Geometric consistency index for interval pairwise comparison matrices
针对决策者无法给出精确判断时的区间成对比较矩阵，提出平均几何一致性指标，并构建优化模型降低不一致性，同时最小化信息损失和控制不确定性，最后通过数值例子验证可行性。
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.