The rapid deployment of artificial intelligence (AI) across healthcare, industrial control, supply-chain management, and Internet of Medical Things (IoMT) environments has intensified the need for computing architectures that can simultaneously provide low-latency inference, scalability, security, and operational resilience. Conventional cloud-centric AI architectures offer substantial computational capacity but may introduce communication latency, bandwidth dependency, privacy exposure, and single-point operational dependencies. Edge-cloud integration addresses these limitations by distributing data processing and AI inference across resource-constrained edge nodes, intermediate fog layers, and centralized cloud infrastructures. This research and review paper examines the architectural principles required to develop resilient and real-time AI decision systems through intelligent edge-cloud integration. The study synthesizes the provided literature on fog-cloud security, federated learning, intrusion detection, machine learning, blockchain-enabled IoMT, serverless computing, and healthcare cybersecurity. A conceptual architecture is developed around five functional layers: data acquisition, edge intelligence, collaborative fog coordination, cloud intelligence, and resilient decision orchestration. The analysis indicates that effective edge-cloud AI systems require adaptive workload placement, privacy-preserving distributed learning, security-aware inference, explainability, fault tolerance, and continuous resource optimization rather than simple physical distribution of computation. The findings further indicate that federated and lightweight learning mechanisms can reduce centralized exposure, while fog-cloud coordination can improve responsiveness for latency-sensitive applications. However, heterogeneous hardware, communication failures, model synchronization overhead, adversarial threats, and resource constraints remain significant barriers. The paper positions intelligent edge-cloud integration as an architectural strategy in which resilience, security, and inference performance are jointly optimized rather than treated as independent system properties.