Decision support systems often rely on a mathematical decision model allowing the comparison of alternatives and the selection of a proper solution. In the field of Multicriteria Decision Making, an aggregation function is often used to synthesize the different evaluations of each alternative into an aggregated value representing its overall utility. The aggregation function must be sufficiently expressive to efficiently approximate the decision maker's preferences in human decision support, or simulate a prescribed decision behavior in automated decision systems. This explains the diversity of decision models available in the literature but also the increasing interest for sophisticated parameterized models such as the Choquet integral [32, 14] which enables the representation of complex preferences and includes many other models as special cases (e.g. leximin and lexicographic aggregators , the Ordered Weighted Average operator , and Weighted Ordered Weighted Average ). To make use of such models, one needs to assess the model parameters in order to fit to the decision maker's preferences. Most of the previous work on the elicitation of Choquet integral parameters consider a static database of preference statements, and focus on the determination of the parameters that best fit to the available database (e.g. [16, 26, 27, 13, 15]) for instance by minimizing a quadratic error. However, these approaches require a relatively large number of preference statements to model the decision maker's behaviour accurately which are not always possible to obtain. Preference elicitation with limited available information is a crucial task in many application domains, including recommender systems and interface customization . Departing from these standard approaches , we consider incremental elicitation methods based on the minimax regret which is a decision criterion that has been advocated as a means for robust optimization in the presence of data uncertainty  and has been used for decision making with utility function uncertainty [5, 31, 6]. The general principle of this approach is to iteratively ask questions to the decision maker so as to reduce the set of possible parameters until the preferred alternative can be detected with some guarantees (as given by the minimax regret). This elicitation approach enables limiting the decision maker's burden as preference information is only required to discriminate between alternatives (not to assess the model parameters). Incremental elicitation methods have been proposed for the simple case of linear utilities but have never been studied for Choquet Integrals.
The 4th International Conference on Algorithmic Decision Theory http://hal.upmc.fr/hal-01217672 The 4th International Conference on Algorithmic Decision Theory, Sep 2015, Lexington, United States. 2015, <10.1007/978-3-319-23114-3_34>ARRAY(0x7f4f389471f0) 2015-09-27