On Normalizing Fuzzy Coincidence Matrices to Compare Fuzzy and/or Possibilistic Partitions with the Rand Index

Most already existing indices used to compare two strict partitions with different number of clusters are based on coincidence matrices. To extend such indices to fuzzy partitions, one can define fuzzy coincidence matrices by means of triangular norms. It has been shown this can require some kind of normalization to reinforce the corresponding indices. We propose in this paper a generic solution to perform this normalization considering the generators of the used triangular norms. Although the solution is not index-dependant, we focus on the Rand index and some of its fuzzy counterparts.