This research focuses on complex systems characterized by multi-state properties, which can exhibit multiple discrete or continuous behavioral patterns under varying internal states or external conditions. The aim is to develop mathematical models and computational frameworks that can precisely characterize the system's multi-state properties, state evolution paths, and interactions with the environment. Through dynamic simulation, data-driven analysis, and multi-criteria evaluation, it systematically uncovers the patterns of performance, reliability, and vulnerability across different states. Ultimately, the research is dedicated to developing intelligent optimization and collaborative decision-making methods for multi-stage and multi-objective scenarios, achieving global optimization of system mode switching, resource allocation, and operational strategies under complex constraints, thereby providing theoretical support and technical tools for enhancing system adaptability, resilience, and overall effectiveness.