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

In many multi-criteria decision-making problems the decision criteria present some interaction whose nature may vary from one situation to another. For example, some criteria may be statistically correlated, thus making them somewhat redundant or opposed. Some others may be somewhat substitutive or complementary depending on the behavior of the decision maker. Some others may be decisive in the sense that the global score (of any alternative) obtained by aggregation is bounded by the partial score along one of them. In this paper we analyze this latter form of interaction. When a criterion bounds the global score from above, it is called a blocker or veto, due to its rather intolerant character. When it bounds the global score from below, it is then called a pusher or a favor. We thus investigate the tolerance of criteria, or equivalently, the tolerance of the weighted aggregation operator (here the Choquet integral) that 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. Previous to this, we also propose global tolerance degrees measuring the extent to which the Choquet integral is conjunctive or disjunctive.