Partitions, Coverings, Reducts and Rule Learning in Rough Set Theory

When applying rough set theory to rule learning, one commonly associates equivalence relations or partitions to a complete information table and tolerance relations or coverings to an incomplete table. Such associations are sometimes misleading.We argue that Pawlak threestep approach for data analysis indeed uses both partitions and coverings for a complete information table. A slightly different formulation of Pawlak approach is given based on the notions of attribute reducts of a classification table, attribute reducts of objects and rule reducts. Variations of Pawlak approach are examined.