Multi- and multi-polar capacities

Aggregation of inputs from different categories generalizes both unipolar (standard) and bipolar aggregation. This aggregation covers two main cases of multi-polar and non-monotone aggregation. Inputs from different categories can be found in classification methods, multi-criteria decision making, game theory and political and sociological sciences. Two main concepts related to aggregation on the unit interval are capacities and aggregation on grid points – Boolean functions. In this paper multi- and multi-polar capacities that extend (bi- and bipolar) capacities are introduced. The position of these capacities is clarified by means of the connection between Boolean (crisp) functions, capacities, aggregation and concepts from other domains of science which are shown for the unipolar, the bipolar and the multi-polar case. The connection between multi- and multi-polar capacities and the concept of games with n players and r alternatives is described.