  In comparing clustering partitions, Rand index (RI) and Adjusted Rand index
(ARI) are commonly used for measuring the agreement between the partitions.
Both these external validation indexes aim to analyze how close is a cluster to
a reference (or to prior knowledge about the data) by counting corrected
classified pairs of elements. When the aim is to evaluate the solution of a
fuzzy clustering algorithm, the computation of these measures require
converting the soft partitions into hard ones. It is known that different fuzzy
partitions describing very different structures in the data can lead to the
same crisp partition and consequently to the same values of these measures. We
compare the existing approaches to evaluate the external validation criteria in
fuzzy clustering and we propose an extension of the ARI for fuzzy partitions
based on the normalized degree of concordance. Through use of real and
simulated data, we analyze and evaluate the performance of our proposal.
