On Some Generalizations of the Choquet Integral

Abstract

In the present paper we survey several generalizations of the discrete Choquet integrals and we propose and study a new one. Our proposal is based on the Lovász extension formula, in which we replace the product operator by some binary function F obtaining a new n-ary function JFm. We characterize all functions F yielding, for all capacities m, aggregation functions JFm with a priori given diagonal section.