Matrix computation for rule extraction in inconsistent decision tables

Rule extraction from decision tables is one of the most important tasks in rough set theory. Usually, it is difficult to keep an information system consistent. Therefore, how to extract rules from inconsistent decision tables is valuable. The decision matrices based on distribution reduction, maximum distribution reduction and assignment reduction are defined first. Then rule extraction from inconsistent decision tables is realized by comparing the decision matrix and the matrix determined by condition attribute subsets. Finally, an experiment proves the validity of this method. The method shows the merits in extracting all rules from inconsistent decision tables and achieving expected reduction.