{"title":"On Generalized Exponential Fuzzy Entropy","authors":"Rajkumar Verma, Bhu Dev Sharma","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1895,"pagesEnd":1899,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9417","abstract":"In the present communication, the existing measures of\nfuzzy entropy are reviewed. A generalized parametric exponential\nfuzzy entropy is defined.Our study of the four essential and some\nother properties of the proposed measure, clearly establishes the\nvalidity of the measure as an entropy.","references":"[1] D. Bhandari and N. R. Pal, Some new information measures for fuzzy\nsets, Information Sciences, 67,204-228,1993.\n[2] A. Deluca and S. Termini, A definition of Non-Probabilistic entropy in\nthe Setting of Fuzzy Set Theory, Information and Control, 20, 301-312,\n1971.\n[3] J. L. Fan and Y. L. Ma, Some new fuzzy entropy formulas, Fuzzy sets\nand Systems, 128(2),277-284, 2002.\n[4] C. H. Hwang and M. S.Yang, On entropy of fuzzy sets, International\nJournal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(4),\n519-527, 2008.\n[5] D. S. Hooda, On generalized measures of fuzzy entropy, Mathematica\nSlovaca, 54(3), 315-325, 2004.\n[6] T. O. Kvalseth, On Exponential Entropies, IEEE International Conference\non Systems, Man, and Cybernetics, 4, 2822-2826, 2000.\n[7] J. N. Kapur, Measures of Fuzzy Information. Mathematical Sciences Trust\nSociety, New Delhi, 1997.\n[8] N. R. Pal and S. K. Pal, Object-background segmentation using new\ndefinitions of entropy, IEE Proceedings, 136, 284-295, 1989.\n[9] N. R. Pal and S. K. Pal, Entropy: a new definitions and its applications,\nIEEE Transactions on systems, Man and Cybernetics, 21(5), 1260-1270,\n1999.\n[10] A. R`enyi,On measures of entropy and information, Proceedings of the\nFourth Berkeley Symposium on Mathematical Statistics and Probability,\nBerkeley, CA: University of California Press,547-561,1961.\n[11] C. E. Shannon, A mathematical theory of communication, Bell System\nTechnical Journal, 27, 379-423; 623-656, 1948.\n[12] R. R.Yager, On the measure of fuzziness and negation, Part I: Membership\nin the unit interval, International Journal of General Systems, 5,\n221-229, 1979.\n[13] L. A. Zadeh, Fuzzy sets, Information Control, 8, 94-102, 1948.\n[14] L. A. Zadeh, Probability measure of fuzzy event, Journal of Mathematical\nAnalysis and Application, 23(2), 421-427, 1968.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}