Exponential entropy on intuitionistic fuzzy sets
Rajkumar Verma; Bhu Dev Sharma
Kybernetika (2013)
- Volume: 49, Issue: 1, page 114-127
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topVerma, Rajkumar, and Sharma, Bhu Dev. "Exponential entropy on intuitionistic fuzzy sets." Kybernetika 49.1 (2013): 114-127. <http://eudml.org/doc/252500>.
@article{Verma2013,
abstract = {In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that the proposed entropy measure for Atanassov's intuitionistic fuzzy set is consistent by comparing it with other existing entropies.},
author = {Verma, Rajkumar, Sharma, Bhu Dev},
journal = {Kybernetika},
keywords = {fuzzy set; fuzzy entropy; Atanassov's intuitionistic fuzzy set; intuitionistic fuzzy entropy; exponential entropy; fuzzy set; fuzzy entropy; Atanassov's intuitionistic fuzzy set; intuitionistic fuzzy entropy; exponential entropy},
language = {eng},
number = {1},
pages = {114-127},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exponential entropy on intuitionistic fuzzy sets},
url = {http://eudml.org/doc/252500},
volume = {49},
year = {2013},
}
TY - JOUR
AU - Verma, Rajkumar
AU - Sharma, Bhu Dev
TI - Exponential entropy on intuitionistic fuzzy sets
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 114
EP - 127
AB - In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that the proposed entropy measure for Atanassov's intuitionistic fuzzy set is consistent by comparing it with other existing entropies.
LA - eng
KW - fuzzy set; fuzzy entropy; Atanassov's intuitionistic fuzzy set; intuitionistic fuzzy entropy; exponential entropy; fuzzy set; fuzzy entropy; Atanassov's intuitionistic fuzzy set; intuitionistic fuzzy entropy; exponential entropy
UR - http://eudml.org/doc/252500
ER -
References
top- Atanassov, K., Intuitionistic fuzzy sets., Fuzzy Sets and Systems 20 (1986), 1, 87-96. Zbl1247.03112MR0852871
- Atanassov, K., 10.1016/0165-0114(94)90229-1, Fuzzy Sets and Systems 61 (1994), 2, 137-142. MR1262464DOI10.1016/0165-0114(94)90229-1
- Burillo, P., Bustince, H., 10.1016/0165-0114(96)84611-2, Fuzzy Sets and Systems 78 (1996), 3, 305-316. Zbl0872.94061MR1378726DOI10.1016/0165-0114(96)84611-2
- Bustince, H., Burillo, P., 10.1016/0165-0114(95)00154-9, Fuzzy Sets and Systems 79 (1996), 3, 403-405. Zbl0871.04006MR1388413DOI10.1016/0165-0114(95)00154-9
- Luca, A. De, Termini, S., 10.1016/S0019-9958(72)90199-4, Inform. Control 20 (1972), 4, 301-312. MR0327383DOI10.1016/S0019-9958(72)90199-4
- De, S. K., Biswas, R., Roy, A. R., Some operations on intuitionistic fuzzy sets., Fuzzy Sets and Systems 114 (2000), 3, 477-484. Zbl0961.03049MR1775284
- Kaufmann, A., Introduction to the Theory of Fuzzy Subsets., Academic-Press, New York 1975. Zbl0332.02063MR0485402
- Li, F., Lu, Z. H., Cai, L. J., The entropy of vague sets based on fuzzy sets., J. Huazhong Univ. Sci. Tech. 31 (2003), 1, 24-25. MR1993200
- Pal, N. R., Pal, S. K., Object background segmentation using new definitions of entropy., IEEE Proc. 366 (1989), 284-295.
- Prakash, O., Sharma, P. K., Mahajan, R., New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle., Inform. Sci. 178 (2008), 11, 2839-2395. MR2416989
- Shannon, C. E., A mathematical theory of communication., Bell Syst. Tech. J. 27 (1948), 379-423, 623-656. Zbl1154.94303MR0026286
- Szmidt, E., Kacprzyk, J., 10.1016/S0165-0114(98)00402-3, Fuzzy Sets and Systems 118 (2001), 3, 467-477. Zbl1045.94007MR1809394DOI10.1016/S0165-0114(98)00402-3
- Vlachos, I. K., Sergiagis, G. D., 10.1016/j.patrec.2006.07.004, Pattern Recognition Lett. 28 (2007), 2, 197-206. DOI10.1016/j.patrec.2006.07.004
- Wei, C. P., Gao, Z. H., Guo, T. T., An intuitionistic fuzzy entropy measure based on the trigonometric function., Control and Decision 27 (2012), 4, 571-574. MR2976003
- Ye, J., Two effective measures of intuitionistic fuzzy entropy., Computing 87 (2010), 1-2, 55-62. Zbl1192.94076MR2601774
- Zadeh, L. A., 10.1016/S0019-9958(65)90241-X, Inform. Control 8 (1965), 3, 338-353. Zbl0942.00007MR0219427DOI10.1016/S0019-9958(65)90241-X
- Zadeh, L. A., 10.1016/0022-247X(68)90078-4, J. Math. Anal. Appl. 23 (1968), 2, 421-427. MR0230569DOI10.1016/0022-247X(68)90078-4
- Zhang, Q. S., Jiang, S. Y., 10.1016/j.ins.2008.07.003, Inform. Sci. 178 (2008), 21, 4184-4191. MR2454647DOI10.1016/j.ins.2008.07.003
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.