Non-dominated sorting genetic-based algorithm for exploiting a large-sized fuzzy outranking relation

Abstract

Electre III is a well-known multiple criteria decision aiding method based on pairwise comparisons. However, it cannot be applied to ranking problems involving many alternatives, because the number of pairwise comparisons can then be rather large. In this paper, we present an evolution-based approach for exploiting large fuzzy outranking relations and deriving a crisp outranking relation with desirable properties. Therefore, the utilization of a fuzzy outranking relation is modeled as a three-objective optimization problem, which is solved by an evolutionary algorithm. The proposed ranking algorithm is a hybrid of the elitist non-dominated sorting genetic algorithm-II (NSGA-II) and a reference point method with the repeated use of a choice mechanism. In addition, a method that portrays the obtained ranking in a Hasse diagram is used for recommendation purposes. We designate the new method RP2-NSGA-II+H. In our experiments, the proposed ranking procedure demonstrates a better performance in terms of ranking error rates than other ranking procedures based on multi-objective evolutionary algorithms. Our experimental results also demonstrate that, with the new procedure, this method can be scaled for hundreds of alternatives.