Exploring $\<i>beta$</i>-Basic Rough Sets and Their Applications in Medicine

Advancements in the rough set theory of Pawlak have opened new avenues for enhancing decision-making processes, particularly in identifying disease risk factors in medical diagnoses. While traditional rough set methodologies have provided a solid foundation, there is a continuous need for improvements to increase accuracy and reliability. This study introduces mathematical techniques grounded in basic rough sets, incorporating $\beta$-open concepts to enhance precision. We present nearly basic rough sets and $\beta$-basic-approximations ($\beta _b$-approximations), examining their core properties and interrelationships. Our findings reveal that these novel constructs offer superior accuracy compared to traditional methods. Both theoretical analysis and practical examples support this, with our approach achieving a 100% accuracy rate in the medical diagnosis of COVID-19. This significant improvement highlights the potential of the methods of us to outperform existing ones in terms of precision and reliability. The introduction of $\beta _b$-approximations represents a significant advancement in rough set theory, offering enhanced accuracy in decision-making applications. Our results indicate that these methods can substantially outperform traditional techniques, especially in critical areas such as medical diagnosis. Additionally, we provide a mathematical algorithm suitable for implementation in programming languages, facilitating future research and applications across various theoretical and applied fields. This work lays the groundwork for further exploration and utilization of advanced rough set methodologies in diverse domains.