On Ordinal Information-Based Weighting Methods and Comparison Analyses

In this paper, we focus on weighting methods within multi-attribute utility/value theory (MAUT/MAVT). In these methods, the decision maker (DM) provides ordinal information about the relative importance of criteria, but also additional information concerning the strength of the differences between the ranked criteria, which can be expressed in different forms, including precise/imprecise cardinal information, ratio-based methods, a ranking of differences, a semantic scale, or preference statements. Although many comparison analyses of weighting methods based on ordinal information have been carried out in the literature, these analyses do not cover all of the available methods, and it is not possible to identify the best one depending on the information provided by the DM. We review the analyses comparing the performance of these weighting methods based on empirical and simulated data using different quality measures. The aim is to identify weighting methods that could be recommended for use in each situation (depending on the available information) or the missing comparison analyses that should be carried out to arrive at a recommendation. We conclude that in the case of additional information in the form of a semantic scale, the cardinal sum reciprocal method can definitively be recommended. However, when only ordinal information is provided by the DM and in cases where additional information is provided in the form of precise/imprecise cardinal information or a ranking of differences, although there are some outstanding methods, further comparison analysis should be carried out to recommend a weighting method.