Multiple-criteria decision aiding (MCDA) proposes models and methods for different types of decision problems such as choice, ranking or sorting. Such models involve various parameters that must be elicited. In the elicitation process, all necessary information has to be taken from the decision-maker. For this, several direct and indirect elicitation methods are suggested in the literature. In this work, we concentrate on direct elicitation: we aim at providing a rigorous elicitation procedure for the parameters of the Non-Compensatory Sorting model (NCS), which has been characterized by an axiomatic analysis. A basic version of the NCS model is considered, i.e., a model with two categories and no vetoes. The parameters are the set of sufficient coalitions of criteria and the profile separating the two categories. Regarding the sufficient coalitions, we propose several questioning algorithms that engraft questions on classical graph exploration algorithms such as depth-first search. Such algorithms are implemented and evaluated by simulation. For eliciting the limit profile, we design a questioning algorithm using dichotomy. Questioning algorithms can be optimal in the worst case or on average. An optimal algorithm in the worst case has been proposed by Hansel in the framework of monotone Boolean functions. We implement and evaluate this algorithm as a variant of the depth-first search approaches. Regarding optimal questioning strategies on average, we evaluate decision trees for up to four criteria. On the other hand, we assess how more general is NCS as compared to MR-Sort, a particular case of the NCS model in which sufficient coalitions can be represented by additive weights.

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