Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

In this paper, we introduce a fuzzy extension of a class of measures to compare clustering structures, namely, measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast with previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure.