Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.

中文翻译：

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软预粗糙集及其在决策中的应用

软粗糙集模型表示可以将许多实际数据连接到的不同数学模型。实际上，该理论代表了软集合理论和粗糙集合理论之间的联系。本文的主要目的是介绍一种新的方法来修改和推广软粗糙集。我们正在讨论和探索这些方法的基本属性。此外，我们将建议的方法用作不确定数据的数学建模并处理歧义。比较了所提出的方法和先前的方法。最后，说明了建议的近似值在COVID-19诊断决策中的医学应用。此外，我们根据这些概念开发了一种算法，并将其应用于决策问题，以证明所提出方法的适用性。