Knowledge reduction of dynamic covering decision information systems when varying covering cardinalities

In covering-based rough set theory, non-incremental approaches are time-consuming for performing knowledge reduction of dynamic covering decision information systems when the cardinalities of coverings change as a result of object immigration and emigration. Because computing approximations of sets is an important step for knowledge reduction of dynamic covering decision information systems, efficient approaches to calculating the second and sixth lower and upper approximations of sets using the type-1 and type-2 characteristic matrices, respectively, are essential. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings whose cardinalities vary with the immigration and emigration of objects. We also design incremental algorithms to compute the second and sixth lower and upper set approximations. Experimental results demonstrate that the incremental approaches effectively improve the efficiency of set approximation computation. Finally, we employ several examples to illustrate the feasibility of the incremental approaches for knowledge reduction of dynamic covering decision information systems when increasing the cardinalities of coverings.