The use of role engineering has grown in importance with the expansion of highly abstracted access control frameworks in organizations. In particular, the use of role mining techniques for the discovery of roles from previously deployed authorizations has facilitated the configuration of such frameworks. However, the literature lacks from a clear basis for appraising and leveraging the learning outcomes of the role mining process. In this paper, the authors provide such a formal basis. They compare sets of roles by projecting roles from one set into the other set. This approach allows to measure how comparable the two configurations of roles are, and to interpret each role. They formally define the problem of comparing sets of roles, and prove that the problem is NP-complete.