Dependence-space-based attribute reduction in consistent decision tables

Abstract

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 ? {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, T r and T R , and two families of closed sets, C r and C R are then constructed with respect to the two equivalence relations. After discussing the properties of C r and C R the necessary and sufficient condition for C r = C R is obtained and employed to formulate an approach to attribute reduction in consistent decision tables. It is also proved, under the condition C r = C R that a relative reduct is equivalent to a R-reduction defined by Novotny and Pawlak (Fundam Inform 16:275-287, 1992). © 2010 Springer-Verlag.