How to score alternatives when criteria are scored on an ordinal scale

We address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale $E$. We show that in general, the ordinal scale $E$ has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. The paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focusses on describing practical algorithms and examples.