Attribute reduction of formal decision contexts

Rough set theory and formal concept analysis are two complementary mathematical tools for data analysis. In this paper, based on object oriented concept lattice, we first propose one kind of consistency of conditional concepts and decision concepts. Subsequently, notions of consistent set and reduct set of attributes are introduced, and some judgment theorems for consistent set are presented. Finally, discernibility matrix is employed to determine consistent sets and calculate reduct sets in consistent formal decision contexts.