Choquet integral calculus on a continuous support and its applications

Mustapha Ridaoui (1) , Michel Grabisch (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

In this paper we give representation results about the calculation of the Choquet integral of a monotone function on the nonnegative real line. Next, we represent the Choquet integral of nonmonotone functions, by construction of monotone functions from nonmonotone ones, by using the increasing and decreasing rearrangement of a nonmono-tone function. Finally, this paper is completed with some applications of these results to the continuous agregation operator OWA, and to the representation of risk measures by Choquet integral.

Mots clés: Choquet integral; distorted Lebesgue measure; risk measure; OWA oper-ator

Domaines: Mathématique discrète [cs.DM]; Economies et finances

Mustapha Ridaoui, Michel Grabisch. Choquet integral calculus on a continuous support and its applications. Operations Research and Decisions, 2016. ⟨hal-01373325⟩