On matrix representation of three types of covering-based rough sets

Rough set theory is a useful tool for dealing with inexact, uncertain or vague knowledge of information systems. The core concepts of classical rough sets are lower and upper approximation operators based on equivalence relations. However, it is inefficient to compute the lower and upper approximations using set operations. Matrix is widely used in scientific computation. In this paper, three types of covering-based rough set operators are represented through matrix. In the first part, a matrix representation of a covering is given. Moreover, in order to construct a matrix representation of a neighborhood, two operators are introduced. Then the relationship of the matrix representation of a neighborhood between a covering and its reduct is studied. In the second part, three types of lower and upper approximation operators based on neighborhood are represented by matrix. Moreover, the relationship among them is also discussed. In a word, the matrix representation provides a new and effective approach to the computation of approximation operators in rough sets.