The measurement of coherence in the evaluation of criteria and its effects or ranking problems illustrated using a multicriteria decision method

This paper aims to pursue two closely connected purposes. The first is to provide a theoretical framework, based on coherence constraints, for a technique of multicriteria analysis that allows to convert a partial pre-order into a total pre-order. The second it to show the possibility of measuring statistically the amount of modification implicitly made to the evaluations concretely expressed in the binary comparisons in order to make them coherent. This information may be useful both to the decision-maker who may wish to redefine certain evaluation criteria, and to the user of the ranking obtained with the multicriteria method, in order to determine its reliability.