Measures of rank correlation are commonly used in statistics to capture the degree of concordance between two orderings of the same set of items. Standard measures like Kendall's tau and Spearman's rho coefficient put equal emphasis on each position of a ranking. Yet, motivated by applications in which some of the positions (typically those on the top) are more important than others, a few weighted variants of these measures have been proposed. Most of these generalizations fail to meet desirable formal properties, however. Besides, they are often quite inflexible in the sense of committing to a fixed weighing scheme. In this paper, we propose a weighted rank correlation measure on the basis of fuzzy order relations. Our measure, called scaled gamma, is related to Goodman and Kruskal's gamma rank correlation. It is parametrized by a fuzzy equivalence relation on the rank positions, which in turn is specified conveniently by a so-called scaling function. This approach combines soundness with flexibility: it has a sound formal foundation and allows for weighing rank positions in a flexible way.

翻译：秩相关度量常用于统计学中，用于捕捉同一组物品的两种排序之间的一致性程度。标准度量如Kendall's tau和Spearman's rho系数对排序中的每个位置赋予同等重要性。然而，受某些应用（特别是顶部位置比其他位置更重要）的启发，已有研究者提出了这些度量的几种加权变体。但大多数此类推广未能满足理想的形式化性质，且往往因固守固定加权方案而缺乏灵活性。本文基于模糊序关系提出了一种加权秩相关度量，称为缩放伽马，它与Goodman和Kruskal的伽马秩相关系数相关联。该度量由秩位置上的模糊等价关系参数化，而该关系可通过所谓的缩放函数便捷地指定。该方法兼具严谨性与灵活性：既具有扎实的形式化基础，又能灵活地对秩位置进行加权。