Grained matrix and complementary matrix: Novel methods for computing information descriptions in covering approximation spaces

Abstract

As two important tools of information descriptions, minimal description (MinD) and maximal description (MaxD) are used to eliminate redundant information when describing an object in covering-based rough sets (CbRSs). Hence, there are many key issues (such as reductions, neighborhoods and approximations) have to do with them in CbRSs. However, it is complicated and time-consuming to use set approaches to compute them in a large cardinal covering approximation space. So the matrix approaches have been used to calculate them by which computers can implement the corresponding calculations easily. Based on the previous research work and inspired by the demand of knowledge discovery under large scale covering information systems, we propose two new matrix methods to calculate MinD and MaxD in CbRSs in this paper. Firstly, a note on the existing methods (matrix approach-1 and approach-2) is presented. Secondly, a new matrix, called grained matrix, is presented. After combining grained matrices and the mean of “sum”, the new matrix approach-1 is presented to calculate MinD and MaxD. Thirdly, three new matrix operations and the notion of complementary matrix are given which can simplify the calculation of computers. Based on new operations, we present the new matrix approach-2 to compute MinD and MaxD. Finally, the computational efficiency of the presented approaches are shown and compared with other methods by experiments on several UCI data sets.