Paper:

# New Similarity Measures of Intuitionistic Fuzzy Sets

## Hassan Rezaei and Masao Mukaidono

Department of Computer Science, Meiji University, 1-1-1 Higashi-Mita, Tama-Ku, Kawasaki-shi 214-8571, Japan

In this review of existing similarity measures of intuitionistic fuzzy sets (IFSs), we apply some numerical examples showing that not all existing similarity measures are effective and reasonable in some cases. We propose properties based on intuition and the human thinking process that should be satisfied by all dissimilarity and similarity measures, together with new similarity measures of IFSs that overcome drawbacks of existing measures. In examples, we compare the proposed similarity measures to existing measures and present two propositions on the relationship between similarity and dissimilarity measures of IFSs. We also propose that a suitable combination of similarity measures may be a similarity measure.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.2, pp. 202-209, 2007.

- [1] D. Li and C. Cheng, “New Similarity Measures of Intuionistic Fuzzy Sets and Application to Pattern Recognition,” Pattern Recognition Letters, 23, pp. 221-225, 2002.
- [2] H. B. Mitchell, “On the Dengfeng-Chuntian Similarity Measures and its Application to Pattern Recognition,” Pattern Recognition Letters, 24, pp. 3101-3104, 2003.
- [3] Z. Liang and P. Shi, “Similarity Measures on Intuitionistic Fuzzy Sets,” Pattern Recognition Letters, 24, pp. 2686-2693, 2003.
- [4] W. L. Hung and M. S. Yang, “Similarity Measures of Intuitionistic Fuzzy Sets based on Hausdorff Distance,” Pattern Recognition Letters, 25, pp. 1603-1611, 2004.
- [5] W. Wang and X. Xin, “Distance Measure between Intuitionistic Fuzzy Sets,” Pattern Recognition Letters, 26, pp. 2063-2069, 2005.
- [6] P. Grzeogorzewski, “Distances between Intuitionistic Fuzzy Sets and/or Interval-Valued Fuzzy Sets based on the Hausdorff metric,” Fuzzy Sets and Systems, 148, pp. 319-328, 2004.
- [7] K. T. Atarassov, “Intuitionistic Fuzzy Set,” Fuzzy Sets and Systems, 20, pp. 87-96, 1986.
- [8] W. L. Gau and D. J. Buchere, “Vague Sets,” IEEE Trans. System Man Cybernet, 23, pp. 610-614, 1993.
- [9] H. Bustince and P. Burillo, “Vague Sets are Intuisionistic Fuzzy Sets,” Fuzzy Sets and Systems, 79, pp. 403-405, 1996.
- [10] A. Lu and W. Ng, “Vague Sets on Intuitionnistic Fuzzy Sets for Handling Vague Data: Which On Is Better?” 24
^{th}International Conference on Concepual Modeling (ER 2005), Klagenfurt, Austria, October 24-28, pp. 401-416, 2005. - [11] K. T. Atarassov, “New Operations defined over the Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, 61, pp. 137-142, 1994.
- [12] K. T. Atarassov, “Intuitionistic Fuzzy Sets: Theory and Applications,” Physica-Verlag, Heidelberg, New York, 1999.
- [13] E. Szmidt and J. Kacprzyk, “On Measuring Distances between Intuitionistic Fuzzy Sets,” Notes IFS, 3, pp. 1-13, 1997.
- [14] E. Szmidt and J. Kacprzyk, “Distances between Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, 114, pp. 505-518, 1997.
- [15] R. Zwick, E. Carlstein, and D. Budescu, “Measures of Similarity among Fuzzy Sets: A Comparative Analysis,” Int. J. Approximate Reasoning, 1, pp. 221-242, 1987.
- [16] S. M. Chen, “A New Approach to Handling Fuzzy Decision Making Problems,” IEEE Trans. Systems, Man Cybernet, 18, pp. 1012-1016, 1988.
- [17] L. Xuecheng, “Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and their relations,” Fuzzy Sets and Systems, 52, pp. 305-318, 1992.
- [18] C. P. Pappis and N. I. Karacapilidis, “A Comparative Assessment of Measures of Similarity of Fuzzy Values,” Fuzzy Sets and Systems, 56, pp. 171-174, 1993.
- [19] L. K. Hyung, Y. S. Song, and K. M. Lee, “Similarity Measures between Fuzzy Sets and between Elements,” Fuzzy Sets and Systems, 62, pp. 291-293, 1994.
- [20] S. M. Chen, M. S. Yeh, and P. Y. Hsiao, “A Comparison of Similarity Measures of Fuzzy Values,” Fuzzy Sets and Systems, 72, pp. 79-89, 1995.
- [21] W. J. Wang, “New Similarity Measures on Fuzzy Sets and on Elements,” Fuzzy Sets and Systems, 85, pp. 305-309, 1997.
- [22] H. Rezaei, M. Emoto, and M. Mukaidono, “New Similarity Measure Between Two Fuzzy Sets,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.6, pp. 946-953, 2006.
- [23] J. Kacprzyk, “Multistage Fuzzy Control,” Wiely, Chichester, 1997.
- [24] L. A. Zadeh, “Fuzzy Sets,” Inform. Control, pp. 338-353, 1965.