A new approach of soft rough sets and a medical application for the diagnosis of Coronavirus disease

<abstract><p>Rough set and soft set theories presents the mathematical foundations for studying decision making problems in different contexts. Some authors have established their own approaches regarding this theory, such as the "soft pre-rough approximation" and "soft $ \beta $-rough approaximation". In this study, the rationale and results of these two approaches were rigorously analyzed and it was concluded that they are the same. In addition, it was proven that some of the results established with the aforementioned approaches are not true, so we present two proposed modifications to the soft rough approximations, one of which represents an improvement in accuracy with respect to the exposed methods. The approaches addressed in this document were implemented to diagnose COVID-19 in a contextualized situation of a group of patients in Colombia, showing that our proposal obtained the highest accuracy. In addition, an algorithm was designed, which allows analyzing data with a larger universe and set of parameters than those presented in the theoretical and practical examples.</p></abstract>