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This article deals with approaches to knowledge reductions in inconsistent information systems (ISs). The main objective of this work was to introduce a new kind of knowledge reduction called a maximum distribution reduct, which preserves all maximum decision classes. This type of reduction eliminates the harsh requirements of the distribution reduct and overcomes the drawback of the possible reduct that the derived decision rules may be incompatible with the ones derived from the original system. Then, the relationships among the maximum distribution reduct, the distribution reduct, and the possible reduct were discussed. The judgement theorems and discernibility matrices associated with the three reductions were examined, from which we can obtain approaches to knowledge reductions in rough set theory (RST). © 2003 Wiley Periodicals, Inc.