Partially Bipolar Choquet Integrals

Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to situations where the values to be aggregated lie on a bipolar scale. The resulting continuous piecewise linear aggregation function has the ability to represent decisional behaviors that depend on the ldquopositiverdquo or ldquonegativerdquo satisfaction of some of the criteria. Its main drawback is that it holds a huge number of parameters that makes its determination problematic in practice. From the observation that the decision maker usually adopts a bipolar reasoning only with respect to a (small) subset of criteria, we investigate Choquet-like aggregation models that are fully bipolar only with respect to certain criteria and whose number of parameters is much lower than that of the bipolar Choquet integral. The use of the proposed concepts is illustrated in an example.