Geometric consistency index for interval pairwise comparison matrices

Interval pairwise comparison matrices are widely accepted for practical decision making problems when the decision maker is unable to provide an exact judgment on the alternatives. However, as measuring the preference consistencies in pairwise comparison decision making problems is important, this paper proposes a new interval pairwise comparison matrix consistency measure, the average geometric consistency index, that assumes that the preference in a given interval follows the lognormal distribution. This geometric consistency measure accounts for the interval boundaries and uncertainties. As it is often difficult to rationally rank alternatives when interval pairwise comparison matrices are highly uncertain and/or inconsistent, we propose an optimization model to reduce the inconsistencies of these matrices while minimizing information loss and controlling uncertainties. An interval priority vector is derived to rank the alternatives. The feasibility and efficiency of the models are demonstrated using numerical examples.