LIP6 2003/002

• Reports
  Bi-capacités
• M. Grabisch, Ch. Labreuche
• 27 pages - 05/23/2003- document en - http://www.lip6.fr/lip6/reports/2003/lip6.2003.002.pdf - 354 Ko
• Contact : Michel.Grabisch (at) nulllip6.fr
• Ancien Thème : SYSDEF
We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the M""obius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bi-capacities are introduced. It is shown that symmetric and asymmetric integrals are recovered. Lastly, we introduce the Shapley value and interaction indices. It is seen that besides a generalization based on the classical definitions, a definition involving two arguments is natural.
• Keywords : bi-capacity, Choquet integral, Möbius transform, Shapley value, interaction index
• Publisher : Nicole.Nardy (at) nulllip6.fr