Semi-monolayer covering rough set on set-valued information systems and its efficient computation

For set-valued information systems, there are many original dot-based approximation models based on tolerance relations and other developed tolerance relations. Because of the lack of efficient algorithms, they are not to accommodate the bigger and bigger set-valued information table. Therefore, it is a real challenge on how to efficiently calculate a high-quality approximation set in set-valued information systems. To address the challenge, we propose reliable approximation operators based on semi-monolayer covering for set-valued information systems. Benefiting from considerable research about tolerance rough set models and covering rough set models, the proposed approximation operators used a piecewise design to effectively reduce the negative effects of the set-valued records and provided high-quality approximation sets for set-valued information systems. Furthermore, the reliable semi-monolayer covering approximation sets are more easily granulated and efficiently calculated than before. Based on the equivalent granule-based forms, the corresponding granular algorithms are designed for the improved approximation sets. The experiments on some UCI data sets show the improved approximation sets are high quality and efficient computational in set-valued information systems.