Incremental approaches to knowledge reduction of covering decision information systems with variations of coverings

In practical situations, calculating approximations of concepts is the central step for knowledge reduction of dynamic covering decision information system, which has received growing interests of researchers in recent years. In this paper, the second and sixth lower and upper approximations of sets in dynamic covering information systems with variations of coverings are computed from the perspective of matrix using incremental approaches. Especially, effective algorithms are designed for calculating the second and sixth lower and upper approximations of sets in dynamic covering information systems with the immigration of coverings. Experimental results demonstrate that the designed algorithms provide an efficient and effective method for constructing the second and sixth lower and upper approximations of sets in dynamic covering information systems. Two examples are explored to illustrate the process of knowledge reduction of dynamic covering decision information systems with the covering immigration.