The automatic generation of an explanation of the prescription made by a multi-attribute decision model is crucial in many applications, such as recommender systems. This task is complex since the quantitative models are not designed to be easily explainable. The major limitation of the previous research is that there is no formal justification of the arguments that are selected in the explanation. The goal of this paper is to define a general framework to justify which arguments shall be selected, in the case where the decision model is based on weights assigned to the attributes. Due to the complexity of explaining a preference model based on utility theory, several explanation reasonings are necessary to cover all cases – ranging from situations where the prescription is trivial to situations where the prescription is much more tight. The set of selected arguments is, in this framework, a non-dominated element of a combinatorial structure in the sense of an order relation. Our general approach is instantiated precisely on three models: the probabilistic expected utility model, the qualitative pessimistic minmax model and the concordance rule, which are all constructed from a weight vector.
