Abstract
The regional accident risk in industrialized towns is a critical foundation for optimizing urban industrial layouts and dynamically managing regional risks. However, assessing production safety risks in urban areas often encounters challenges such as incomplete information and fuzzy index judgments due to limited small-sample data. This study proposes a dynamic control model for coupling risks in industrialized urban areas, integrating system engineering principles and focusing on two dimensions: the inherent risk of production safety accidents and the vulnerability of regional safety protection systems. For inherent risk analysis, the fuzzy set theory treats probability distribution as a mapping from events to probabilities. A set-valued fuzzy mathematics approach is employed to process single sample points, and an information diffusion model compensates for data deficiencies by appropriately expanding incomplete information. An extension grey clustering vulnerability assessment model is developed for vulnerability analysis, combining extension theory with grey clustering correlation functions. This model calculates the comprehensive correlation degree between the assessment object and vulnerability levels, thereby evaluating the safety system's capacity to withstand accident impacts. Application of the model to an urban district demonstrates that while inherent risks are widespread in industrialized regions, the safety protection systems exhibit minimal vulnerability and robust resilience. These findings align with observed conditions and offer a scientific basis for effectively managing production safety risks in urban areas.