Real-world applications now deal with enormous amounts of data, especially in the area of high dimensional features. In the present study, we provide an approach for the rough set which is simply* alpha open set (briefly, \(\mathop S\limits^{M*} - \alpha\) open set). This approach was used to introduce a new concept of separation axioms, from which fundamental properties and theorems of preservation were studied. The relationship between basic properties and preservation theorems was also discussed. New near continuous function definitions have also been developed and their characteristics have been discussed. Through an application presented in the work, the relationship between the simply* alpha open set and near continuous function was justified. The simply* alpha open set was studied by the rough set and accordingly new accuracies were obtained. Moreover, an accurate proposal was examined, which competes with that of the methods of Yao and Pawlak. To obtain the results, MATLAB software has been used.

现实世界的应用程序现在处理大量数据，尤其是在高维特征领域。在本研究中，我们提供了一种粗糙集的方法，它只是* alpha 开集（简言之，\(\mathop S\limits^{M*} - \alpha\)开集）。这种方法被用来引入分离公理的新概念，从中研究了基本性质和保存定理。还讨论了基本性质和保存定理之间的关系。还开发了新的近连续函数定义，并讨论了它们的特性。通过工作中提出的一个应用程序，简单* alpha 开集和近连续函数之间的关系被证明是合理的。粗糙集研究了 simple* alpha 开放集，从而获得了新的精度。此外，还审查了一个准确的建议，与姚和帕拉克的方法相媲美。为了获得结果，使用了 MATLAB 软件。