A prioritized measure for multi-criteria aggregation and its Shapley index

We focus on a particular type of multi-criteria aggregation imperative called prioritized aggregation. This imperative is characteristic of situations where lack of satisfaction for criteria denoted as higher priority cannot be compensated by increased satisfaction for those denoted as lower priority. We consider an approach to the formulation of this type of aggregation process based on an integral type aggregation using a special monotonic set measure to convey the prioritized imperative. In order to get a better understanding of this measure we look at its Shapley index.