Novel matrix-based approaches to computing minimal and maximal descriptions in covering-based rough sets

Abstract

Minimal and maximal descriptions of concepts are two important notions in covering-based rough sets. Many issues in covering-based rough sets (e.g., reducts, approximations, etc.) are related to them. It is well known that, it is time-consuming and error-prone when set representations are used to compute minimal and maximal descriptions in a large scale covering approximation space. To address this problem, matrix-based methods have been proposed in which calculations can be conveniently implemented by computers. In this paper, motivated by the need for knowledge discovery from large scale covering information systems and inspired by the previous research work, we present two novel matrix-based approaches to compute minimal and maximal descriptions in covering-based rough sets, which can reduce the computational complexity of traditional methods. First, by introducing the operation “sum” into the calculation of matrix instead of the operation “⊕”, we propose a new matrix-based approach, called approach-1, to compute minimal and maximal descriptions, which does not need to compare the elements in two matrices. Second, by using the binary relation of inclusion between elements in a covering, we propose another approach to compute minimal and maximal descriptions. Finally, we present experimental comparisons showing the computational efficiency of the proposed approaches on six UCI datasets. Experimental results show that the proposed approaches are promising and comparable with other tested methods.