Attribute reduction in formal decision contexts has become one of the key issues in the research and development of formal concept analysis (FCA) and its applications. As far as we know, however, most of the existing reduction methods for formal decision contexts are time-consuming especially for the large-scale data. This paper investigates the attribute reduction method for large-scale formal decision contexts. The computation of a discernibility matrix is an important step in the development of the corresponding reduction method. A simple and powerful method to efficiently calculate the discernibility matrix of formal decision contexts is first presented. In addition, a heuristic algorithm for searching the optimal reduct is then proposed. Thirdly, as an application of the new results, we discuss the problem of finding the minimal subbases of finite topological spaces. It has shown that the method of attribute reduction in formal decision contexts can be used to obtain all the minimal subbases of a finite topological space. Furthermore, we present an algorithm for computing the minimal subbase of a topological space, based on the attribute reduction method proposed in this paper. Finally, two groups of experiments are carried out on some large-scale data sets to verify the effectiveness of the proposed algorithms.

形式决策上下文中的属性约简已成为形式概念分析（FCA）及其应用研究和开发中的关键问题之一。然而，据我们所知，大多数现有的用于正式决策上下文的约简方法非常耗时，尤其是对于大规模数据而言。本文研究了大规模形式决策环境下的属性约简方法。区分矩阵的计算是相应归约方法开发中的重要一步。首先介绍了一种简单有效的方法，可以有效地计算形式决策上下文的可分辨矩阵。另外，提出了一种搜索最优归约的启发式算法。第三，作为新结果的应用，我们讨论寻找有限拓扑空间的最小底基的问题。结果表明，形式决策上下文中的属性约简方法可用于获得有限拓扑空间的所有最小子库。此外，我们基于本文提出的属性约简方法，提出了一种计算拓扑空间最小子库的算法。最后，在一些大型数据集上进行了两组实验，以验证所提出算法的有效性。基于本文提出的属性约简方法。最后，在一些大型数据集上进行了两组实验，以验证所提出算法的有效性。基于本文提出的属性约简方法。最后，在一些大型数据集上进行了两组实验，以验证所提出算法的有效性。