Dynamic composite decision-theoretic rough set under the change of attributes

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 data, numerical dada, interval-valued data and set-valued data. The extended rough sets can deal with single type 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. Subsequently, we present a novel matrix-based approach to compute the upper and lower approximations in proposed model. Moreover, we propose the incremental updating mechanisms and algorithms under the addition and deletion of attributes. Finally, experimental valuations are conducted to illustrate the efficiency of proposed method and algorithms.