On tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral

In many multi-criteria decision making problems the criteria present some interaction whose nature may vary from one situation to another. When a criterion bounds the global score from above, it is called a veto, due to its rather intolerant character. When it bounds the global score from below, it is then called a favor. In this paper we investigate the tolerance of criteria, or equivalently, the tolerance of the weighted aggregation operator (here the Choquet integral) which is used to aggregate criteria. More specifically, we propose (axiomatically) indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the Choquet integral.