AbstractThe application of compromise solutions to discrete multi-objective problems brings about some technical flexibilities, such as the selection of distance function for computing both normalized attribute ratings and distances between two alternatives, and the choice between the ideal and negative-ideal alternatives for implementing the axiom of choice. These flexibilities are undesirable, since the method may yield conflicting preference-alternative rankings, depending on parameter choice. This paper introduces a credibility measurement of distance function and takes a broader concept of the axiom of choice in order to reconcile disagreement among compromise solutions.