Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
On Nearly Basic Rough Sets and Their Medical Applications
El-Gayar, M. A., Kandil, S. A., El-Bably, M. K.
Corresponding Email: mkamel_bably@yahoo.com
Received date: 18 February 2025
Accepted date: 12 October 2025
Abstract:
The rapid advancement of Pawlak's rough set (PRS) theory has motivated researchers to develop enhanced methodologies for decision-making, including applications in medical diagnosis particularly in identifying disease risk factors. The primary objective of this study is to introduce new mathematical techniques based on basic rough sets (as defined by Abu-Gdairi et al., 2021), employing nearly open concepts to enhance precision. Specifically, we propose the framework of nearly basic rough sets, incorporating pre-, semi-, and γ-approximations, and present three distinct approximation methods. Their fundamental properties and interrelationships are systematically examined. The proposed approaches demonstrate superior accuracy compared with existing methods, as confirmed through both theoretical analysis and illustrative case studies. In particular, the application to COVID-19 diagnosis yielded an accuracy of 100% in the tested case. Moreover, we introduce a mathematical algorithm suitable for implementation in programming languages, thereby facilitating broader applications in medical research, economic modeling, and related theoretical domains.
Keywords: \(\mathfrak{b}-\)neighborhoods; \(\mathfrak{b}-\)rough sets; Nearly \(\mathfrak{b}-\)rough sets; COVID-19 variants.
