Rect@ (Jun 2013)
Semiorders, Intervals Orders and Pseudo Orders Preference Structures in Multiple Criteria Decision Aid Methods
Abstract
During the last decades, an important number of Multicriteria Decision Aid Methods (MCDA) has been proposed to help the decision maker to select the best compromise alternative. Meanwhile, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) family of outranking method and their applications has attracted much attention from academics and practitioners. In this paper, an extension of these methods is presented, consisting of analyze its functioning under New Preference Structures (NPS). The preference structures taken into account are, namely: semiorders, intervals orders and pseudo orders. 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 NPS incorporation is carried out in 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 NPS
