Abstract: :In inconsistent incomplete decision systems (IIDSs),some tolerance classes in tolerance partition overlap more than one decision class,so asto produce complex overlapping subsets between tolerance partition and decision partition.This leads to occurrence of many concepts of reductions in IIDSs and makes the reduction problem more complex.Therefore,the concept of maximum distributionreduct is extended to IIDSs in this paper,then,some of its properties in IIDSsare analyzed.It is found that,unlike other reducts' core attributes,the maximumdistribution reduct's core attribute does not have inheritable trait.This shows that the maximum distribution reduct can not be generated by adding attributes tocore attribute set.But,by using the testing and deleting operations repeatedly,an algorithm for computing the maximum distribution reduct in IIDSs is successfully constructed in this paper.The algorithm's description and its complexity analysis are also given.Finally,the proposed algorithm is illustrated to be effective and be of practical significance through sample analysis.

Key words: decision system, inconsistency, incompleteness, maximumdistribution reduct