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Classifying Entropy Measures

Fundamental Mathematics Department, Faculty of Sciences UNED, Paseo Senda del Rey 9. 28040-Madrid, Spain
Symmetry 2011, 3(3), 487-502;
Received: 27 April 2011 / Revised: 6 July 2011 / Accepted: 6 July 2011 / Published: 20 July 2011
(This article belongs to the Special Issue Symmetry Measures on Complex Networks)
PDF [357 KB, uploaded 20 July 2011]


Our paper analyzes some aspects of Uncertainty Measures. We need to obtain new ways to model adequate conditions or restrictions, constructed from vague pieces of information. The classical entropy measure originates from scientific fields; more specifically, from Statistical Physics and Thermodynamics. With time it was adapted by Claude Shannon, creating the current expanding Information Theory. However, the Hungarian mathematician, Alfred Rényi, proves that different and valid entropy measures exist in accordance with the purpose and/or need of application. Accordingly, it is essential to clarify the different types of measures and their mutual relationships. For these reasons, we attempt here to obtain an adequate revision of such fuzzy entropy measures from a mathematical point of view. View Full-Text
Keywords: mathematical analysis; measure theory; fuzzy systems; information theory mathematical analysis; measure theory; fuzzy systems; information theory
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Garrido, A. Classifying Entropy Measures. Symmetry 2011, 3, 487-502.

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