Discrete integrals based on comonotonic modularity

Miguel Couceiro (1, 2) , Jean-Luc Marichal (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 ORPAILLEUR - Knowledge representation, reasonning
3 SMA - Service de Mathématiques Appliquées

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals.

Domaines: Mathématiques [math]

Miguel Couceiro, Jean-Luc Marichal. Discrete integrals based on comonotonic modularity. Axioms, 2013, 2 (3), pp.14. ⟨10.3390/axioms2030390⟩. ⟨hal-01090567⟩