The multiplicative AHP, SMART and ELECTRE in a common context

This paper presents a comparative study of three popular methods for multicriteria decision analysis based on a particular model of human preferential judgement. Since decisions are invariably made within a given context, we model relative preferences as ratios of increments or decrements in an interval on an axis of desirability. Next we sort the ratio magnitudes into a small number of categories, represented by numerical values on a geometric scale. We explain why the analytic hierarchy process (AHP) and the French collection of ELECTRE methods, typically based on pairwise comparison methods, are concerned with categories of ratio magnitudes, whereas the simple multiattribute rating technique (SMART) essentially uses orders of magnitude of these ratios. This phenomenon provides a common basis for the analysis of the methods in question and for a cross-validation of their results. We illustrate the approach via a well-known case study, the choice of a location for a nuclear power plant. We conclude by discussing the scope of the comparative study.