Partial attribute reduction approaches to relation systems and their applications

Attribute reduction has long been an active subject of research in rough set theory, and constitutes an important step in data analysis. A relation system is an extension of a typical information system. This paper proposes the concepts of X-lower and -upper approximation reductions, and develops corresponding reduction algorithms for general relation systems. By using these types of reduction, we derive lower and upper approximation reductions for relation decision systems. As a special case, we obtain a reduction algorithm for the positive region for decision tables. Finally, we provide two examples from the University of California-Irvine (UCI) datasets to verify our theoretical results.