Quantitative composite decision-theoretic rough set

In practical decision-making, we prefer to characterize the uncertain problems with the hybrid data, which consists of various types of data, e.g., categorical, numerical, set-valued and interval-valued. The extended rough sets can deal with single types of data based on specific binary relation, including the equivalence relation, neighborhood relation, partial order relation, tolerance relation, etc. However, the fusion of these relations is a significant challenge task in such composite information table. To tackle this issue, this paper proposes the intersection and union composite relation, and further introduces a quantitative composite decision-theoretic rough set model. Moreover, we present a novel matrix-based approach to compute the upper and lower approximations in proposed model. Finally, an numerical example is conducted to illustrate the efficiency of proposed method.