Towards scalable algorithms for discovering rough set reducts

Rough set theory allows one to find reducts from a decision table, which are minimal sets of attributes preserving the required quality of classification. In this article, we propose a number of algorithms for discovering all generalized reducts (preserving generalized decisions), all possible reducts (preserving upper approximations) and certain reducts (preserving lower approximations). The new RAD and CoreRAD algorithms, we propose, discover exact reducts. They require, however, the determination of all maximal attribute sets that are not supersets of reducts. In the case, when their determination is infeasible, we propose GRA and CoreGRA algorithms, which search approximate reducts. These two algorithms are well suited to the discovery of supersets of reducts from very large decision tables.