Using assignment examples to infer weights for ELECTRE TRI method: Some experimental results

Given a ®nite set of alternatives A, the sorting (or assignment) problem consists in the assignment of each alternative to one of the pre-de®ned 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 (weights, thresholds, category limits,. . .) in order to construct a preference model which the decision maker (DM) accepts as a working hypothesis in the decision aid study. A direct elicitation of these parameters requiring a high cognitive e€ort from the DM (V. Mosseau, R. Slowinski, Journal of Global Optimization 12 (2) (1998) 174), 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 nonlinear optimization program. In this paper, we consider the subproblem of the determination of the weights only (the thresholds and category limits being ®xed). This subproblem leads to solve a linear program (rather than nonlinear in the global inference model). Numerical experiments were conducted so as to check the behaviour of this disaggregation tool. Results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify ``inconsistencies'' in the assignment examples. Ó 2001 Elsevier Science B.V. All rights reserved.