Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 384241, 11 pages
http://dx.doi.org/10.1155/2014/384241
Research Article

A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

School of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, China

Received 22 April 2014; Accepted 13 August 2014; Published 27 August 2014

Academic Editor: Maria A. Ragusa

Copyright © 2014 Yafei Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at MathSciNet · View at Scopus
  2. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Z. Xu and R. R. Yager, “Dynamic intuitionistic fuzzy multi-attribute decison making,” International Journal of Approximate Reasoning, vol. 48, no. 1, pp. 246–262, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. W. Gau and D. J. Buehrer, “Vague sets,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 2, pp. 610–614, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. H. Bustince and P. Burillo, “Vague sets are intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 79, no. 3, pp. 403–405, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Xia and Z. Xu, “Some new similarity measures for intuitionistic fuzzy values and their application in group decision making,” Journal of Systems Science and Systems Engineering, vol. 19, no. 4, pp. 430–452, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Ye, “Cosine similarity measures for intuitionistic fuzzy sets and their applications,” Mathematical and Computer Modelling, vol. 53, no. 1-2, pp. 91–97, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505–518, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. W. Wang and X. Xin, “Distance measure between intuitionistic fuzzy sets,” Pattern Recognition Letters, vol. 26, no. 13, pp. 2063–2069, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Grzegorzewski, “Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,” Fuzzy Sets and Systems, vol. 148, no. 2, pp. 319–328, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T.-Y. Chen, “A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,” Fuzzy Sets and Systems, vol. 158, no. 22, pp. 2523–2525, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. W. L. Hung and M. S. Yang, “Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance,” Pattern Recognition Letters, vol. 25, no. 14, pp. 1603–1611, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Dengfeng and C. Chuntian, “New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions,” Pattern Recognition Letters, vol. 23, no. 1–3, pp. 221–225, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. H. B. Mitchell, “On the Dengfeng—Chuntian similarity measure and its application to pattern recognition,” Pattern Recognition Letters, vol. 24, no. 16, pp. 3101–3104, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Liang and P. Shi, “Similarity measures on intuitionistic fuzzy sets,” Pattern Recognition Letters, vol. 24, no. 15, pp. 2687–2693, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Li, D. L. Olson, and Z. Qin, “Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis,” Pattern Recognition Letters, vol. 28, no. 2, pp. 278–285, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. C. M. Hwang, M. S. Yang, W. L. Hung, and M. G. Lee, “A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition,” Information Sciences, vol. 189, pp. 93–109, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. Z. Xu, “Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making,” Fuzzy Optimization and Decision Making, vol. 6, no. 2, pp. 109–121, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Z. S. Xu and J. Chen, “An overview of distance and similarity measures of intuitionistic fuzzy sets,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 16, no. 4, pp. 529–555, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. Z. S. Xu and R. R. Yager, “Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group,” Fuzzy Optimization and Decision Making., vol. 8, no. 2, pp. 123–139, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. W. Zeng and P. Guo, “Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship,” Information Sciences, vol. 178, no. 5, pp. 1334–1342, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. Wei, P. Wang, and Y. Zhang, “Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications,” Information Sciences, vol. 181, no. 19, pp. 4273–4286, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. F. E. Boran and D. Akay, “A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition,” Information Sciences, vol. 255, pp. 45–57, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. H. Zhang and L. Yu, “New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets,” Information Sciences, vol. 245, pp. 181–196, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. J. Li, G. Deng, H. Li, and W. Zeng, “The relationship between similarity measure and entropy of intuitionistic fuzzy sets,” Information Sciences, vol. 188, pp. 314–321, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. B. Farhadinia, “A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure,” Knowledge-Based Systems, vol. 39, pp. 79–84, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. D.-F. Li, “Some measures of dissimilarity in intuitionistic fuzzy structures,” Journal of Computer and System Sciences, vol. 68, no. 1, pp. 115–122, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. G. A. Papakostas, A. G. Hatzimichailidis, and V. G. Kaburlasos, “Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view,” Pattern Recognition Letters, vol. 34, no. 14, pp. 1609–1622, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. S. M. Chen, “Measures of similarity between vague sets,” Fuzzy Sets and Systems, vol. 74, no. 2, pp. 217–223, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. D. H. Hong and C. Kim, “A note on similarity measures between vague sets and between elements,” Information Sciences, vol. 115, no. 1–4, pp. 83–96, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. F. Li and Z. Xu, “Similarity measures between vague sets,” Journal of Software, vol. 12, no. 6, pp. 922–927, 2001. View at Google Scholar · View at Scopus
  32. Y. Li, Z. Chi, and D. Yan, “Similarity measures between vague sets and vague entropy,” Journal of Computer Science, vol. 29, pp. 129–132, 2002. View at Google Scholar
  33. I. K. Vlachos and G. D. Sergiadis, “Intuitionistic fuzzy information—applications to pattern recognition,” Pattern Recognition Letters, vol. 28, no. 2, pp. 197–206, 2007. View at Publisher · View at Google Scholar · View at Scopus
  34. C. M. Own, “Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis,” Applied Intelligence, vol. 31, no. 3, pp. 283–291, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. E. Szmidt and J. Kacprzyk, “A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning,” in Proceedings of the 7th International Conference on Artificial Intelligence and Soft Computing (ICAISC '04), pp. 388–393, June 2004. View at Scopus
  36. E. Szmidt and J. Kacprzyk, “Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis,” in Computational Science—ICCS 2001, vol. 2074 of Lecture Notes in Computer Science, pp. 263–271, 2001. View at Publisher · View at Google Scholar