolative Reasoning Method. In: Proceedings of the 1995 IEEE International Conference on Fuzzy Systems, pp. 2117–2122 (1995)Google Scholar
  14. 14.
    Shi, Y., Mizumoto, M., Qiao, W.Z.: Reasoning Conditions on Koczy’s Interpolative Reasoning Method in Sparse Fuzzy Rule Bases. Fuzzy Sets and Systems 75(1), 63–71 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Tikk, D., Baranyi, P.: Comprehensive Analysis of a New Fuzzy Rule Interpolation Method. IEEE Transactions on Fuzzy Systems 8(3), 281–296 (2000)CrossRefGoogle Scholar
  16. 16.
    Vass, G., Kalmar, L., Koczy, L.T.: Extension of the Fuzzy Rule Interpolation Method. In: Proceedings of the International Conference on Fuzzy Sets Theory Applications, pp. 1–6 (1992)Google Scholar
  17. 17.
    Wong, K.W., Tikk, D., Gedeon, T.D.: Fuzzy Rule Interpolation for Multidimensional Input Spaces with Applications: A Case Study. IEEE Transactions on Fuzzy Systems 13(6), 809–819 (2005)CrossRefGoogle Scholar
  18. 18.
    Yam, Y., Wong, M.L., Baranyi, P.: Interpolation with Function Space Representation of Membership Functions. IEEE Transactions on Fuzzy Systems 14(3), 398–411 (2006)CrossRefGoogle Scholar
  19. 19.
    Zaheh, L.A.: The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-1. Information Sciences 8(1), 199–249 (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Li-Wei Lee
    • 1
  • Shyi-Ming Chen
    • 1
    • 2
  1. 1.Department of Computer Science and Information EngineeringNational Taiwan University of Science and TechnologyTaipeiTaiwan, R. O. C.
  2. 2.Department of Computer Science and Information EngineeringJinwen University of Science and TechnologyTaipei CountyTaiwan, R. O. C.

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