Upper Performance Limits and Distribution Invariance for Surrogate Weights in MCDA

This paper proposes a simple approach to determining the upper performance limit (approximate the maximum hit ratio) for surrogate weight models in additive models of multi-criteria decision analysis. The approach is called the Approximate Maximum Hit Ratio (AMHR). As a partial result, simulations show that hit ratios resulting from so-called mean ordered weights as surrogate weight vectors resemble the AMHR reasonably well. Further, we scrutinise the case of different distributions for the sampling of alternative values, with the result that it seems to be invariant, i.e. the general behaviour of surrogate weight methods does not change significantly. We also study the use of different filters on the AMHR. Finally, the corresponding already well-performing methods (e.g., ROC, RS, and SR) show good overall results. Thus, we conclude that the existing methods are fairly effective and provide decision-makers (individual or in groups) with a valuable means of efficiently eliciting and dealing with imprecise criteria information.