两两比较不一致指标的公理化性质
Axiomatic properties of inconsistency indices for pairwise comparisons
摘要：
成对比较是一个众所周知的方法，用于表示决策者的主观偏好。评价它们的不一致性一直是一个广泛研究和讨论的话题，并在文献中提出了几个指标来执行这项任务。由于可接受的一致性水平与偏好的可靠性密切相关，因此选择合适的不一致性指数是决策过程中的一个关键阶段。使用不同的方法来衡量一致性必须仔细评估，因为它可以影响在实际应用中的决策结果。在本文中，我们提出了五个公理，旨在表征不一致性指数。此外，我们证明了文献中提出的一些指数满足这些公理，而其他人没有，因此，在我们看来，他们可能无法正确地评估不一致。
英文摘要：
Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in the literature to perform this task. Since an acceptable level of consistency is closely related with the reliability of preferences, a suitable choice of an inconsistency index is a crucial phase in decision making processes. The use of different methods for measuring consistency must be carefully evaluated, as it can affect the decision outcome in practical applications. In this paper, we present five axioms aimed at characterizing inconsistency indices. In addition, we prove that some of the indices proposed in the literature satisfy these axioms, while others do not, and therefore, in our view, they may fail to correctly evaluate inconsistency.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
