Coarsening of fuzzy partitions

A vague partition U of a finite universal set X into c clusters, where each cluster is described by a fuzzy set on X, is considered. The concept of p-level sets [3] of fuzzy sets is extended to p-level matrices of fuzzy partitions. A method of gradual coarsening of U based on a sequence of p-level matrices derived from the membership grades of clusters of U is suggested. Modifications of p-level matrices to extended p-level matrices and to strict p-level matrices are proposed.