New Preference Structures for multiple criteria decision making: Its extension to PROMETHEE Methods

The PROMETHEE Methods are a very important class of outranking methods in the multicriteria analysis for decision aid. In this paper, an extension of these methods is presented, consisting of analyzing its functioning under New Preference Structures (NEP). The new preference structures to take into account are, namely: semiorders, intervals orders and pseudoorders. These structures outstandingly improve the modelization as they give more flexibility, amplitude and certainty at the preferences formulation, since they tend to abandon the Complete Transitive Comparability Axiom of Preferences in order to substitute it by the Partial Comparability Axiom of Preferences. It must be remarked the introduction of Incomparability relations to the analysis and the consideration of preference structures that accept the Indifference intransitivity. The NEP incorporation is carried out in the three phases that the PROMETHEE Methodology takes in: ‘preference structure enrichment’, ‘dominance relation enrichment’ and ‘outranking relation exploitation for decision aid’, in order to finally arrive at solving the alternatives ranking problem through the PROMETHEE I or the PROMETHEE II utilization, according to whether a partial ranking or a complete one, is respectively required under the NEP. In addition to the model presentation the paper studies the application of both methodologies to a case presented in the literature about the theme with the aim of comparing the results. Finally, some of the conclusions that can be taken from the functioning of PROMETHEE Methods in the frame of the proposed analysis, are distinguished.