Numerical integration for the Choquet integral

• Study of the Choquet integral for continuous functions.
• Numerical integration for the Choquet integral on the real line.
• Numerical examples of the computation of the numerical Choquet integral.
• Numerical computation of the Hellinger distance for fuzzy measures.

Choquet integrals with respect to non-additive (or fuzzy measures) have been used in a large number of applications because they permit us to integrate information from different sources when there are interactions. Successful applications use a discrete reference set.In the case of measures on a continuous reference set, as e.g. the real line, few results have been obtained that permit us to have an analytical expression of the integral. However, in most of the cases there is no such analytical expression.In this paper we describe how to perform the numerical integration of a Choquet integral with respect to a non-additive measure.