Coherence of preferences, and the measurement of its violation, has been a long-standing issue in decision analysis. This paper continues the inquiry into coherence conditions for pairwise comparisons following a distance-based approach, in which the deviations from coherence conditions are measured on a continuous scale. Firstly, we consider eight coherence conditions already introduced in the literature and provide a complete study on their inclusion relations. Then, we consider four of these conditions and introduce optimization problems to quantify the extent of their violation.

中文翻译：

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成对比较的不一致性测度和相干条件之间的关系

在决策分析中，偏好的一致性及其违反程度的度量一直是一个长期存在的问题。本文继续基于基于距离的方法对成对条件进行探究，以进行成对比较，其中以连续尺度测量与相干条件的偏差。首先，我们考虑了文献中已经引入的八个相干条件，并对它们的包含关系进行了完整的研究。然后，我们考虑其中的四个条件，并引入优化问题以量化其违反程度。