Generalized Ordered Nano-Topological Rough Approximations for Decision-Making and COVID-19 Risk Assessment

Rough set theory is widely used to deal with uncertainty in information systems, but its classical form mainly depends on equivalence relations, which limits its use in many practical situations involving ordered or partially related data. In this work, we introduce a generalized rough approximation model based on neighborhood structures and partial order relations within an ordered nano-topological setting. The proposed approach defines new approximation operators that describe increasing and decreasing behaviors in ordered spaces. We study their main properties and show that the model offers more accurate approximations and smaller boundary regions compared with several existing approaches. To illustrate its effectiveness, the framework is applied to COVID-19 risk assessment, where medical indicators naturally involve uncertainty and partial ordering. The obtained results indicate that the proposed method can improve the identification of important risk factors and support more reliable decision-making in complex environments.