Abstract
A basic problem in multi-criteria decision-making (MCDM) is to find a ranking for alternatives which are not directly comparable with each other. A number of different methods exists. In this paper, a new ranking method is proposed by turning a statistical function into an MCDM ranking function. In particular, cone distribution functions from multivariate statistics are used as ranking functions and their features are investigated. Our findings demonstrate that this procedure can be considered as an upgrade of the weighted sum ranking insofar as it absorbs a whole collection of weighted sums at once instead of fixing a particular one in advance. The new ranking–in contrast to a pure weighted sum ranking–is also able to detect ‘‘non-convex’’ parts of the Pareto frontier. The rank reversal phenomenon is studied, and it is explained why it might even be useful for analyzing the ranking procedure. The ranking is extended to sets providing unary indicators for set preferences which establishes the link between set optimization methods and set-based multi-objective optimization. This also provides a new tool for evaluating the outcomes of evolutionary algorithms for multi-criteria optimization. The proposed method has implications for preferences learning and categorization of multi-dimensional data points, both with respect to an underlying non-complete order relation.