Aggregation of Choquet integrals

Abstract

Aggregation functions acting on the lattice of all Choquet integrals on a fixed measurable space (X,A) are discussed. The only direct aggregation of Choquet integrals resulting into a Choquet integral is linked to the convex sums, i.e., to the weighted arithmetic means. We introduce and discuss several other approaches, for example one based on compatible aggregation systems. For X finite, the related aggregation of OWA operators is obtained as a corollary. The only exception, with richer structure of aggregation functions, is the case card X = 2, when the lattice of all OWA operators forms a chain.