Multi-criteria decision making via multivariate quantiles

A novel approach for solving a multiple judge, multiple criteria decision making (MCDM) problem is proposed. The ranking of alternatives that are evaluated based on multiple criteria is difficult, since the presence of multiple criteria leads to a non-total order relation. This issue is handled by reinterpreting the MCDM problem as a multivariate statistics one and by solving it via set optimization methods. A function that ranks alternatives as well as additional functions that categorize alternatives into sets of "good" and "bad" choices are presented. Moreover, the paper shows that the properties of these functions ensure a logical and reasonable decision making process.