Searching for Reductive Attributes in Decision Tables

Most decision support systems based on rough set theory are related to the minimal reduct calculation problem, which is NP-hard. This paper investigates the problem of searching for the set of useful attributes that occur in at least one reduct. By complement, this problem is equivalent to searching for the set of redundant attributes, i.e. the attributes that do not occur in any reducts of the given decision table. We show that the considered problem is equivalent to a Sperner system for relational data base system and prove that it can be solved in polynomial time. On the base of these theoretical results, we also propose two different algorithms for elimination of redundant attributes in decision tables.