不完全两两比较矩阵和加权方法
Incomplete pairwise comparison matrices and weighting methods
摘要：
一类特殊的偏好，给出了一个有向无圈图，被认为是。它们由不完整的成对比较矩阵表示，因为只有部分信息可用：对于某些对，图中没有给出比较。加权方法满足线性顺序保持性质，如果它总是导致排序，使得直接优选于另一个的备选方案不具有较低的排序。我们研究两个程序，特征向量法和对数最小二乘法是否满足这一公理。这两种加权方法都破坏了线性序保持，而且，根据特征向量方法的排名取决于所选择的不完全成对比较表示。
英文摘要：
A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.
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