Similarity Measure Design for Non-Overlapped Data

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 235)


Study on similarity measure on fuzzy sets (FSs) for the case of non-overlapped data was proposed, and analyzed. Comparison with similarity measure on overlapped case was done. Different approach to similarity measure was analyzed, and adequate similarity measure on non-overlapped data was designed by considering neighbor information. With artificial data rational calculation results were obtained.


Similarity measure Non-overlapped data Intuitionistic data 


  1. 1.
    Zadeh LA (1965) Fuzzy sets and systems. In: Proceedings of a symposium on systems theory, Polytechnic Institute of Brooklyn, New York, pp 29–37Google Scholar
  2. 2.
    Pal NR, Pal SK (1989) Object-background segmentation using new definitions of entropy. IEEE Proc 36:284–295Google Scholar
  3. 3.
    Kosko B (1992) Neural networks and fuzzy systems. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  4. 4.
    Liu X (1992) Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst 52:305–318MATHCrossRefGoogle Scholar
  5. 5.
    Bhandari D, Pal NR (1993) Some new information measure of fuzzy sets. Inform Sci 67:209–228MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    De L, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy entropy. J Gen Syst 5:301–312Google Scholar
  7. 7.
    Hsieh CH, Chen SH (1999) Similarity of generalized fuzzy numbers with graded mean integration representation, Proc 8th Int Fuzzy Syst Associ World Congr 2:551–555Google Scholar
  8. 8.
    Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans on Fuzzy Syst 11(1):45–56CrossRefGoogle Scholar
  9. 9.
    Lee SH, Pedrycz W, Sohn G (2009) Design of similarity and dissimilarity measures for fuzzy sets on the basis of distance measure. Int J Fuzzy Syst 11:67–72MathSciNetGoogle Scholar
  10. 10.
    Lee SH, Ryu KH, Sohn GY(2009) Study on entropy and similarity measure for fuzzy set. IEICE Trans Inf Syst E92-D:1783–1786Google Scholar
  11. 11.
    Lee SH, Kim SJ, Jang NY (2008) Design of fuzzy entropy for non convex membership function. CCIS 15:55–60Google Scholar
  12. 12.
    Wang Z, Klir GJ (1992) Fuzzy measure theory. Plenum Press, New YorkMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringXi’an Jiaotong-Liverpool UniversitySuzhouChina

Personalised recommendations