有和无连接的有序成对比较方法中的不一致性
Inconsistency in the ordinal pairwise comparisons method with and without ties
摘要：
成对比较备选方案是一种众所周知的排名创建方法。专家们被要求进行一系列的二元比较，然后使用数学方法，准备最终的排名。由于专家们进行的是个别评估，因此评估结果可能并不总是一致的。个人评估之间的不一致程度被广泛接受为衡量排名质量的一个指标。排名质量越高，其可信度就越高。确定配对比较之间的不一致性水平的一种方法是计算不一致性指数的值。最早和最广泛的不一致性指标之一是由Kendall和Babington Smith定义的一致性系数。在他们的工作中，作者考虑了二元成对比较，即，个别比较的结果只能是：好或坏。所提出的工作扩展了肯德尔和巴宾顿史密斯指数的配对比较与领带。因此，这种扩展允许决策者确定成对比较集合的不一致性，其中结果也可以是“相等的”。“这篇文章包含了一个定义和分析的最不一致的一组成对比较有和没有关系。它还表明，最不一致的一组两两比较领带代表了一个特殊的情况下，更一般的集合覆盖问题。
英文摘要：
Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual assessments, they may not always be consistent. The level of inconsistency among individual assessments is widely accepted as a measure of the ranking quality. The higher the ranking quality, the greater its credibility. One way to determine the level of inconsistency among the paired comparisons is to calculate the value of the inconsistency index. One of the earliest and most widespread inconsistency indexes is the consistency coefficient defined by Kendall and Babington Smith. In their work, the authors consider binary pairwise comparisons, i.e., those where the result of an individual comparison can only be: better or worse. The presented work extends the Kendall and Babington Smith index to sets of paired comparisons with ties. Hence, this extension allows the decision makers to determine the inconsistency for sets of paired comparisons, where the result may also be "equal." The article contains a definition and analysis of the most inconsistent set of pairwise comparisons with and without ties. It is also shown that the most inconsistent set of pairwise comparisons with ties represents a special case of the more general set cover problem.
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