On the structure of reduction of information system

In this paper a deeper investigation on the structure of reduction of information system is presented. The definition of local reduction is proposed in information system to describe the minimal description of a definable set by attributes of the given information system. The local reduction can present more optimal description for single decision class than the existing relative reductions. It is proven that the core of reduction or relative reduction can be expressed as the union of the cores of local reductions. The discernibility matrix of reduction and relative reduction can be obtained by composing discernibility matrices of local reduction. So deep insight on the structure of reductions of rough sets is presented and the existing reductions of rough sets can be brought into the framework of local reduction.