LIP6 2003/002

• Informes de investigación «Bi-capacités»
• M. Grabisch, Ch. Labreuche
• 27 pages - 23/05/2003 - document en - http://www.lip6.fr/lip6/reports/2003/lip6.2003.002.pdf 354 Ko
• Contacto 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.