Integration based on fusion functions

Abstract

In this paper, we present an approach to data aggregation  based on a generalization of the discrete  Choquet integral by means of fusion functions. Inspired by \cite{MKB}, we merge information contained in capacities $m$ of criteria sets and values of score vectors by a fusion function $F$ instead of the product operator. We give the conditions under which fusion functions $F$ yield well-defined functionals $C_F^m$ and we also discuss properties of these functionals. Some examples for particular capacities $m$ and particular fusion functions $F$ are given.