SUB ADDITIVE MEASURES OF FUZZY INFORMATION
Keywords:
Fuzzy sets; fuzzy directed divergence; monotonic functions and convex functions.Abstract
In the present communication, we review the existing measures of fuzzy information. We define and characterize two fuzzy information measures which are sub additive and different from known measures of fuzzy information. We also study monotonic behavior and particular cases of these fuzzy information measures.
Downloads
References
Bhandari, D. and Pal, N.R. (1993). Some new information measures for fuzzy sets,
Information Science, 67, p. 204 – 228.
Deluca, A. and TerminI, S. (1971). A definition of non-probabilistic entropy in the
setting of fuzzy set theory, Inform. and Control 20, p. 30 – 35.
Havrda, J. H. and Charvat, F.(1967). Quantification method of classification
processes – concept of structural Į- entropy, Kybernetika 3, p. 30 – 35.
Hooda, D.S. (2004). On Generalized Measures of Fuzzy Entropy, Mathematica
Slovaca, 54, p. 315 – 325.
Kapur, J.N. (1997). Measures of Fuzzy Information, Mathematical Science Trust
Society, New Delhi.
Kaufman, A. (1980). Fuzzy subsets. Fundamental Theoretical Elements 3,
Academic Press, New York.
Pal, N. R. and Pal, S. K. (1989). Object background segmentation using new
definition of entropy, Proc. IEEE 136, p. 284 – 295.
Renyi, A. (1961). On measures of entropy and information, In: Proc. 4th Berkeley
Symp. Math. Stat. Probab. 1, p. 547-561.
Sharma, B.D. and Mittal, D.P. (1975). New non-additive measures of entropy for
discrete probability distribution, J. Math. Sci. (Calcutta) 10, p. 28 – 40.
Sharma, B.D. and Taneja, I.J (1977). Three generalized Additive Measures of
Entropy, Elec.Inform. Kybern, 13, p. 419-433.
Shannon, C. E. (1948). The Mathematical theory of Communication, Bell System.
Tech. Journal 27, p. 423 – 467.
Zadeh, L.A.(1966). Fuzzy Sets, Inform. And Control 8, p. 94 – 102.
