三元组不一致指数的公理化
Axiomatizations of inconsistency indices for triads
摘要：
成对比较矩阵往往表现出不一致性，因此，许多指标已被建议来衡量他们的偏差从一个一致的矩阵。最近提出了一组公理，要求满足任何合理的不一致性指数。这个集合似乎并不详尽，因为通过一个例子来说明，因此通过添加两个新属性来扩展它。所有公理都被认为是三元组的集合，具有三个选择的成对比较矩阵，这是最简单的不一致情况。我们选择的逻辑上独立的属性，并证明他们的特点，也就是说，唯一确定的不一致性排名引起的大多数不一致性指标，在这个限制域上一致。由于黑社会起着突出的作用，在一些不一致的指标，我们的研究结果也可以有助于测量不一致的两两比较矩阵有三个以上的替代品。
英文摘要：
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any reasonable inconsistency index. This set seems to be not exhaustive as illustrated by an example, hence it is expanded by adding two new properties. All axioms are considered on the set of triads, pairwise comparison matrices with three alternatives, which is the simplest case of inconsistency. We choose the logically independent properties and prove that they characterize, that is, uniquely determine the inconsistency ranking induced by most inconsistency indices that coincide on this restricted domain. Since triads play a prominent role in a number of inconsistency indices, our results can also contribute to the measurement of inconsistency for pairwise comparison matrices with more than three alternatives.
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