Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems

In this paper, we investigate the incremental elicitation of the capacity through a sequence of preference queries (questions) selected one-by-one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret (the worst-case “loss” due to reasoning with only partially specified capacities) is low enough. We propose a new approach designed to efficiently compute minimax regret for the Choquet model and we show how this approach can be used in different settings: 1) the problem of recommending a single alternative, 2) the problem of ranking alternatives from best to worst, and 3) sorting several alternatives into ordered categories. Numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations.