Computing random consistency indices and assessing priority vectors reliability

The paper deals with two crucial steps in multi-criteria decision analysis, that are consistency of the judgments and priority vectors for alternatives/criteria. From a side, several consistency indices are proposed for measuring the consistency of a Pairwise Comparison Matrix. From another one, conditions weaker than consistency, such as transitivity and weak consistency, are proposed for representing further levels of coherence of a Decision Maker when he/she expresses his/her preferences by means of reciprocal Pairwise Comparison Matrix. Firstly, in this paper, a simulation is performed in order to establish a relation between random consistency index and coherence level. Then, since weak consistency ensures reliability to priority vectors proposed in literature, a second simulation is performed in order to measure, in case of no weak consistency, the reliability of these priority vectors. (C) 2017 Elsevier Inc. All rights reserved.