A topological tool to develop novel rough set

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 M_ξ-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, α-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.