Exploring the Applications of Grill Rough Topological Structures Generated by Different Minimal Neighborhood Types (European Journal of Pure and Applied Mathematics, 2025)
A variety of grill-based topologies are developed and contrasted with earlier topologies. The results demonstrate that the present ones exceed their predecessors. This study distinguishes itself by highlighting the advantages of certain topologies and identifying both the minimum and maximum values. These structural topologies are later utilized to conduct a more thorough investigation of extended rough sets. Compared to earlier models, the suggested approximate models reduce vagueness and uncertainty, which makes them especially important when applied to rough sets (rhss). Furthermore, the suggested models differ from their predecessors in that they exhibit all of Pawlak’s properties, including the capability of contrasting various approximations (Aprs), and have the quality of monotonicity across all relations. In addition, the importance of new discoveries was highlighted by demonstrating their use for human health. Besides examining its limitations, the benefits of the chosen technique were assessed. The paper ends with a summary of the main ideas of the proposed methodology and recommendations for future research paths.
Keywords: upper-lower Apr; grill; minimal neighborhood; (rhss).