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Inconsistent and contradictory judgements in pairwise comparison method in the AHP

机译：AHP中成对比较方法中的矛盾判断和矛盾判断

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The aim of this paper is to show the relationship between inconsistent and contradictory matrices of data obtained as a result of the pairwise comparison of factors in the sense of the analytic hierarchy process. The consistency check is performed to ensure that judgements are neither random nor illogical. This paper shows that even if a matrix will pass a consistency test successfully, it can be contradictory. Moreover an algorithm of checking contradictions is proposed. Scope and purpose A consistency of judgements in the pairwise comparison method in the analytic hierarchy process can be measured using the consistency index of judgement matrices. The consistency index is based on a judgement matrix rank. Depending on its value judgement matrices can be classified into two sets, namely a set of consistent and a set of inconsistent matrices. The paper introduces a new class of judgement matrices which is defined as contradictory and shows that a judgement matrix can be very closed to fully consistent in sense of the assumed consistency index but still to be contradictory.
机译：本文的目的是显示在层次分析法意义上因素成对比较的结果下，数据矩阵前后矛盾之间的关系。进行一致性检查以确保判断既不随机也不合逻辑。本文表明，即使矩阵成功通过一致性测试，也可能是矛盾的。此外，提出了一种检查矛盾的算法。范围和目的可以使用判断矩阵的一致性指标来衡量层次分析过程中成对比较方法中的判断一致性。一致性指标基于判断矩阵等级。根据判断矩阵的值，可以将其分为两套，即一组一致的矩阵和一组不一致的矩阵。本文介绍了定义为矛盾的一类新的判断矩阵，并表明，从假设的一致性指标来看，判断矩阵可以非常接近完全一致，但仍然是矛盾的。

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