Benefits of the combined use of stochastic multi-criteria evaluation with principal components analysis

Abstract

Multi-criteria analysis techniques are well known decision support methods and are widely applied in various disciplines. However, defining the input criteria values for the basic decision matrix which contains all criteria values for every alternative considered is normally not an easy task. Especially qualitative criteria variables which are frequently represented as linguistic terms may be hard to quantify. Moreover, some criteria cannot be represented by just one crisp value, but they may offer a range of possible values. Stochastic multi-criteria approaches which call for distribution models instead of single numerical values can be used in these cases. Outranking multi-criteria methods proved that simulation based stochastic techniques are well suited to give better insight into the preference structure of a variety of decision alternatives. However, besides the knowledge of the preference structure, it is also important to find out about the similarity of decision alternatives which allows a modeller to categorize a decision alternative as a really unique option or as just one option out of a greater subset of very similar alternatives. To be able to perform this categorization, principal components analysis (PCA) was used. The results of the PCA are compared to the results of a stochastic outranking analysis.