Comparing Multi-Criteria Decision aid methods through a ranking stability index

Decision tasks are often characterized by the presence of multiple and conflicting criteria used for judging a finite set of alternatives. From such a decision making context arises the need for practical procedures helping the decision maker (DM) doing the right selection, assignment or ranking. Over the last few decades, various Multi-Criteria Decision Making (MCDM) procedures have been proposed and used in order to respond to such decision aiding tasks. A major criticism of these different methods is that they may yield different results when applied to the same problem. A comparative study is proposed here to identify similarities and divergences between a number of most used MCDM methods. A case study from the literature concerned with seismic structural retrofitting of a reinforced concrete (RC) building and for which eight conflicting criteria are taken into account, is presented. Obtained results employing six MCDM methods (ELECTRE III, PROMETHEE I and II, TOPSIS, AHP and PEG-MCDM) are compared. A Gini index is introduced to quantify dispersion of Pareto optima ranking provided by various applied methods. The results highlight the sensitivity of the best Pareto compromise design and ranking to the applied MCDM method.