论文标题
对成对比较矩阵的词素最佳完成和缺少条目的矩阵
A lexicographically optimal completion for pairwise comparison matrices with missing entries
论文作者
论文摘要
估计缺失判断是许多多标准决策技术的关键组成部分，尤其是在分析层次结构过程中。受Koczkodaj不一致索引的启发，以及一种称为Nucleolus的合作游戏理论的解决方案概念，目前的研究提出了为此目的的新算法。特别是，丢失的值被变量代替，最不一致的三合会的不一致首先减少，然后是第二最不一致的三合会的不一致之处，依此类推。证明所建议的词典最佳完成的独特性的必要条件被证明是一个简单的图理论概念：与成对比较相关的无向图，其中边缘代表已知元素，应连接。至关重要的是，我们的方法不取决于任意选择的不一致措施，因为本质上存在一个合理的三合会不一致索引。
Estimating missing judgements is a key component in many multi-criteria decision making techniques, especially in the Analytic Hierarchy Process. Inspired by the Koczkodaj inconsistency index and a widely used solution concept of cooperative game theory called the nucleolus, the current study proposes a new algorithm for this purpose. In particular, the missing values are substituted by variables, and the inconsistency of the most inconsistent triad is reduced first, followed by the inconsistency of the second most inconsistent triad, and so on. The necessary and sufficient condition for the uniqueness of the suggested lexicographically optimal completion is proved to be a simple graph-theoretic notion: the undirected graph associated with the pairwise comparisons, where the edges represent the known elements, should be connected. Crucially, our method does not depend on an arbitrarily chosen measure of inconsistency as there exists essentially one reasonable triad inconsistency index.
