A multi-attribute ranking solutions confirmation procedure

Ranking problems arise from the knowledge of several binary relations defined on a set of alternatives, which we intend to rank. In a previous work, the authors introduced a tool to confirm the solutions of multi-attribute ranking problems as linear extensions of a weighted sum of preference relations. An extension of this technique allows the recognition of critical preference pairs of alternatives, which are often caused by inconsistencies. Herein, a confirmation procedure is introduced and applied to confirm the results obtained by a multi-attribute decision methodology on a tender for the supply of buses to the Porto Public Transport Operator. © 2005 Springer Science + Business Media, Inc.