Abstract: For a consistent information system,the definitions of two closure operators C(R)and C(r) on the power set of conditional attribute set were first defined respectively,and then the properties of two closed set families C_r and CR were also discussed.The relationships among C_r,CR and the set of all discernibility attribute sets Ω were examined,from which we provided a simple method to attribute reduction in consistent decision table defined in reference [4]．Meanwhile,the sufficient and necessary condition of C_r=CR was proved．Finally,we proved that under condition C_r=CR,the proposed method is equivalent to those in references [4] and [7].

Key words: Attribute reduction,Closure operator,Rough set,Equivalence relation,Information system