On Some Generalizations of the Choquet Integral

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 Lovasz extension formula, in which we replace the product operator by some binary function F obtaining a new n-ary function \(\mathfrak {I}^F_{m}\). We characterize all functions F yielding, for all capacities m, aggregation functions \(\mathfrak {I}^F_{m}\) with a priori given diagonal section.