A Statistical Approach to Complex Multi-Criteria Decisions

Complex decision problems have most of the time multi-criteria dimensions. Many existing multi-criteria decision tools are however plagued with difficulties due to uncertainties on data and preference weights, multiple decision-makers, correlations between criteria, etc., and last but not least, undesirable properties, like rank reversal. This chapter investigates an original approach using the correlations between criteria, as a measure of distance between ranking solutions. Geometrical interpretations are given for two and three-dimensional problems. It is shown how the proposed framework, which is valid for any dimension, addresses uncertainties, and how it enhances the rank-reversal immunity. This methodology serves two objectives: firstly, it provides a statistical tool for interpreting decision-making processes for large samples of customers, or clients on markets; secondly, it provides a support for multiple-criteria ranking of alternatives in the presence of uncertainties. The on-going development of the approach, and several future research directions are also indicated.