In comparing clustering partitions, the Rand index (RI) and the adjusted Rand index (ARI) are commonly used for measuring the agreement between partitions. Such external validation indexes can be used to quantify how close the clusters are to a reference partition (or to prior knowledge about the data) by counting classified pairs of elements. To evaluate the solution of a fuzzy clustering algorithm, several extensions of the Rand index and other similarity measures to fuzzy partitions have been proposed. An extension of the ARI for fuzzy partitions based on the normalized degree of concordance is proposed. The performance of the proposed index is evaluated through Monte Carlo simulation studies.

中文翻译：

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Adjusted Concordance Index：Adjusted Rand Index to Fuzzy Partitions

在比较聚类分区时，通常使用 Rand 指数 (RI) 和调整后的 Rand 指数 (ARI) 来衡量分区之间的一致性。通过对分类的元素对进行计数，此类外部验证索引可用于量化集群与参考分区（或有关数据的先验知识）的接近程度。为了评估模糊聚类算法的解决方案，已经提出了对模糊分区的兰德指数和其他相似性度量的几种扩展。提出了基于归一化一致性程度的模糊分区的 ARI 扩展。建议指标的性能通过蒙特卡罗模拟研究进行评估。