A systematic study on attribute reduction with rough sets based on general binary relations

Attribute reduction is considered as an important preprocessing step for pattern recognition, machine learning, and data mining. This paper provides a systematic study on attribute reduction with rough sets based on general binary relations. We define a relation information system, a consistent relation decision system, and a relation decision system and their attribute reductions. Furthermore, we present a judgment theorem and a discernibility matrix associated with attribute reduction in each type of system; based on the discernibility matrix, we can compute all the reducts. Finally, the experimental results with UCI data sets show that the proposed reduction methods are an effective technique to deal with complex data sets.