The Symmetric and Asymmetric Choquet integrals on finite spaces for decision making

Michel Grabisch (1) , Christophe Labreuche (2)

1 SYSDEF - Systèmes d'aide à la décision et à la formation
2 Thales Research and Technology [Palaiseau]

In this paper, we give a mathematical analysis of symmetric and asymmetric Choquet integrals in the view of decision making in a finite setting. These integrals present two ways of dealing with negative integrands. The analysis is done with the aid of the Möbius and interaction transforms, this last one having an interesting interpretation in multicriteria decision making (MCDM). The last part of the paper shows the application of these two integrals in MCDM.

Mots clés: Choquet integral; symmetric integral; Möbius transform; interaction

Domaines: Economies et finances; Méthodes et statistiques

Michel Grabisch, Christophe Labreuche. The Symmetric and Asymmetric Choquet integrals on finite spaces for decision making. Statistical Papers, 2002, 43 (1), pp.37-52. ⟨10.1007/s00362-001-0085-4⟩. ⟨halshs-00273184⟩