On the coincidence of optimal completions for small pairwise comparison matrices with missing entries
研究了在小型成对比较矩阵中，使用两种不一致性指标（Saaty指标和几何不一致性指标）进行缺失值补全时，最优填充结果是否一致。发现对于四阶及以下矩阵两者一致，五阶及以上则不一定。
Abstract Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely used inconsistency indices for this purpose are Saaty’s inconsistency index and the geometric inconsistency index, which are closely related to the eigenvector and the logarithmic least squares priority deriving methods, respectively. The two measures are proven to imply the same optimal filling for incomplete pairwise comparison matrices up to order four but not necessarily for order at least five.