Abstract
The rapid evolution of rough-set theory has prompted the need for enhanced methodologies in medical diagnostics, particularly regarding COVID-19 variant detection. This study introduces refined mathematical techniques based on topological structures (called nearly initial-rough sets) derived directly from initial-rough sets. Four categories of rough-set methodologies are presented, demonstrating heightened accuracy through comprehensive comparisons against existing methods. By leveraging these techniques, a rule-based classification system for COVID-19 variants is established, achieving 100 % accuracy measures through rigorous testing against real-world and computer-generated data. The implications of these advancements in medical diagnosis hold promise for future research, offering accessible and precise tools for variant identification and prediction. Using a medical application as a case study, we demonstrate superiority through comparative analyses, aligning mathematical results with medical data and showcasing the potential for broader applications beyond experts in topology. Furthermore, the study outlines an algorithm simplifying implementation, particularly in MATLAB, and suggests future explorations in medical, economic, and diverse theoretical frameworks to enhance applicability.