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A Form of Information Entropy

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DOI: 10.4236/ns.2014.617118    3,427 Downloads   4,151 Views   Citations
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ABSTRACT

In this paper, by axiomatic way, a form of information entropy will be presented on crisp and fuzzy setting. Information entropy is the unavailability of information about a crisp or fuzzy event. It will use measure of information defined without any probability or fuzzy measure: for this reason it is called general information.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Divari, M. and Vivona, D. (2014) A Form of Information Entropy. Natural Science, 6, 1282-1285. doi: 10.4236/ns.2014.617118.

References

[1] Shannon, C. and Weaver, W. (1949) The Mathematical Theory of Communication. University of Illinois Press, Urbana.
[2] Halmos, P.R. (1965) Measure Theory. Van Nostrand Company, New York.
[3] Aczél, J. (2004) Entropies, Characterizations, Applications and Some History. Proceedings of IPMU-2004, Perugia, 4-9 July 2004, 1825-1830.
[4] Aczél, J. (1969) Probability and Information Theory. Lectures Notes in Mathematics, 89. Springer-Verlag, Berlin, 1-11.
[5] Rényi, A. (1961) On Measures of Entropy and Information. Proceedings IV Berkeley Symposium on Mathematical Statistics and Probability, 1, 547-561.
[6] Rényi, A. (1970) Probability Theory. Nord Holland/Elsevier, Amsterdam, New York.
[7] Tsallis, C. (1988) Possible Generalization of Bolzmann-Gibbs Statistics. Journal of Statistical Physics, 52, 479-487.
http://dx.doi.org/10.1007/BF01016429
[8] Forte, B. (1969) Measures of Information: The General Axiomatic Theory. RAIRO Informatique Théorique et Applications, R3, 63-90.
[9] Forte, B. (1970) Functional Equations in Generalized Information Theory. In: Cremonese, Ed., Applications of Functional Equations and Inequalities to Information Theory, Roma, 113-140.
[10] Kampé de Fériet, J. and Forte, B. (1967) Information et Probabilité. Comptes Rendus de l’Académie des Sciences Paris, 265, 110-114, 142-146, 350-353.
[11] Kampé de Feriét, J. and Benvenuti, P. (1969) Sur une classe d’informations. Comptes Rendus de l’Académie des Sciences Paris, 269, 97-101.
[12] Benvenuti, P., Vivona, D. and Divari, M. (1990) A General Information for Fuzzy Sets. Uncertainty in Knowledge Bases, Lectures Notes in Computer Sciences, 521, 307-316.
http://dx.doi.org/10.1007/BFb0028117
[13] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[14] Klir, G.J. and Folger, T.A. (1988) Fuzzy Sets, Uncertainty and Information. Prentice-Hall International Editions, Englewood Cliffs.
[15] Khinchin, A.Y. (1957) Mathematical Foundation of Information Theory. Dover Publications, New York.
[16] Aczél, J. (1966) Lectures on Functional Equations and Their Applications. Academic Press, New York.
[17] Ling, C.H. (1995) Representation of Associative Functions. Publicationes Mathematicae Debrecen, 12, 189-212.

  
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