GAIA-SMAA-PROMETHEE for a hierarchy of interacting criteria

In this paper, we propose an extension of the PROMETHEE methods. Despite PROMETHEE are among the most applied methods in Multiple Criteria Decision Aiding (MCDA), some drawbacks can be underlined with respect to their applicability since they do not take into account few characteristics of multicriteria decision problems that are very relevant in real world applications: (i) robustness regarding the plurality of compatible preference parameters; (ii) interaction between criteria; (iii) hierarchies of criteria. Even if different extensions of the PROMETHEE methods have taken into account all these aspects singularly, we propose to deal with all of them simultaneously presenting a new version which incorporates Robust Ordinal Regression (ROR), Stochastic Multicriteria Acceptability Analysis (SMAA), bipolar Choquet integral and Multiple Criteria Hierarchy Process (MCHP). ROR and SMAA permit to consider all the instances of the considered preference model compatible with the preference information provided by the DM; the bipolar Choquet integral is able to represent the possible positive and negative interactions between criteria as well as the antagonistic effect between some of them; finally, the MCHP permits to decompose the problem in small parts so that each of them can be analyzed more in detail with respect to the problem at hand. Moreover, we also introduce an extension of the GAIA technique to handle visualization in MCDA problems presenting interactions and antagonistic effects between criteria organized in a hierarchy. Furthermore it gives the possibility to display the plurality of instances of the preference model considered by SMAA. A didactic example will illustrate the proposed methodology.