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 “$\oplus$”, 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.

概念的最小和最大描述是基于覆盖的粗糙集中的两个重要概念。基于覆盖的粗糙集中的许多问题（例如归约，近似等）都与它们有关。众所周知，当使用集合表示来在覆盖近似空间的大规模中计算最小和最大描述时，这既费时又容易出错。为了解决这个问题，已经提出了基于矩阵的方法，其中可以通过计算机方便地实现计算。在本文中，由于需要从大规模覆盖信息系统中发现知识，并且受先前研究工作的启发，我们提出了两种新颖的基于矩阵的方法来计算基于覆盖的粗糙集中的最小和最大描述，这可以减少传统方法的计算复杂性。$\oplus$”，我们提出了一种新的基于矩阵的方法，称为“方法1”，用于计算最小和最大描述，该方法不需要比较两个矩阵中的元素。其次，通过使用覆盖图中元素之间包含的二进制关系，我们提出了另一种方法来计算最小和最大描述。最后，我们进行实验比较，以显示所提出的方法在六个UCI数据集上的计算效率。实验结果表明，所提出的方法是有希望的，并且可以与其他测试方法进行比较。