Non additive measures for Group Multi AttributeDecision Models

This paper extends the Choquet integral, widely used in multi-attribute decision problems, to the non monotone case in the context of Group Decision Theory. Even if not so often, preference structures which violate the monotonicity axiom can be observed in real applications. Our aim is twofold. First, we propose the Choquet integral with non monotone non additive measure. Then, we apply the Choquet integral in the context of multi person decision problem, a typical framework of many real world applications, for which the Choquet integral was rarely proposed. Thus in our model this aggregation function is applied twice, both in the cases with possible negative interactions. For this reason, our proposal can be defined as two-step signed Choquet integral.