Evaluating and Comparing Soft Partitions: An Approach Based on Dempster–Shafer Theory

In evidential clustering, cluster-membership uncertainty is represented by Dempster–Shafer mass functions. The notion of evidential partition generalizes other soft clustering structures such as fuzzy, possibilistic, or rough partitions. In this paper, we propose two extensions of the Rand index for evaluating and comparing evidential partitions, called similarity and consistency indices. The similarity index is suitable for measuring the closeness of two soft partitions, whereas the consistency index allows one to assess the agreement, or lack of conflict, between a soft partition and the true hard partition. Simulation experiments illustrate some applications of these indices.