The aim of this article is to present an axiomatization of a generalization of Shannon's entropy starting from partitions of finite sets. The proposed axiomatization defines a family of entropies depending on a real positive parameter that contains as a special case the Havrda-Charvat (1967) entropy, and thus, provides axiomatizations for the Shannon entropy, the Gini index, and for other types of entropy used in classification and data mining.
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Simovici et al. (2002) studied this question.
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