## 1 Introduction  
With the rapid development of society and the continuous advancement of technology, the physical protection system (PPS) has been playing an increasingly important role in areas such as critical infrastructure protection, public security management, and smart city construction. Integrating various technological measures including video surveillance, intrusion detection, and access control, the PPS provides crucial support for safeguarding social security, and preventing, and responding to diverse security threats. However, with the continuous expansion of system scale and increasing complexity, the PPS itself faces numerous vulnerability issues [1]. These system vulnerabilities may originate from hardware failures, software system flaws, network communication defects, or even human operational errors. If these vulnerabilities are maliciously exploited, they may lead to system malfunctions, data breaches, or even trigger severe security incidents [2]. Therefore, conducting scientific and comprehensive vulnerability assessments of PPSs, identifying system weaknesses, and implementing effective protective measures are of significant importance for enhancing overall system security. Traditional vulnerability assessment methods for PPSs can be primarily categorized into two types. The first type involves establishing an indicator system for system components, typically using weighted calculation methods to progressively assess vulnerabilities from basic components to subsystems and ultimately to the complete physical protection system [3; 4; 5]. This approach offers simplicity and intuitiveness when dealing with a relatively simple PPS. Its notable drawbacks are as follows: (1) such methods assume independence among system components, neglecting their complex interrelationships; (2) they focus on the types and quantities of physical protection system components while overlooking the system's spatial characteristics. The second category analyzes the shortest intrusion path in the PPS, evaluating system vulnerability by connecting components from outer to inner layers to form a quantifiable pathway. These methods are primarily represented by the Estimate of Adversary Sequence Interruption (EASI) method and its derivatives [2]. The advantage of this approach lies in its partial mitigation of the subjectivity inherent in expert judgment, while quantitatively reflecting how spatial configurations affect PPS vulnerability in path selection. Notable limitations include the following: (1) The EASI method and its extensions (e.g., System Analysis of Vulnerability to Intrusion, SAVI) predominantly focus on shortest-path analysis, neglecting alternative intrusion paths and their interdependencies. (2) These methods typically assume independence among component vulnerabilities, failing to account for vulnerability propagation and accumulation effects within the system. This assumption may lead to underestimation of overall system vulnerability. To address these issues, this paper proposes a vulnerability assessment method for PPS based on complex network theory and fuzzy Petri net (FPN). Complex network theory effectively characterizes inter-component relationships, providing a powerful tool for modeling PPS topology, while FPN theory simulates vulnerability propagation processes and quantitatively evaluates overall system vulnerability. The integrated approach demonstrates enhanced adaptability and flexibility, enabling more comprehensive and accurate PPS vulnerability assessment to inform security protection and risk control. The primary contributions of this work include the following:  
1. A complex network-based PPS topology modeling method characterizing inter-component relationships;
2. A fuzzy Petri net-driven vulnerability propagation model to simulate cascading failure mechanisms and quantify systemic risks. 3. Demonstration of method validity through case studies illustrating vulnerability assessment reasoning and computation processes.