Synergistic Integration of Rough Set Theory and Fuzzy Metric Spaces for Enhanced Decision-Making in Uncertain Environments

Decision-making under uncertainty is a critical challenge in various fields, including healthcare, finance, and industrial automation. Traditional decision-making models often struggle to handle the inherent vagueness and imprecision in real-world data. This paper proposes a novel framework that integrates Rough Set Theory (RST) and Fuzzy Metric Spaces (FMS) to address these challenges. By combining the granularity of RST with the nuanced expressiveness of FMS, our approach enhances the accuracy and reliability of decisions made under uncertain conditions.By leveraging the strengths of RST in handling imprecise information and the capabilities of FMS in modelling vagueness and partial truth, our approach provides a robust mechanism for decision-making. We validate our framework using real-world datasets, demonstrating its effectiveness in diverse applications such as medical diagnosis, financial forecasting, and industrial process control. Experimental results show significant improvements in accuracy, robustness, and interpretability, underscoring the potential of this hybrid approach in tackling complex decision-making problems.The Fuzzy-Rough Decision Support System (FRDSS) is an advanced decision-making platform developed from the integrated concepts of Rough Set Theory (RST) and Fuzzy Metric Spaces (FMS). This system leverages the analytical strengths of RST in managing imprecise information and the nuanced capabilities of FMS in modelling vagueness and partial truth. Designed to handle real-world scenarios where data is often incomplete and uncertain, FRDSS offers a comprehensive solution for a range of applications, including healthcare, finance, and industrial automation.