Kybernetika 49 no. 1, 114-127, 2013

Exponential entropy on intuitionistic fuzzy sets

Rajkumar Verma and Bhu Dev Sharma

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.

Keywords:

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

Classification:

94A17

paper.pdf

References:

  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