Comparative Study with Fuzzy Entropy and Similarity Measure: One-to-One Correspondence

  • Sanghyuk Lee
  • Sangjin Kim
  • DongYoup Lee
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 15)


In this paper we survey the relation between fuzzy entropy measure and similarity measure. Each measure has data uncertainty and similarity. By the one-to-one correspondence, distance measure and similarity measure have complementary characteristics. First we construct similarity measure using distance measure. Verification of usefulness is proved. Furthermore analysis of similarity measure from fuzzy entropy measure is also discussed.


Similarity measure distance measure fuzzy entropy one-to-one correspondence 


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  1. 1.
    Lee, S.H., Cheon, S.P., Kim, J.: Measure of Certainty with Fuzzy Entropy Function. In: Huang, D.-S., Li, K., Irwin, G.W. (eds.) ICIC 2006. LNCS (LNAI), vol. 4114, pp. 134–139. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Lee, S.H., Kim, J.M., Choi, Y.K.: Similarity Measure Construction Using Fuzzy Entropy and Distance Measure. In: Huang, D.-S., Li, K., Irwin, G.W. (eds.) ICIC 2006. LNCS (LNAI), vol. 4114, pp. 952–958. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Yager, R.R.: Monitored Heavy Fuzzy Measures and Their Role in Decision Making under Uncertainty. Fuzzy Sets and Systems 139(3), 491–513 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Rébillé, Y.: Decision Making over Necessity Measures through the Choquet Integral Criterion. Fuzzy Sets and Systems 157(23), 3025–3039 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Sugumaran, V., Sabareesh, G.R., Ramachandran, K.I.: Fault Diagnostics of Roller Bearing Using Kernel Based Neighborhood Score Multi-class Support Vector Machine. Expert Syst. Appl. 34(4), 3090–3098 (2008)CrossRefGoogle Scholar
  6. 6.
    Kang, W.S., Choi, J.Y.: Domain Density Description for Multiclass Pattern Classification with Reduced Computational Load. Pattern Recognition 41(6), 1997–2009 (2008)zbMATHCrossRefGoogle Scholar
  7. 7.
    Shih, F.Y., Zhang, K.: A Distance-based Separator Representation for Pattern Classification. Image Vis. Comput. 26(5), 667–672 (2008)CrossRefGoogle Scholar
  8. 8.
    Chen, S.M.: New Methods for Subjective Mental Workload Assessment and Fuzzy Risk Analysis. Cybern. Syst. 27(5), 449–472 (1996)zbMATHCrossRefGoogle Scholar
  9. 9.
    Hsieh, C.H., Chen, S.H.: Similarity of Generalized Fuzzy Numbers with Graded Mean Integration Representation. In: Proc. 8th Int. Fuzzy Systems Association World Congr., vol. 2, pp. 551–555 (1999)Google Scholar
  10. 10.
    Lee, H.S.: An Optimal Aggregation Method for Fuzzy Opinions of Group Decision. In: Proc. 1999 IEEE Int. Conf. Systems, Man, Cybernetics, vol. 3, pp. 314–319 (1999)Google Scholar
  11. 11.
    Chen, S.J., Chen, S.M.: Fuzzy Risk Analysis Based on Similarity Measures of Generalized Fuzzy Numbers. IEEE Trans. Fuzzy Syst. 11(1), 45–56 (2003)CrossRefGoogle Scholar
  12. 12.
    Lee, S.H., Kim, Y.T., Cheon, S.P., Kim, S.S.: Reliable Data Selection with Fuzzy Entropy. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 203–212. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Liu, X.: Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations. Fuzzy Sets and Systems 52, 305–318 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Bhandari, D., Pal, N.R.: Some New Information Measure of Fuzzy Sets. Inform. Sci. 67, 209–228 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kosko, B.: Neural Networks and Fuzzy Systems. Prentice-Hall, Englewood Cliffs (1992)zbMATHGoogle Scholar
  16. 16.
    Pal, N.R., Pal, S.K.: Object-background Segmentation Using New Definitions of Entropy. IEEE Proc. 36, 284–295 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sanghyuk Lee
    • 1
  • Sangjin Kim
    • 1
  • DongYoup Lee
    • 1
  1. 1.School of MechatronicsChangwon National UniversityGyeongnamKorea

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