Temporal three-way decision-making for emergency admission integrating multigranulation neighborhood rough set with Gaussian mixture-hidden Markov model

Accurate and timely admission prediction in emergency departments is essential for improving resource allocation, enhancing patient outcomes, and mitigating overcrowding. However, the progression of emergency patients often exhibits strong temporal dynamics, and clinical decisions typically involve not only admission and non-admission but also an intermediate state of wait-and-see. To address this challenge, this study proposes a novel temporal three-way decision-making method that integrates Temporal Feature-based Multigranulation Neighborhood Rough Set (TMNRS) with Gaussian Mixture–Hidden Markov Model (GMM-HMM). Specifically, TMNRS is utilized to quantify and characterize the initial distribution of patient states from both theoretical and data-driven perspectives, thereby providing parameter support for subsequent modeling. Building on this foundation, GMM-HMM is employed to capture the dynamic evolution of patients’ conditions across three states over time. This integration facilitates interpretable state representation of the model. Finally, comprehensive experiments conducted on real-world clinical data, including comparisons with multiple benchmark models, demonstrate competitive and robust performance of the proposed approach in supporting temporal three-way admission decision-making for emergency patients.