An indirect elicitation method for the parameters of the ELECTRE TRI-nB model using genetic algorithms

Abstract

Indirect approaches for eliciting preference model parameters for multiple criteria decision aiding are of growing interest because they imply relatively less cognitive effort from the decision-maker (DM). Direct approaches are particularly hard in the case of the new ELECTRE TRI-nB method, because the task involves eliciting a number of limiting profiles for each category boundary. However, in ELECTRE methods, the simultaneous inference of the whole set of parameters needs the construction and resolution of a non-linear non-convex programming problem, which is typically very hard to solve. Therefore, an evolutionary-based method to infer the parameters of the ELECTRE TRI-nB model is proposed in this paper. The quality of the solutions is tested by measuring the capacity to restore the assignment examples and the capacity to make consistent assignments of new actions. In extensive computer experiments, using the pseudo-conjunctive assignment procedure, some main conclusions arise: (i) the capacity of the method to restore the training examples reaches high values, mainly with three and five limiting profiles per category; and (ii) the capacity to make appropriate assignments of new actions (not belonging to the training information) can be greatly improved by increasing the number of limiting profiles.