A topological tool to develop novel rough set
Volume 33, Issue 2, pp 204--216
https://dx.doi.org/10.22436/jmcs.033.02.08
Publication Date: January 13, 2024
Submission Date: November 12, 2023
Revision Date: November 30, 2023
Accteptance Date: December 05, 2023
Authors
A. A. Azzam
- Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia.
- Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt.
Abstract
Here, we introduce a new rough set model-building topological method. This concept is based on "somewhat open sets," one of the popular generalizations of open sets. First, we create a few topologies using different kinds of \(\mathcal{M}_{\xi}\)-adhesion neighborhoods. Then, we create new kinds of rough approximations and accuracy metrics with respect to somewhat closed and somewhat open sets. We examine their key characteristics and demonstrate that the monotonic requirement is maintained by the accuracy and roughness metrics. Their ability to be compared is one of their special qualities. We demonstrate that our method is more accurate than those resulting from open, \(\alpha\)-open, and semi-open sets by comparing it with the previous approaches. We also evaluate the applicability of the technique in a heart failure problem. Lastly, we evaluate the benefits and drawbacks of our approach and make some recommendations for further research.
Share and Cite
ISRP Style
A. A. Azzam, A topological tool to develop novel rough set, Journal of Mathematics and Computer Science, 33 (2024), no. 2, 204--216
AMA Style
Azzam A. A., A topological tool to develop novel rough set. J Math Comput SCI-JM. (2024); 33(2):204--216
Chicago/Turabian Style
Azzam, A. A.. "A topological tool to develop novel rough set." Journal of Mathematics and Computer Science, 33, no. 2 (2024): 204--216
Keywords
- Topology
- somewhat open set
- \(\mathcal{M}_{\xi}\)-adhesion neighborhood space
- lower/upper approximation
- accuracy
- rough set
MSC
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