关于成对比较法中差异的注记
Notes on discrepancy in the pairwise comparisons method
摘要：
当需要确定不同概念（备选方案）之间的相对顺序时，成对比较方法是一种方便的工具。该方法的一个流行的实现是基于解决成对比较矩阵的特征值问题。在这种情况下，采用成对比较矩阵的主特征向量的排序结果，而特征值用于确定不一致性指数。大量的研究已经致力于基于特征值的方法的临界分析。其中之一就是工作（Bana e Costa and Vansnick，2008）。在他们的工作中，作者定义了顺序保持（COP）的条件，并表明，即使是一个足够一致的成对比较矩阵，这个条件也不能满足。目前的工作为确定何时达到缔约方会议确定了更精确的标准。为了制定标准，使用差异因子来描述对排名过程的输入与排名结果有多远。
英文摘要：
The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the pairwise comparisons matrix. In such cases the ranking result the principal eigenvector of the pairwise comparison matrix is adopted, whilst the eigenvalue is used to determine the index of inconsistency. A lot of research has been devoted to the critical analysis of the eigenvalue based approach. One of them is the work (Bana e Costa and Vansnick, 2008). In their work authors define the conditions of order preservation (COP) and show that even for a sufficiently consistent pairwise comparisons matrices, this condition can not be met. The present work defines a more precise criteria for determining when the COP is met. To formulate the criteria a discrepancy factor is used describing how far the input to the ranking procedure is from the ranking result.
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