Finding minimal reducts from incomplete information systems

In real decision-making system, people often face huge amounts of data, hence the importance of knowledge reduction. There are a lot of methods to compute the minimal reducts in complete information systems. But for incomplete information systems, the research of this aspect is less or more difficult. Incomplete data sets may be transformed into complete data sets by similarity measures or by removing objects with unknown values before handling with them. But transforming incomplete data sets into complete data sets is only by what we have supposed, and may not accord with the fact. So it is necessary to find reducts directly from incomplete data sets without guessing unknown attribute values. A theorem is proved on the basis of binary discernible matrix and similarity relation. And a genetic algorithm based on this theorem is proposed for finding the minimal reducts from incomplete information systems. We also propose a genetic algorithm directly based on binary discernible matrix in incomplete information systems. Many experiments have been done towards the two methods and the results of the experiments have been analyzed, which have proved the efficiency of the two methods.