Theoretical study on attribute reduction of rough set theory: comparison of algebra and information views

Attribute reduction is an important issue of rough set theory and has already been separately studied in algebra view and information view. However, conceptions of attribute reduction based on the two views are not necessarily equivalent, they are the same only in consistent decision systems. In this paper, we theoretically study the quantitative relation between some basic notions of rough set theory like attribute reduction, attribute significance and attribute core defined in the two views. The results show that the relation between those corresponding conceptions in algebra view and information view is typically inclusion rather than equivalence, and its reason is that information view restricts attributes and systems more specifically than algebra view. The results are necessary and significant for the development and application of attribute reduction methods.