Exploring $\beta$-Basic Rough Sets and Their Applications in Medicine

Authors

  • M. K. El-Bably Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt https://orcid.org/0000-0002-7779-2443
  • R. Abu-Gdairi Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
  • K. K. Fleifel Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 19117, Jordan
  • M. A. El-Gayar Department of Mathematics, Faculty of Science, Helwan University, Helwan 11795, Egypt

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5545

Keywords:

b-neighborhoods, b-rough sets, β_b-rough sets, COVID-19

Abstract

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.

Author Biography

  • M. K. El-Bably, Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

    Mostafa K. El-Bably
    He received his Master's degree in Pure Mathematics (Topology) from the Faculty of Science, Tanta University, Egypt, in 2008, focusing on “Generalized Approximation Spaces.” In 2015, he earned his Ph.D. from the same institution, specializing in “Granular Computing and Topological Structures.” He has published numerous papers on topics such as topology and its applications, rough sets and their applications, and soft sets and their applications in various international ISI-indexed journals and conferences. His research interests include topology, rough sets, fuzzy sets, soft sets, and granular computing. Currently, his h-index is 16 on Google Scholar with 798 citations, and his h-index on SCOPUS is 15.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Exploring $\beta$-Basic Rough Sets and Their Applications in Medicine. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3743-3771. https://doi.org/10.29020/nybg.ejpam.v17i4.5545