Entropy of capacities on lattices and set systems

Aoi Honda (1) , Michel Grabisch (2, 3)

1 Kyutech - Kyushu Institute of Technology
2 CES - Centre d'économie de la Sorbonne
3 DECISION

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.

Mots clés: entropy; capacity; lattice; convex geometry; antimatroid

Domaines: Mathématique discrète [cs.DM]; Statistiques [math.ST]; Théorie [stat.TH]

Aoi Honda, Michel Grabisch. Entropy of capacities on lattices and set systems. Information Sciences, 2006, 176 (23), pp.3472-3489. ⟨10.1016/j.ins.2006.02.011⟩. ⟨hal-00179852⟩