Multi-criteria decision making via multivariate quantiles

TL;DR

This paper introduces a new multivariate quantile-based method for multi-criteria decision making, transforming the problem into a multivariate statistical framework to improve ranking and categorization of alternatives.

Contribution

It proposes a novel set optimization approach for MCDM, providing functions that rank and categorize alternatives with logical consistency.

Findings

Provides a new multivariate quantile-based ranking method

Ensures logical and consistent decision-making process

Offers functions for categorizing alternatives into 'good' and 'bad' sets

Abstract

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.