Approaches to approximation reducts in inconsistent decision tables

In this paper, two new concepts of lower approximation reduction and upper approximation reduction are introduced. Lower approximation reduction is the smallest attribute subset that preserves the lower approximations of all decision classes, and upper approximation reduction is the smallest attribute subset that preserves the upper approximations of all decision classes. For an inconsistent DT, an upper approximation consistent set must be a lower approximation consistent set, but the converse is not true. For a consistent DT, they are equivalent. After giving their equivalence definitions, we examine the judgement theorem and discernibility matrices associated with the two reducts, from which we can obtain approaches to knowledge reduction in inconsistent decision tables.