<p>The exponential growth of Internet of Things (IoT) applications and the increasing complexity of cloud-edge architectures demand advanced task scheduling strategies that can simultaneously optimize multiple objectives, including energy efficiency, computational and transmission delay, and load balancing. In this paper, we propose a novel tri-objective system model for IoT cloud-edge task scheduling, integrating server energy consumption, task latency, and a capacity-aware load balancing mechanism. To solve this optimization problem, we introduce the Fuzzy-enhanced Slime Mould Algorithm (FSMA), which incorporates an adaptive fuzzy logic controller to dynamically regulate selection pressure. This adaptive mechanism enables FSMA to balance exploration and exploitation, avoid premature convergence, and effectively navigate complex search spaces. The effectiveness of FSMA is demonstrated through simulations on both standard benchmark functions and real-world IoT task scheduling scenarios, with comparisons against state-of-the-art evolutionary algorithms. Statistical analyses, including the Friedman test, confirm the robustness, scalability, and significance of the observed improvements. Experimental results show that FSMA achieves an average performance gain of 21% over the standard Slime Mould Algorithm (SMA), highlighting its superior optimization capability. This work not only advances metaheuristic algorithm design but also provides a practical, adaptive, and scalable framework for sustainable, high-performance task scheduling in dynamic IoT cloud-edge environments.</p>