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

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.