Correlation, Distance and Similarity Measures of Intuitionistic Fuzzy Sets

  • Zeshui Xu
  • Xiaoqiang Cai

Abstract

Correlation, distance and similarity measures are an important research topic in the IFS theory, which has received great attention in recent years. In this chapter, we shall give a thorough and systematic introduction to the existing research results on this topic.

Keywords

Similarity Measure Correlation Measure Multiple Attribute Decision Pattern Recognition Letter Weighted Euclidean Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Atanassov K, Gargov G. 1989. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31: 343–349.Google Scholar
  2. Atanassov K. 1983. Intuitionistic fuzzy sets. In: Sgurev V. VII ITKR’s Session. Sofia, Bulgaria June.Google Scholar
  3. Atanassov K. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20: 87–96.Google Scholar
  4. Bustince H, Burillo P. 1995. Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 74: 237–244.Google Scholar
  5. Gerstenkorn T, Manko J. 1991. Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems, 44: 39–43.Google Scholar
  6. Grzegorzewski P. 2004. Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 148: 319–328.Google Scholar
  7. Hong D H, Hwang S Y. 1995. Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems, 75: 77–81.Google Scholar
  8. Hong D H. 1998. A note on correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 95: 113–117.Google Scholar
  9. Hung W L, Wu J W. 2002. Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences, 144: 219–225.Google Scholar
  10. Hung W L, Yang M S. 2004. Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Letters, 25: 1603–1611.Google Scholar
  11. Hung W L. 2001. Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. International Journal of Uncertainty Fuzziness Knowledge-Based Systems, 9: 509–516.Google Scholar
  12. Hwang C L, Yoon K. 1981. Multiple Attribute Decision Making: Methods and Applications. Berlin: Springer-Verlag.Google Scholar
  13. Li D F, Cheng C T. 2002. New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23: 221–225.Google Scholar
  14. Liang Z Z, Shi P F. 2003. Similarity measures on intuitionistic fuzzy sets. Pattern Recognition letters, 24: 2687–2693.Google Scholar
  15. Mitchell H B. 2003. On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24: 3101–3104.Google Scholar
  16. Mitchell H B. 2004. A correlation coefficient for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 19: 483–490.Google Scholar
  17. Nadler S B. 1978. Hyperspaces of Sets. New York: Marcel Deckker.Google Scholar
  18. Szmidt E, Kacprzyk J. 2000. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114: 505–518.Google Scholar
  19. Szmidt E, Kacprzyk J. 2004. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lecture Notes in Artificial Intelligence, 3070: 388–393.Google Scholar
  20. Wang W Q, Xin X L. 2005. Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters, 26: 2063–2069.Google Scholar
  21. Xu Z S, Chen J, Wu J J. 2008. Clustering algorithm for intuitionistic fuzzy sets. Information Sciences, 178: 3775–3790.Google Scholar
  22. Xu Z S, Chen J. 2008. An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16: 529–555.Google Scholar
  23. Xu Z S. 2006h. On correlation measures of intuitionistic fuzzy sets. Lecture Notes in Computer Science, 4224: 16–24.Google Scholar
  24. Xu Z S. 2007k. Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optimization and Decision Making, 6:109–121.Google Scholar

Copyright information

© Science Press Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zeshui Xu
    • 1
  • Xiaoqiang Cai
    • 2
  1. 1.Institute of SciencesPLA University of Science and TechnologyNanjing, JiangsuP.R. China
  2. 2.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatin, N.T.Hong Kong

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