A New Similarity Measure on Intuitionistic Fuzzy Sets
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.
[1] Atanassov, K., 1986. Intuitionistic fuzzy sets, Fuzzy Sets Systems 20
(1), 87-96.
[2] Atanassov, K., 1989. More on intuitionistic fuzzy sets. Fuzzy Sets
Systems 33, 37-46.
[3] Atanassov, K., 1994a. New operations defined over the intuitionistic
fuzzy sets. Fuzzy Sets Systems 61, 137-142.
[4] Atanassov, K., 1994b. Operations over interval valued intuitionistic
fuzzy sets. Fuzzy Sets Systems 64, 159-174.
[5] Atanassov, K., 1995. Remarks on the intuitionistic fuzzy sets. Fuzzy
Sets Systems 75 (3), 401-402.
[6] Atanassov, K., 1999. Intuitionistic Fuzzy Sets: Theory and Applications.
Physica-Verlag, Heidelberg.
[7] Atanassov, K., Georgeiv, G., 1993. Intuitionistic fuzzy prolog. Fuzzy
Sets Systems 53, 121-128.
[8] Bustince, H., Burillo, P., 1996. Vague sets are intuitionistic fuzzy sets.
Fuzzy Sets Systems 79 (3), 403-405.
[9] 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.
[1] Atanassov, K., 1986. Intuitionistic fuzzy sets, Fuzzy Sets Systems 20
(1), 87-96.
[2] Atanassov, K., 1989. More on intuitionistic fuzzy sets. Fuzzy Sets
Systems 33, 37-46.
[3] Atanassov, K., 1994a. New operations defined over the intuitionistic
fuzzy sets. Fuzzy Sets Systems 61, 137-142.
[4] Atanassov, K., 1994b. Operations over interval valued intuitionistic
fuzzy sets. Fuzzy Sets Systems 64, 159-174.
[5] Atanassov, K., 1995. Remarks on the intuitionistic fuzzy sets. Fuzzy
Sets Systems 75 (3), 401-402.
[6] Atanassov, K., 1999. Intuitionistic Fuzzy Sets: Theory and Applications.
Physica-Verlag, Heidelberg.
[7] Atanassov, K., Georgeiv, G., 1993. Intuitionistic fuzzy prolog. Fuzzy
Sets Systems 53, 121-128.
[8] Bustince, H., Burillo, P., 1996. Vague sets are intuitionistic fuzzy sets.
Fuzzy Sets Systems 79 (3), 403-405.
[9] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50420", author = "Binyamin Yusoff and Imran Taib and Lazim Abdullah and Abd Fatah Wahab", title = "A New Similarity Measure on Intuitionistic Fuzzy Sets", abstract = "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.", keywords = "Intuitionistic fuzzy sets, similarity measures, multicriteriadecision making.", volume = "5", number = "6", pages = "800-5", }
