Entropy of capacities on lattices and set systems

Details Entropy of capacities on lattices and set systems Entropy of capacities on lattices and set systems

2007-11-13

arxiv.org/abs/0711.1993v1

Information Sciences 176 (2006) 3472-3489

Computer Science

Discrete Mathematics

Scientific paper

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and examples are given.

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