Matrix-based set approximations and reductions in covering decision information systems

Abstract

In this paper, we propose matrix-based methods for computing set approximations and reducts of a covering decision information system. First, some matrices and matrix operations are introduced to compute the set approximations, and further to compute the positive region of a covering decision system. Second, the notions of minimal and maximal descriptions in a covering decision system are proposed which can be easily obtained by the matrix-based methods. Then the minimal and maximal descriptions are employed to construct a new discernibility matrix. We claim that by using the minimal and maximal descriptions, we can dramatically reduce the total number of discernibility sets that need to be computed in the new discernibility matrix, thus dramatically reducing the computational time for finding all reducts and one optimal reduct of a covering decision system. In the end, several numerical experiments are conducted to examine the efficiency of the proposed methods.