Abstract
The COVID-19 pandemic has imposed significant challenges on global health, emphasizing the persistent threat of large-scale infectious diseases in the future. This study addresses the need to enhance pooled testing efficiency for large populations. The common approach in pooled testing involves consolidating multiple test samples into a single tube to efficiently detect positivity at a lower cost. However, what is the optimal number of samples to be grouped together in order to minimize costs? i.e. allocating ten individuals per group may not be the most cost-effective strategy. In response, this paper introduces the hierarchical quotient space, an extension of fuzzy equivalence relations, as a method to optimize group allocations. In this study, we propose a cost-sensitive multi-granularity intelligent decision model to further minimize testing costs. This model considers both testing and collection costs, aiming to achieve the lowest total cost through optimal grouping at a single layer. Building upon this foundation, two multi-granularity models are proposed, exploring hierarchical group optimization. The experimental simulations were conducted using MATLAB R2022a on a desktop with Intel i5-10500 CPU and 8G RAM, considering scenarios with a fixed number of individuals and fixed positive probability. The main findings from our simulations demonstrate that the proposed models significantly enhance the efficiency and reduce the overall costs associated with pooled testing. For example, testing costs were reduced by nearly half when the optimal grouping strategy was applied, compared to the traditional method of grouping ten individuals. Additionally, the multi-granularity approach further optimized the hierarchical groupings, leading to substantial cost savings and improved testing efficiency.