On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables

Abstract

In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithmcomputing reducts of decision tables by relational database approach. LetDS = (U, C ∪ {d}) be a consistent decision table, we say that A ⊆ C is arelative reduct of DS if A contains a reduct of DS. Let s = <C ∪ {d} , F>be a relation schema on the attribute set C ∪ {d}, we say that A ⊆ C isa relative minimal set of the attribute d if A contains a minimal set of d.Let Qd be the family of all relative reducts of DS, and Pd be the family ofall relative minimal sets of the attribute d on s. We prove that the problem whether Qd ⊆ Pd is co-NP-complete. However, the problem whether Pd ⊆ Qd is in P .