Set partition principles revisited

Abstract

Two principles for partitioning a set into groups are revisited in the paper. In addition to the well-known cluster analysis principle, two other set partition principles are considered: the similarity principle and the antictuster principle. In similarity principle the initial set is partitioned into groups, so that each group possesses property similar to the properly of the initial set. In anticluster principle, the initial set is partitioned into groups in such a way, that elements belonging to each group are dissimilar but the groups are similar. If a criterial function for quality of partitioning is defined on the set of all possible partitions, then the set partitioning problem is to construct such a partition, for which the criterial function is extrernal. Optimization procedures are suggested for both partitioning principles.