Decision-Making Problems with Local Extremes: Comparative Study Case

Many MCDA methods have been developed to support the decision-maker in solving complex decision-making problems. Most of them suppose the use of monotonic criteria, such as profit or cost. These methods do not consider the possibility of occurring local extremes in the space of the decision-making problem. Therefore, the question arises about how MCDA methods work when a decision problem consists of non-monotonic criteria. We present a short comparative analysis for four popular MCDA methods, i.e., TOPSIS, VIKOR, PROMETHEE II and COMET. For this purpose, we have used simulations for two different decision-making models. In each case, sets of decision alternatives are generated, then evaluated by the model and selected MCDA methods. The obtained results create rankings from which rank similarity coefficients are calculated. The conducted research shows that the COMET method works better in such conditions than the others, and the VIKOR method does the least well in this task.