The classic theory of Rough sets is based on incomplete information systems. In practicing, decision tables are, however, usually incomplete due to the causes of data outputting or processing. That is to say, there are often default values. In order to deal with incomplete systems, Kryszkiewicz put a Rough sets model on the basis of error tolerance relations. According to this model, constructing discernibility matrixes and discernibility functions is the familiar approach by the current knowledge reduction algorithms. By this means, all reductions can work out. But it has been proved that it ...
