An axiomatic approach to the definition of the entropy of a discrete Choquet capacity

An axiomatization of the concept of entropy of a discrete Choquet capacity is given. It is based on three axioms: the symmetry property, a boundary condition for which the entropy reduces to the classical Shannon entropy, and a generalized version of the well-known recursivity property. This entropy, recently introduced to extend the Shannon entropy to nonadditive measures, fulfills several properties considered as requisites for defining an entropy-like measure of uncertainty. An interpretation of it in the framework of aggregation by the discrete Choquet integral is given as well.