On Generalized Exponential Fuzzy Entropy

Authors: Rajkumar Verma, Bhu Dev Sharma

Abstract:

In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy.

Keywords: fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072726

References:

[1] D. Bhandari and N. R. Pal, Some new information measures for fuzzy sets, Information Sciences, 67,204-228,1993.
[2] A. Deluca and S. Termini, A definition of Non-Probabilistic entropy in the Setting of Fuzzy Set Theory, Information and Control, 20, 301-312, 1971.
[3] J. L. Fan and Y. L. Ma, Some new fuzzy entropy formulas, Fuzzy sets and Systems, 128(2),277-284, 2002.
[4] C. H. Hwang and M. S.Yang, On entropy of fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(4), 519-527, 2008.
[5] D. S. Hooda, On generalized measures of fuzzy entropy, Mathematica Slovaca, 54(3), 315-325, 2004.
[6] T. O. Kvalseth, On Exponential Entropies, IEEE International Conference on Systems, Man, and Cybernetics, 4, 2822-2826, 2000.
[7] J. N. Kapur, Measures of Fuzzy Information. Mathematical Sciences Trust Society, New Delhi, 1997.
[8] N. R. Pal and S. K. Pal, Object-background segmentation using new definitions of entropy, IEE Proceedings, 136, 284-295, 1989.
[9] N. R. Pal and S. K. Pal, Entropy: a new definitions and its applications, IEEE Transactions on systems, Man and Cybernetics, 21(5), 1260-1270, 1999.
[10] A. R`enyi,On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press,547-561,1961.
[11] C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, 27, 379-423; 623-656, 1948.
[12] R. R.Yager, On the measure of fuzziness and negation, Part I: Membership in the unit interval, International Journal of General Systems, 5, 221-229, 1979.
[13] L. A. Zadeh, Fuzzy sets, Information Control, 8, 94-102, 1948.
[14] L. A. Zadeh, Probability measure of fuzzy event, Journal of Mathematical Analysis and Application, 23(2), 421-427, 1968.