Advertisement

Similarity Measure and Fuzzy Entropy of Fuzzy Number Intuitionistic Fuzzy Sets

  • Juan Li
  • Qi Niu
  • Cheng-yi Zhang
Part of the Advances in Soft Computing book series (AINSC, volume 54)

Abstract

Based on the similarity measure of trigonometric fuzzy numbers, similarity measures for measuring the degree of similarity between elements and between some fuzzy number intuitionistic fuzzy sets are defined by the one-to-one correspondence relation between the distance and similarity measure. At the same time, the fuzzy entropy for fuzzy number intuitionistic fuzzy sets is proposed. After that, their properties are discussed and an example about the application of similarity measure to pattern recognitions is given.

Keywords

Trigonometric Fuzzy Number Fuzzy Number Intuitionistic Fuzzy Set Similarity Measure Fuzzy Entropy 

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, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20(1), 87–96 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Atanassov, K.: Interval valued intuitionistic fuzzv sets. Fuzzy Sets and Systems 31, 343–349 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Liu, F., Yuan, X.: Fuzzy number intuitionistic fuzzv sets. Fuzzy System and Mathematics 21(1), 88–91 (2007) (in chinese)MathSciNetGoogle Scholar
  5. 5.
    Xue-cheng, L.: Entropy, distance measure and similarity measure of fuzzy sets and there relations. Fuzzy Sets and Systems 52(3), 305–318 (1992)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Zhang, C., Shi, Y.: The similarity measure of two kinds of normal fuzzy sets. Computer Engineerings and Applications 14, 49–50 (2005) (in chinese)Google Scholar
  7. 7.
    Hung, W.-l., Yang, M.-s.: Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition 25, 1603–1611 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Juan Li
    • 1
  • Qi Niu
    • 2
  • Cheng-yi Zhang
    • 1
  1. 1.Department of MathematicsHainan Normal UniversityHaikouP.R. China
  2. 2.Department of MathematicsZhumadian Education CollegeZhumadianP.R. China

Personalised recommendations