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Article

MSC: 94A17
Keywords:
fuzzy set; fuzzy entropy; Atanassov's intuitionistic fuzzy set; intuitionistic fuzzy entropy; exponential entropy
Summary:
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.
References:
[1] Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986), 1, 87-96. MR 0852871 | Zbl 1247.03112
[2] Atanassov, K.: New operations defined over intuitionistic fuzzy sets. Fuzzy Sets and Systems 61 (1994), 2, 137-142. DOI 10.1016/0165-0114(94)90229-1 | MR 1262464
[3] Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems 78 (1996), 3, 305-316. DOI 10.1016/0165-0114(96)84611-2 | MR 1378726 | Zbl 0872.94061
[4] Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79 (1996), 3, 403-405. DOI 10.1016/0165-0114(95)00154-9 | MR 1388413 | Zbl 0871.04006
[5] Luca, A. De, Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy set theory. Inform. Control 20 (1972), 4, 301-312. DOI 10.1016/S0019-9958(72)90199-4 | MR 0327383
[6] De, S. K., Biswas, R., Roy, A. R.: Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems 114 (2000), 3, 477-484. MR 1775284 | Zbl 0961.03049
[7] Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Academic-Press, New York 1975. MR 0485402 | Zbl 0332.02063
[8] 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. MR 1993200
[9] Pal, N. R., Pal, S. K.: Object background segmentation using new definitions of entropy. IEEE Proc. 366 (1989), 284-295.
[10] 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. MR 2416989
[11] Shannon, C. E.: A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948), 379-423, 623-656. MR 0026286 | Zbl 1154.94303
[12] Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118 (2001), 3, 467-477. DOI 10.1016/S0165-0114(98)00402-3 | MR 1809394 | Zbl 1045.94007
[13] Vlachos, I. K., Sergiagis, G. D.: Intuitionistic fuzzy information - Application to pattern recognition. Pattern Recognition Lett. 28 (2007), 2, 197-206. DOI 10.1016/j.patrec.2006.07.004
[14] 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. MR 2976003
[15] Ye, J.: Two effective measures of intuitionistic fuzzy entropy. Computing 87 (2010), 1-2, 55-62. MR 2601774 | Zbl 1192.94076
[16] Zadeh, L. A.: Fuzzy sets. Inform. Control 8 (1965), 3, 338-353. DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0942.00007
[17] Zadeh, L. A.: Probability measure of fuzzy events. J. Math. Anal. Appl. 23 (1968), 2, 421-427. DOI 10.1016/0022-247X(68)90078-4 | MR 0230569
[18] Zhang, Q. S., Jiang, S. Y.: A note on information entropy measure for vague sets. Inform. Sci. 178 (2008), 21, 4184-4191. DOI 10.1016/j.ins.2008.07.003 | MR 2454647
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