<p>The rapid growth of Internet of Things (IoT) applications demands intelligent analytics with strict privacy preservation, low latency, and high energy efficiency. Federated learning enables decentralized model training at edge devices; however, conventional cloud-centric federated architectures suffer from excessive communication overhead, slow convergence, and poor adaptability to heterogeneous and dynamic IoT environments. To overcome these limitations, this paper proposes a multi-objective optimized fog-coordinated federated edge AI framework for efficient and scalable IoT analytics. In the proposed framework, fog nodes function as hierarchical coordinators that perform intermediate aggregation, adaptive client clustering, and resource-aware task scheduling. A hybrid multi-objective optimization strategy combining NSGA-III and deep reinforcement learning (DRL) is employed to jointly optimize communication latency, energy consumption, aggregation delay, and model accuracy. NSGA-III generates a diverse Pareto-optimal solution set for federated client selection and aggregation scheduling, while the DRL agent dynamically learns optimal coordination policies under varying network conditions and non-IID data distributions. The framework effectively addresses challenges such as device heterogeneity, intermittent connectivity, and unbalanced data distribution by enabling fog-level adaptive orchestration of federated learning processes. Extensive experimental evaluations demonstrate that the proposed method achieves faster convergence, reduced communication cost, and improved energy efficiency compared to conventional cloud-based federated learning and single-objective optimization approaches. The proposed fog-coordinated and multi-objective optimized federated edge AI framework provides a practical, scalable, and privacy-preserving solution for real-time IoT analytics in smart cities, healthcare, industrial IoT, and smart agriculture applications.</p>