Non Additive Measures for Group Multi Attribute Decision Models.

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