How can one improve SAW and max-min multi-criteria rankings based on uncertain decision rules?

Abstract

The paper aims to improve a simple additive weighting method (SAW) and the max-min rule designed for M-DMC (multi-13 criteria decision making under certainty) based on already developed extensions for the Laplace and Wald rules (applied to one-criterion decision making under uncertainty, i.e., 1-DMU). Some evident analogies between scenario-based 1-DMU and M-DMC have been recently revealed in the literature, which gives the possibility to implement necessary amendments in M-DMC procedures, particularly in the multiple solutions case. The suggested modifications consist of applying additional decision tools (for SAW) and using the lexicographic approach (for the max-min rule). Thanks to them, options, treated as equivalent according to original M-DMC procedures, may obtain different ranks in the ranking. Such an improvement facilitates the decision making process. Both modified methods are illustrated by employing an example concerning the ranking creation for UE countries.