Table of Contents Author Guidelines Submit a Manuscript
Advances in Fuzzy Systems
Volume 2014 (2014), Article ID 789890, 8 pages
http://dx.doi.org/10.1155/2014/789890
Research Article

On Intuitionistic Fuzzy Entropy of Order-α

1Department of Applied Sciences, HMR Institute of Technology and Management, Guru Gobind Singh Indraprastha University, Hamidpur, Delhi-110036, India
2Department of Mathematics, Jaypee Institute of Information Technology (Deemed University), A-10, Sector 62, Noida-201307, Uttar Pradesh, India

Received 19 January 2014; Revised 15 July 2014; Accepted 17 July 2014; Published 3 September 2014

Academic Editor: Ning Xiong

Copyright © 2014 Rajkumar Verma and BhuDev Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. L. A. Zadeh, “Probability measures of fuzzy events,” Journal of Mathematical Analysis and Applications, vol. 23, no. 2, pp. 421–427, 1968. View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. De Luca and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory,” Information and Computation, vol. 20, no. 4, pp. 301–312, 1972. View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 379–656, 1948. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, NY, USA, 1975. View at MathSciNet
  6. R. R. Yager, “On the measure of fuzziness and negation part I: membership in the unit interval,” International Journal of General Systems, vol. 5, no. 4, pp. 221–229, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. N. R. Pal and S. K. Pal, “Object-background segmentation using new definitions of entropy,” IEE Proceedings E: Computers and Digital Techniques, vol. 136, no. 4, pp. 284–295, 1989. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Bhandari and N. R. Pal, “Some new information measures for fuzzy sets,” Information Sciences, vol. 67, no. 3, pp. 209–228, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. A. Rényi, “On measures of entropy and information,” in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, pp. 547–561, University of California Press, Berkeley, Calif, USA, 1961.
  10. R. Verma and B. D. Sharma, “On generalized exponential fuzzy entropy,” Engineering and Technology, vol. 5, pp. 956–959, 2011. View at Google Scholar
  11. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. K. T. Atanassov, Intuitionistic Fuzzy Sets, Physica, Heidelberg, Germany, 1999.
  13. P. Burillo and H. Bustince, “Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets,” Fuzzy Sets and Systems, vol. 78, no. 3, pp. 305–316, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. E. Szmidt and J. Kacprzyk, “Entropy for intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 118, no. 3, pp. 467–477, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. W. Zeng and H. Li, “Relationship between similarity measure and entropy of interval valued fuzzy sets,” Fuzzy Sets and Systems, vol. 157, no. 11, pp. 1477–1484, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. W. L. Hung and M. S. Yang, “Fuzzy entropy on intuitionistic fuzzy sets,” International Journal of Intelligent Systems, vol. 21, no. 4, pp. 443–451, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. I. K. Vlachos and G. D. Sergiadis, “Intuitionistic fuzzy information—applications to pattern recognition,” Pattern Recognition Letters, vol. 28, no. 2, pp. 197–206, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. Q. Zhang and S. Jiang, “A note on information entropy measures for vague sets and its applications,” Information Sciences, vol. 178, no. 21, pp. 4184–4191, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. K. De, R. Biswas, and A. R. Roy, “Some operations on intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 114, no. 3, pp. 477–484, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus