Supporting the robust ordinal regression approach to multiple criteria decision aiding with a set of representative value functions

TL;DR

This paper introduces a new methodology to represent robust ordinal regression results using a family of representative value functions, enhancing clarity in decision-making preferences in multiple criteria decision aiding.

Contribution

It proposes a novel approach to depict robust ordinal regression outcomes with representative value functions, aiding decision makers' understanding.

Findings

Provides a set of representative value functions satisfying specific preference conditions.

Enhances interpretability of robust ordinal regression results for decision makers.

Supports constructive discussion in multiple criteria decision aiding.

Abstract

In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions are satisfied: 1) if for all compatible value functions $a$ is evaluated not worse than $b$ and for at least one value function $a$ has a better evaluation, then the evaluation of $a$ is greater than the evaluation of $b$ for all representative value functions; 2) if there exists one compatible value function giving $a$ an evaluation greater than $b$ and another compatible value function giving $a$ an evaluation smaller than $b$, then there are also at least one representative function giving a better evaluation to $a$ and another representative value function giving $a$ an evaluation smaller than $b$. This family of representative value functions intends to provide the Decision Maker (DM) a more clear idea of the preferences obtained by the compatible value functions, with the aim to support the discussion in constructive approach of Multiple Criteria Decision Aiding.