Kybernetika 49 no. 1, 114-127, 2013

Exponential entropy on intuitionistic fuzzy sets

Rajkumar Verma and Bhu Dev Sharma


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.


fuzzy set, fuzzy entropy, Atanassov's intuitionistic fuzzy set, intuitionistic fuzzy entropy, exponential entropy




  1. K. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986), 1, 87-96.   CrossRef
  2. K. Atanassov: New operations defined over intuitionistic fuzzy sets. Fuzzy Sets and Systems 61 (1994), 2, 137-142.   CrossRef
  3. P. Burillo and H. Bustince: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems 78 (1996), 3, 305-316.   CrossRef
  4. H. Bustince and P. Burillo: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79 (1996), 3, 403-405.   CrossRef
  5. A. De Luca and S. Termini: A definition of non-probabilistic entropy in the setting of fuzzy set theory. Inform. Control 20 (1972), 4, 301-312.   CrossRef
  6. S. K. De, R. Biswas and A. R. Roy: Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems 114 (2000), 3, 477-484.   CrossRef
  7. A. Kaufmann: Introduction to the Theory of Fuzzy Subsets. Academic-Press, New York 1975.   CrossRef
  8. F. Li, Z. H. Lu and L. J. Cai: The entropy of vague sets based on fuzzy sets. J. Huazhong Univ. Sci. Tech. 31 (2003), 1, 24-25.   CrossRef
  9. N. R. Pal and S. K. Pal: Object background segmentation using new definitions of entropy. IEEE Proc. 366 (1989), 284-295.   CrossRef
  10. O. Prakash, P. K. Sharma and R. Mahajan: 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.   CrossRef
  11. C. E. Shannon: A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948), 379-423, 623-656.   CrossRef
  12. E. Szmidt and J. Kacprzyk: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118 (2001), 3, 467-477.   CrossRef
  13. I. K. Vlachos and G. D. Sergiagis: Intuitionistic fuzzy information - Application to pattern recognition. Pattern Recognition Lett. 28 (2007), 2, 197-206.   CrossRef
  14. C. P. Wei, Z. H. Gao and T. T. Guo: An intuitionistic fuzzy entropy measure based on the trigonometric function. Control and Decision 27 (2012), 4, 571-574.   CrossRef
  15. J. Ye: Two effective measures of intuitionistic fuzzy entropy. Computing 87 (2010), 1-2, 55-62.   CrossRef
  16. L. A. Zadeh: Fuzzy sets. Inform. Control 8 (1965), 3, 338-353.   CrossRef
  17. L. A. Zadeh: Probability measure of fuzzy events. J. Math. Anal. Appl. 23 (1968), 2, 421-427.   CrossRef
  18. Q. S. Zhang and S. Y. Jiang: A note on information entropy measure for vague sets. Inform. Sci. 178 (2008), 21, 4184-4191.   CrossRef