An algorithm to elicitate ELECTRE II, III and IV parameters

This paper presents an algorithm that can elicitate all or any combination of parameters for the ELECTRE II, III or IV, methods. The algorithm takes some steps of a machine learning ensemble technique, the random forest, and for that, the authors named the approach as Ranking Trees Algorithm.

First, for a given method, the authors generate a set of ELECTRE models, where each model solves a random sample of criteria and actions (alternatives). Second, for each generated model, all actions are projected in a 1D space; in general, the best actions have higher values in a 1D space than the worst ones; therefore, they can be used to guide the genetic algorithm in the final step, the optimization phase. Finally, in the optimization phase, each model has its parameters optimized.

The results can be used in two different ways; the authors can merge all models, to find the elicitated parameters in this way, or the authors can ensemble the models, and the median of all ranks represents the final rank. The numerical examples achieved a Kendall Tau correlation rank over 0.85, and these results could perform as well as the results obtained by a group of specialists.

For the first time, the elicitation of ELECTRE parameters is made by an ensemble technique composed of a set of uncorrelated multicriteria models that can generate robust solutions.