Validity Measures for Fuzzy Partitions

The validation of cluster methods provides important information on how to select and apply cluster methods. In the crisp case the indices of Rand (1971) and Fowlkes and Mallows (1983) are commonly used for this purpose. The application of these indices to the comparison of fuzzy partitions has been discussed in this paper. The paper shows that a comparison of truly fuzzy partitions does not make sense if these classical measures are used. A new measure, the MC index, which allows to compare fuzzy partitions directly, has therefore been proposed. A simulation study has been carried out to investigate the properties of these measures. The results show the advantages of the MC index over the classical measures: the MC index is independent of the number of objects and classes and shows no variation with respect to object displacements.