Using assignment examples to infer category limits for the ELECTRE TRI method

Given a finite set of alternatives, the sorting (or assignment) problem consists in the assignment of each alternative to one of the predefined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (importance coefficients, thresholds, profiles, etc.) in order to construct the decision-maker's (DM) preference model. A direct elicitation of these parameters being sometimes difficult, Mousseau and Slowinski proposed an interactive aggregation–disaggregation approach that infers ELECTRE TRI parameters indirectly from holistic information, i.e. assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restore the assignment examples is formulated through a non-linear optimization program. Also in this direction, Mousseau et al. considered the subproblem of the determination of the importance coefficients only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather than non-linear in the global inference model). We pursue the idea of partial inference model by considering the complementary subproblem which determines the category limits (the importance coefficients being fixed). With some simplification, it also leads to solve a linear program. Together with the result of Mousseau et al., we have a couple of complementary models which can be combined in an interactive approach inferring the parameters of an ELECTRE TRI model from assignment examples. In each interaction, the DM can revise his/her assignment examples, to give additional information and to choose which parameters to fix before the optimization phase restarts.