World Academy of Science, Engineering and Technology
Published June 25, 2011 | Version 1280
Journal article Open

A New Similarity Measure on Intuitionistic Fuzzy Sets

Description

Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems.

Files

1280.pdf

Files (225.9 kB)

Name Size Download all
md5:5b6de69ef70a82209131cdd1f362a3e4
225.9 kB Preview Download

Additional details

References

  • Atanassov, K., 1986. Intuitionistic fuzzy sets, Fuzzy Sets Systems 20 (1), 87-96.
  • Atanassov, K., 1989. More on intuitionistic fuzzy sets. Fuzzy Sets Systems 33, 37-46.
  • Atanassov, K., 1994a. New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Systems 61, 137-142.
  • Atanassov, K., 1994b. Operations over interval valued intuitionistic fuzzy sets. Fuzzy Sets Systems 64, 159-174.
  • Atanassov, K., 1995. Remarks on the intuitionistic fuzzy sets. Fuzzy Sets Systems 75 (3), 401-402.
  • Atanassov, K., 1999. Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg.
  • Atanassov, K., Georgeiv, G., 1993. Intuitionistic fuzzy prolog. Fuzzy Sets Systems 53, 121-128.
  • Bustince, H., Burillo, P., 1996. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Systems 79 (3), 403-405.
  • Chen, S.M., 1995. Measures of similarity between vague sets. Fuzzy Sets Systems 74 (2), 217-223. [10] Chen, S.M., 1997. Similarity measures between vague sets and between elements. IEEE Trans. Syst. Man Cybernet. 27 (1), 153-158. [11] De, S.K., Biswas, R., Roy, A.R., 2001. An application of intuitionistic fuzzy set in medical diagnosis. Fuzzy Sets Systems 117, 209-213. [12] Dengfeng, L., Chuntian, C., 2002. New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Lett. 23, 221-225. [13] Fan, L., Zhangyan, X., 2001. Similarity measures between vague sets. J. Software 12 (6), 922-927 (in Chinese). [14] Gau, W.L., Buehrer, D.J., 1993. Vague sets. IEEE Trans. Syst. Man Cybernet. 23 (2), 610-614. [15] Hong, D.H., Kim, C., 1999. A note on similarity measures between vague sets and between elements. Inform. Science 115, 83-96. [16] Hung, W.-L., Yang, M.-S., 2004. Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Lett. 25, 1603-1611. [17] Hyung, L.K., Song, Y.S., Lee, K.M., 1994. Similarity measures between fuzzy sets and between elements. Fuzzy Sets Systems 62 (3), 291-293. [18] Li, Y., Zhongxian, C., Degin, Y., 2002. Similarity measures between vague sets and vague entropy. J. Computer Sci. 29 (12), 129-132 (in Chinese). [19] Li, Y., Olson, D.L., Qin, Z., 2007. Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis. Pattern Recognition Letters 28, 278-285. [20] Mitchell, H.B., 2003. On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Lett. 24, 3101-3104. [21] Pappis, C.P., Karacapilidis, N.I., 1993. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Systems 56 (2), 171- 174. [22] Szmidt, E., Kacprzyk, J., 1996. Intuitionistic fuzzy sets in group decision making. Notes IFS 2 (1), 11-14. [23] Szmidt, E., Kacprzyk, J., 2000. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114: 505-518. [24] Szmidt, E., Kacprzyk, J., 2006. An application of intuitionistic fuzzy set similarity measures to a multi-criteria decision making problem. LNAI 4029, 314-323. [25] Xu, Z., 2007, Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Making, 6, 109-121. [26] Zadeh, L.A., 1965. Fuzzy sets. Inform. Control 8, 338-356. [27] Zhang, C. et al., 2003. The measures of similarity between vague sets. Comput. Eng. Appl. 39 (17), 92-94 (in Chinese). [28] Zhang, C., Fu, H., 2006. Pattern Recognition Letters 27, 1307-1317. [29] Zhizhen, L., Pengfei, S., 2003. Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Lett. 24, 2687-2693. [30] Atanassov, K. T. (1983). Intuitionistic fuzzy sets. Central Tech. Library, Bulgarian Academy Science, Sofia, Bulgaria, Rep. No. 1697/84.