An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
To extend the classical Shannon entropy to nonadditive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this new concept on the basis of three axioms: the symmetry property, a boundary condition for which the entropy reduces to the Shannon entropy, and a generalized version of the well-known recursivity property. We also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy-like measure. Lastly, we provide an interpretation of it in the framework of aggregation by the discrete Choquet integral. (c) 2004 Elsevier Inc. All rights reserved.
entropy choquet capacity choquet integral information theory