In the current era, IoT-based healthcare solutions play a pivotal role in transforming the healthcare landscape by addressing key challenges and significantly enhancing the quality, accessibility, and efficiency of medical services, particularly for individuals in remote areas. This paper introduces innovative operations on fractional fuzzy sets (FFS), specifically the Hamacher sum and product, and establishes corresponding operational laws. Building upon these foundations, we propose novel aggregation operators (AoPs) leveraging Hamacher norms and rigorously analyze their properties within the FFS framework. Furthermore, we integrate these advancements into decision-making methodologies, including Extended TOPSIS, TODIM, and Extended GRA, tailored for applications in FFS. To illustrate the practicality and effectiveness of our approach, we present a detailed case study on healthcare system selection. Finally, a comparative analysis of the proposed methods with existing aggregation operators highlights the robustness and suitability of our solution in real-world scenarios.
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