Dependence-space-based attribute reduction in consistent decision tables

This paper proposes a novel approach to attribute reduction in consistent decision tables within the framework of dependence spaces. For a consistent decision table $$(U,A\cup \{d\}),$$ an equivalence relation r on the conditional attribute set A and a congruence relation R on the power set of A are constructed, respectively. Two closure operators, Tr and TR, and two families of closed sets, $${\mathcal C}_r$$ and $${\mathcal C}_R,$$ are then constructed with respect to the two equivalence relations. After discussing the properties of $${\mathcal C}_r$$ and $${\mathcal C}_R,$$ the necessary and sufficient condition for $${\mathcal C}_r={\mathcal C}_R$$ is obtained and employed to formulate an approach to attribute reduction in consistent decision tables. It is also proved, under the condition $${\mathcal C}_r={\mathcal C}_R,$$ that a relative reduct is equivalent to a $$R$$-reduction defined by Novotny and Pawlak (Fundam Inform 16:275–287, 1992).