Identifying Critical Fire Risk Transmission Paths in Subway Stations: A PSR–DEMATEL–ISM Approach

Abstract

To enhance the understanding and management of fire risks in subway stations, this study aims to identify critical fire risk transmission paths using an integrated PSR–DEMATEL–ISM approach. A comprehensive evaluation framework is first constructed based on the Pressure–State–Response (PSR) model, systematically categorizing 22 influencing factors into three dimensions: pressure, state, and response. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is then employed to analyze the causal relationships and centrality among these factors, distinguishing between cause and effect groups. Subsequently, Interpretive Structural Modeling (ISM) is applied to organize the factors into a multi-level hierarchical structure, enabling the identification of risk propagation pathways. The analysis reveals five high-centrality and high-causality factors: fire safety education and training, completeness of fire management rules and regulations, fire smoke detection and firefighting capability, operational status of monitoring equipment, and effectiveness of emergency response plans. Based on these key drivers, six major transmission paths are derived, reflecting the internal logic of fire risk evolution in subway environments. Among them, chains originating from Fire Safety Education and Training (S6), Architectural Fire Protection Design (S7), and Completeness of Fire Management Rules and Regulations (S16) exhibit the most significant influence on system-wide safety performance. This study provides theoretical support and practical guidance for proactive fire prevention and emergency planning in urban rail transit systems, offering a structured and data-driven approach to identifying vulnerabilities and improving system resilience.

1. Introduction

Subways, known for their high passenger capacity, rapid transit speed, and operational punctuality, have become a cornerstone of modern urban transportation infrastructure. By 31 December 2024, urban rail transit lines had been established in 58 cities across mainland China, comprising 361 lines and covering a total length of 12,160.77 km. Of these, subway lines accounted for 9306.09 km, representing 76.53% of the total [1]. As critical nodes within the transit network, subway stations play a vital role in ensuring passenger service and operational safety. Statistical data indicate that fire incidents account for approximately 30% of all operational accidents in subway systems, making them the primary threat to subway safety. Notably, subway stations are the most frequent locations for such incidents. For instance, the 2003 Daegu subway arson incident in South Korea resulted in 192 deaths and 147 injuries, with direct property losses of approximately KRW 47 billion and reconstruction costs estimated at KRW 516 billion. On 27 March 2020, a fire in the New York City subway caused one death (the train operator) and 16 injuries, including four serious cases. Several train cars and a platform were damaged, and Line 2 was suspended for about 10 days [2]. Therefore, conducting thorough risk identification and inspections, strengthening safety management practices, and minimizing fire-related occurrences are essential to maintaining the safe and stable operation of subway systems.

To improve fire risk management and reduce operational vulnerabilities in subway stations, numerous studies have been conducted both in China and internationally. Derrible S. et al. [3] analyzed 33 metro systems worldwide and introduced graph theory-based indicators to systematically characterize metro network features from the perspectives of state, form, and structure. Similarly, Ju et al. [4] constructed a fire risk index system by consulting experts and applying a game theory-based weighting method combined with the TOPSIS technique to rank subway stations by risk. Chopra SS et al. [5] proposed an integrated framework to assess the resilience of the London Metro system by analyzing network topology, spatial organization, and passenger flow information. Camillo A [6] analyzed many years of data from the London Underground using probabilistic statistical methods to classify fire risk and establish indicators for casualties. The effectiveness of the fire evacuation model was also verified through simulation experiments. Teodosiu et al. [7] conducted a full-scale CFD simulation to verify that, under an ultra-fast growth fire scenario in the Bucharest Metro, different ventilation schemes can effectively ensure evacuation safety, while also demonstrating the feasibility and practicality of the CFD method in optimizing emergency ventilation for subway fires. Zhang [8] utilized Building Information Modeling (BIM) to simulate subway station fires, employing PyroSim for fire dynamics and Pathfinder for evacuation modeling. Roshan [9] employed the accident tree analysis method to construct event trees for each fire incident, calculate the probabilities of multiple scenarios, and assess the fire risk of the Tehran Metro station. Mortazavi et al. [10] used the fuzzy fault tree analysis method to propose a fault tree model of the main risk factors of metro fires and ranked the critical probability importance of events at the bottom of the fault tree. Nezhad et al. [11] used the Failure Mode and Effects Analysis (FMEA) model and fuzzy theory to assess the Zagros Metro and identified two major fire risks along the Zagros Metro line.

While current research has made significant progress in fire evacuation simulation, emergency response, and risk evaluation, a critical gap remains in understanding the internal mechanisms and interactions among influencing factors. Fire risk factors in subway stations do not operate independently but are embedded within a complex and interconnected system. Therefore, an in-depth exploration of these factors requires a systems-based approach that holistically considers their interdependencies. Zio [12] emphasized that accident causation should be analyzed not only through individual factor characteristics but also through the relationships and interactions among them. Responding to this systems perspective, the present study focuses on identifying the causative chains that underpin fire risks in subway stations by analyzing the interrelationships among key factors. Meanwhile, Qin [13] argued that fire hazard assessment should be conducted from multidimensional and multi-level perspectives by constructing a comprehensive and objective evaluation index system, in which the selected indicators are logically consistent and well-structured. This research fills a theoretical and methodological gap in previous studies and provides practical value for risk prevention, emergency preparedness, and operational safety in subway environments. First, a subway station fire risk assessment index system for China is established using the Pressure–State–Response (PSR) model. Given the complexity, severity, and recurrence of subway fire incidents, the PSR framework—with its dynamic and systematic features—serves as an ideal structure for representing fire risk logic in subway stations. Second, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is combined with Interpretive Structural Modeling (ISM) to further examine the interactions and layered structure among influencing factors. DEMATEL quantifies the degree of influence among system elements and distinguishes between cause and effect factors, while ISM stratifies these factors into a bottom-up hierarchical model. This integration allows for a clear visualization of the multi-level relationships and enables the identification of causative chains [14].

Based on the centrality values and factor classifications derived from DEMATEL, path weights are calculated to reflect the significance of different transmission routes. Subsequently, a risk transmission pathway analysis is performed to identify the most critical fire risk chains in subway stations. This comprehensive approach enhances the scientific rigor of fire risk assessment and offers actionable insights for improving fire prevention and safety management in urban rail systems. The research, as shown in Figure 1, was conducted in three stages, as outlined below: Phase 1: A fire risk assessment indicator system was developed by analyzing past subway fire incidents, official investigation reports, and relevant laws and regulations, both domestic and international. A systematic literature review was conducted to identify influencing factors, leading to the construction of a PSR-based model encompassing pressure, state, and response dimensions. Phase 2: The DEMATEL and ISM methods were applied to examine the interdependencies among influencing factors. DEMATEL was used to distinguish causal and resultant factors and to quantify influence through centrality and causality indices. ISM was then employed to stratify these factors into a multi-level structure, illustrating the underlying logical relationships. Phase 3: Based on the established hierarchy and centrality analysis, key causative chains were identified. A quantitative risk transmission path analysis was subsequently carried out to determine the most critical pathways influencing fire safety in subway stations.

2. Methodology

2.1. PSR Theory

The Pressure–State–Response (PSR) model, originally proposed by Canadian statisticians Rapport and Friend, adopts a “cause–effect–response” logical framework by classifying indicators into three categories: pressure, state, and response [15]. Specifically, pressure refers to external disturbances and stresses acting upon a system, which serve as drivers or catalysts of risk. State reflects the system’s current condition under such pressures, representing its stability and functional performance. Response encompasses the actions taken to mitigate or adapt to these pressures, acting as the system’s feedback mechanism to improve or restore equilibrium [16].

Due to its structured, dynamic, and systemic characteristics, the PSR model is widely used across various fields. It offers a robust analytical framework for addressing existing deficiencies in subway station fire risk assessment systems and for capturing the dynamic features of emergency response mechanisms. In this study, the PSR model forms the foundational structure for evaluating subway station fire safety risks, enabling systematic classification and analysis of influencing factors.

2.2. Establishment of an Evaluation Index System

To capture the full evolution process of fire incidents in subway stations, a set of evaluation indicators was developed following the principles of scientific rigor, representativeness, comprehensiveness, and practical applicability. Based on the subway fire safety assessment framework and previous studies on fire risk management [17,18,19], the analysis was conducted across the three PSR components: pressure (P), state (S), and response (R).

Through a thorough review of historical subway fire incident causes, official investigation reports, and relevant domestic and international safety regulations, a comprehensive set of influencing factors was identified. These factors were then categorized into the PSR framework, resulting in the development of a subway fire safety influence model. A total of 22 secondary indicators were defined and distributed among the three PSR dimensions. The complete risk assessment index system is presented in

Table 1. Fire risk assessment indicator system for subway stations.

Resilience Assessment	Primary Indicator	Secondary Indicator
P PRESSURE	Equipment Factors	S1 Fire Smoke Detection and Firefighting Capability
		S2 Rolling Stock Equipment System
		S3 Power Supply Equipment System
	Personnel Factors	S4 Passenger Fire Safety Awareness
		S5 Staff Emergency Response Skills
		S6 Fire Safety Education and Training
	Environmental Factors	S7 Architectural Fire Protection Design
		S8 Adverse Environmental Factors Inside and Outside the Station
		S9 Emergency Evacuation Design
S STATE	Station Monitoring and Early Warning Capability	S10 Operational Status of Monitoring Equipment
		S11 Effectiveness of Early Warning Systems
		S12 Staff Security Inspection Competence
	Station Emergency Support Capability	S13 Emergency Supplies Support Capability
		S14 Effectiveness of Emergency Plans
	Station Safety Management Capability	S15 Equipment Inspection and Maintenance Cycle
		S16 Completeness of Fire Management Rules and Regulations
R RESPONSE	Emergency Response Capability	S17 Information Dissemination and Reporting Status
		S18 Medical Response Capability
		S19 Emergency Repair and Rescue Capability
	Emergency Recovery Capability	S20 Accident Cause Investigation Capability
		S21 Development and Implementation of Recovery Plans
		S22 Optimization and Improvement of the Management System

.

2.3. DEMATEL-ISM

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method captures expert knowledge and experience by expressing the relationships among indicators in the form of a direct influence matrix. This method transforms the interdependencies among factors into two categories—causal and resultant—and quantifies their influence through measures such as causal degree, centrality, and receptivity. In complex systems, DEMATEL helps identify critical influencing factors through Influence Relation Diagrams [20]. Interpretive Structural Modeling (ISM), proposed by Warfield in 1973, is grounded in system theory and graph theory. It aims to reveal hierarchical structures and interaction mechanisms among system elements. ISM enables the classification of factors into fundamental, intermediate, and direct layers, thereby clarifying their roles within the system [21]. While DEMATEL effectively quantifies influence and distinguishes causality, it lacks explicit capability in structural stratification. ISM addresses this limitation by providing a layered hierarchical representation. When combined, DEMATEL and ISM complement each other—enabling both the measurement of factor importance and the mapping of their logical structure. This integrated approach facilitates the construction of a bottom-up hierarchical model and the identification of critical causative chains, offering a clearer picture of risk transmission pathways in subway fire systems [22]. The specific computational process involves the following five steps [23]:

Step 1: Establishment of the Direct Influence Matrix

Based on the statistical analysis of past accident cases and relevant literature, similar and duplicate factors were eliminated, resulting in the final set of influencing factors, denoted as S = {S1, S2, …, Sn}. Experts and scholars from relevant fields were invited to assess and score the degree of influence among the causative factors. The score represents the intensity of influence that factor Si exerts on factor Sj.

Following the 0–4 scale evaluation criteria, the scoring standards were defined as follows:

0: No influence,

1: Weak influence,

2: Moderate influence,

3: Strong influence,

4: Very strong influence.

Considering the subjective differences and variations in individual knowledge among the experts, the average method was applied to aggregate the evaluation results from multiple experts. Consequently, the initial direct influence matrix A = (S_{i j})n × n was established.

Step 2: Establishment of the Total Influence Matrix

To eliminate the impact caused by differences in measurement scales, the initial direct influence matrix was first normalized according to Equation (1), resulting in the normalized direct influence matrix B. The normalization process ensures that the data is standardized, thereby facilitating accurate subsequent calculations. The normalization formula is given as:

$$B = {\left(b_{ij}\right)}_{\mathrm{n}\times \mathrm{n}}={\displaystyle \frac{a_{\mathit{ij}}}{{}_{1\le i\le n}{}^{\mathit{max}}{\sum }_{j=1}^n{a}_{\mathit{ij}}}}$$

(1)

in Equation (1), the denominator corresponds to the maximum value of the row sums.

Based on the calculated normalized matrix B, the total influence matrix C is obtained using Equation (2):

$$C={\left(C_{ij}\right)}_{\mathrm{n}\times \mathrm{n}}=\underset{n\to \infty }{\mathit{lim}}{(B}^1+\cdots +B^n)=B{\displaystyle \frac{I-B^{n-1}}{I-B}}=B{(I-B)}^{-1}$$

(2)

In Equation (2), I represents the identity matrix.

Step 3: Based on obtaining the matrix C, calculate the influence degree Di, the reception degree Gi, the centrality Mi, and the causality degree Ri of each influencing factor of the subway station in sequence according to the following Equations (3)–(6).

Influence Degree D_i:

The sum of the elements in the i-th row of matrix C, representing the total influence exerted by factor i on all other factors.

Reception Degree G_i:

The sum of the elements in the i-th column of matrix C, representing the total influence received by factor i from all other factors.

Centrality M_i:

The sum of D_i and G_i, indicating the overall importance of factor i within the system of influencing factors. A higher centrality value corresponds to a greater level of importance.

Causality Degree R_i:

The difference between D_i and G_i

If R_i > 0, factor i predominantly influences other factors and is classified as a causal factor.

If R_i < 0, factor i is mainly influenced by other factors and is classified as a resultant factor.

$$D_i={\sum }_{j=1}^{22}{C}_{\mathit{ij}}\left(i=1,2,3,\dots ,22\right)$$

(3)

$$G_j={\sum }_{i=1}^{22}{C}_{\mathit{ji}}\left(j=1,2,3,\dots ,22\right)$$

(4)

$$M_i={ D}_i{+G}_i$$

(5)

$$R_i={ D}_i{-G}_i$$

(6)

Step 4: Establishment of the Reachability Matrix

The overall influence matrix H is calculated based on the reachability matrix R using Equation (7):

$$H = I + C$$

(7)

To simplify the system structure and enable hierarchical modeling, a threshold value λ is introduced. Different values of λ yield different hierarchical models. Selecting an appropriate threshold is critical, as it directly influences the structure and interpretability of the resulting levels. To ensure objectivity in the logical stratification of causative factors, the threshold λ is determined based on the statistical distribution of the elements in the total influence matrix (C). Specifically, the mean and standard deviation of the influence values are used to guide the threshold selection.

The formula for calculating the threshold is given as:

$$\lambda = \alpha + \beta$$

(8)

Let α and β denote the mean and standard deviation, respectively, of all elements in the total influence matrix C, where λ ∈ [0, 1]. The overall influence matrix H is converted into the reachability matrix K using the following rule: if h_{i j} ≥ λ, then k_{i j} = 1; otherwise, k_{i j} = 0.

Step 5: Construction of a Multi-Level Hierarchical Structure Model

Based on the reachability matrix K, the reachable set L(Si), antecedent set P(Si), and common set Q(Si) of each influencing factor can be derived using Equations (9)–(11).

$$L\left(S_i\right)=\left\{S_i\right|a_{i j}= 1\}$$

(9)

$$P\left(S_i\right)=\left\{S_i|a_{i j}=1\right\}$$

(10)

$$Q\left(S_i\right)=L\left(S_i\right)\cap P\left(S_i\right)$$

(11)

Step 6: Identification of Critical Causative Chains

Based on the DEMATEL-ISM method, a risk transmission path analysis was conducted from the perspective of causative factors. Using the hierarchical structure and centrality values, a quantitative analysis was performed to identify the critical causative chains of subway station fire influencing factors.

3. Factor Attribute Analysis Based on DEMATEL-ISM

3.1. Factor Attribute Analysis Based on DEMATEL

To accurately evaluate the interrelationships among subway fire risk factors, five domain experts with extensive experience in urban rail safety were invited to score the influence between factor pairs. The resulting direct influence matrix was constructed from their assessments and is presented in

Table 2. Direct influence matrix A.

Factor	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11	S12	S13	S14	S15	S16	S17	S18	S19	S20	S21	S22
S1	0	3.6	3.2	1.8	1.3	1.5	2.8	3.1	1.3	3.0	3.5	0.7	1.0	1.3	3.1	1.5	0.8	1.1	1.0	0.5	0.7	1.2
S2	2.1	0	3.0	1.2	0.7	1.0	0.6	1.5	0.6	3.1	1.3	0.5	1.5	1.0	2.9	1.5	1.0	0.8	2.4	1.0	1.8	1.0
S3	3.4	3.0	0	1.3	0.8	1.0	1.2	0.5	1.1	3.0	2.1	0.5	1.1	1.0	2.1	1.5	0.7	1.5	1.2	0.6	0.9	0.5
S4	0.5	0.3	0.5	0	1.0	1.4	0.8	2.1	1.2	0.8	1.0	0.6	0.8	2.1	1.3	1.3	1.0	1.5	1.0	1.2	0.7	1.2
S5	0.6	1.1	0.7	2.8	0	2.1	1.6	1.1	0.6	1.2	1.0	2.9	1.2	2.8	2.0	1.5	2.2	0.5	0.7	3.0	1.2	1.5
S6	2.1	1.2	0.8	3.8	3.5	0	2.5	3.6	3.0	1.9	2.3	3.8	3.0	2.5	3.6	3.6	2.8	1.2	1.4	2.5	2.0	1.8
S7	1.4	0.8	0.9	1.4	0.5	1.1	0	1.5	3.5	1.0	0.7	1.2	0.8	2.1	1.0	0.7	1.2	0.5	1.2	0.3	1.0	0.5
S8	2.8	1.0	1.3	0.5	1.2	1.8	0.7	0	1.6	0.7	0.7	0.8	0.3	1.9	0.8	2.0	1.2	1.8	2.5	0.6	0.3	0.6
S9	3.2	1.2	1.6	0.8	1.0	1.3	2.0	0.5	0	1.2	2.0	0.8	1.2	2.5	0.7	0.4	1.2	2.7	3.0	1.5	0.8	1.3
S10	3.0	3.5	2.0	1.3	1.3	2.1	0.6	3.5	1.1	0	2.5	1.0	0.7	0.7	3.2	3.0	1.1	1.5	2.0	1.2	0.7	1.5
S11	3.8	1.5	1.6	1.0	1.3	0.8	0.3	1.0	1.0	2.2	0	1.3	2.3	1.5	0.0	1.2	2.9	1.2	2.0	0.6	0.5	1.1
S12	0.8	0.5	0.5	2.1	1.4	2.0	0.2	1.1	0.3	1.5	0.6	0	0.5	1.1	1.5	0.9	1.2	1.0	1.7	0.4	0.9	1.2
S13	0.6	0.8	0.5	1.2	1.5	1.0	0.3	0.2	1.3	0.6	1.0	0.3	0	0.3	0.5	1.7	0.3	2.0	1.8	0.5	0.8	1.3
S14	3.4	1.8	1.5	3.0	2.3	1.3	0.4	1.0	0.9	1.2	1.5	0.4	3.0	0	1.2	0.5	3.0	3.5	3.8	3.0	2.8	2.5
S15	1.8	2.0	1.5	0.5	0.4	1.2	0.5	1.1	0.6	3.5	2.8	0.6	1.1	0.6	0	1.2	0.7	0.6	1.8	0.5	0.3	0.3
S16	2.1	2.4	2.1	3.0	3.8	3.0	2.3	2.0	1.6	2.7	3.2	2.5	1.8	3.2	3.8	0	1.9	3.0	2.1	1.2	1.8	1.5
S17	0.3	0.4	1.4	2.1	0.8	1.6	0.5	1.2	2.0	1.3	2.5	0.8	1.4	2.9	1.0	0.4	0	1.8	2.7	1.8	1.3	2.8
S18	0.6	0.3	0.3	2.1	1.7	1.5	1.2	2.0	1.9	0.8	1.4	1.2	1.9	1.2	1.0	1.6	2.0	0	2.1	1.1	1.0	0.5
S19	1.2	1.0	1.6	1.3	2.0	1.4	0.6	1.8	2.1	2.4	1.8	0.7	1.1	2.1	0.8	1.5	2.1	3.6	0	1.2	2.5	1.3
S20	1.1	0.8	0.5	1.2	1.2	2.0	0.2	1.2	0.8	0.3	1.3	0.2	0.7	1.2	0.3	1.3	0.8	0.6	1.2	0	1.7	0.8
S21	1.3	0.5	1.0	1.8	2.1	2.0	0.5	1.7	0.8	2.0	0.9	1.3	1.5	0.9	2.0	0.5	1.2	2.3	1.5	2.5	0	2.0
S22	1.6	0.5	1.0	2.1	1.0	2.1	0.5	0.8	1.7	1.3	2.1	0.9	1.2	1.0	2.1	1.7	1.5	2.1	1.3	2.4	1.9	0

.

Subsequently, the normalized influence matrix and the total influence matrix were computed according to Equations (1) and (2), shown in

Table 3. Normalized influence matrix.

Factor	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11
S1	0	0.0681	0.0605	0.0340	0.0246	0.0284	0.0529	0.0586	0.0246	0.0567	0.0662
S2	0.0397	0	0.0567	0.0227	0.0132	0.0189	0.0113	0.0284	0.0113	0.0586	0.0246
S3	0.0643	0.0567	0	0.0246	0.0151	0.0189	0.0227	0.0095	0.0208	0.0567	0.0397
S4	0.0095	0.0057	0.0095	0	0.0189	0.0265	0.0151	0.0397	0.0227	0.0151	0.0189
S5	0.0113	0.0208	0.0132	0.0529	0	0.0397	0.0302	0.0208	0.0113	0.0227	0.0189
S6	0.0397	0.0227	0.0151	0.0718	0.0662	0	0.0473	0.0681	0.0567	0.0359	0.0435
S7	0.0265	0.0151	0.0170	0.0265	0.0095	0.0208	0	0.0284	0.0662	0.0189	0.0132
S8	0.0529	0.0189	0.0246	0.0095	0.0227	0.0340	0.0132	0	0.0302	0.0132	0.0132
S9	0.0605	0.0227	0.0302	0.0151	0.0189	0.0246	0.0378	0.0095	0	0.0227	0.0378
S10	0.0567	0.0662	0.0378	0.0246	0.0246	0.0397	0.0113	0.0662	0.0208	0	0.0473
S11	0.0718	0.0284	0.0302	0.0189	0.0246	0.0151	0.0057	0.0189	0.0189	0.0416	0
S12	0.0151	0.0095	0.0095	0.0397	0.0265	0.0378	0.0038	0.0208	0.0057	0.0284	0.0113
S13	0.0113	0.0151	0.0095	0.0227	0.0284	0.0189	0.0057	0.0038	0.0246	0.0113	0.0189
S14	0.0643	0.0340	0.0284	0.0567	0.0435	0.0246	0.0076	0.0189	0.0170	0.0227	0.0284
S15	0.0340	0.0378	0.0284	0.0095	0.0076	0.0227	0.0095	0.0208	0.0113	0.0662	0.0529
S16	0.0397	0.0454	0.0397	0.0567	0.0718	0.0567	0.0435	0.0378	0.0302	0.0510	0.0605
S17	0.0057	0.0076	0.0265	0.0397	0.0151	0.0302	0.0095	0.0227	0.0378	0.0246	0.0473
S18	0.0113	0.0057	0.0057	0.0397	0.0321	0.0284	0.0227	0.0378	0.0359	0.0151	0.0265
S19	0.0227	0.0189	0.0302	0.0246	0.0378	0.0265	0.0113	0.0340	0.0397	0.0454	0.0340
S20	0.0208	0.0151	0.0095	0.0227	0.0227	0.0378	0.0038	0.0227	0.0151	0.0057	0.0246
S21	0.0246	0.0057	0.0057	0.0340	0.0227	0.0284	0.0057	0.0227	0.0057	0.0227	0.017
S22	0.0302	0.0151	0.0151	0.0397	0.0189	0.0397	0.0095	0.0151	0.0321	0.0246	0.0397
Factor	S12	S13	S14	S15	S16	S17	S18	S19	S20	S21	S22
S1	0.0132	0.0189	0.0246	0.0586	0.0284	0.0151	0.0208	0.0189	0.0095	0.0132	0.0227
S2	0.0095	0.0284	0.0189	0.0548	0.0284	0.0189	0.0151	0.0454	0.0189	0.0246	0.0189
S3	0.0095	0.0208	0.0189	0.0397	0.0284	0.0132	0.0284	0.0227	0.0113	0.0095	0.0095
S4	0.0113	0.0151	0.0397	0.0246	0.0246	0.0189	0.0284	0.0189	0.0227	0.0132	0.0227
S5	0.0548	0.0227	0.0529	0.0378	0.0284	0.0416	0.0095	0.0132	0.0567	0.0227	0.0284
S6	0.0718	0.0567	0.0473	0.0681	0.0681	0.0529	0.0227	0.0265	0.0473	0.0378	0.0340
S7	0.0227	0.0151	0.0397	0.0189	0.0132	0.0227	0.0095	0.0227	0.0057	0.0095	0.0095
S8	0.0151	0.0057	0.0359	0.0151	0.0378	0.0227	0.0340	0.0473	0.0113	0.0057	0.0113
S9	0.0151	0.0227	0.0473	0.0132	0.0076	0.0227	0.0510	0.0567	0.0284	0.0151	0.0246
S10	0.0189	0.0132	0.0132	0.0605	0.0567	0.0208	0.0284	0.0378	0.0227	0.0151	0.0284
S11	0.0246	0.0435	0.0284	0.0000	0.0227	0.0548	0.0227	0.0378	0.0113	0.0095	0.0208
S12	0	0.0095	0.0208	0.0284	0.0170	0.0227	0.0189	0.0321	0.0076	0.0076	0.0227
S13	0.0057	0	0.0057	0.0095	0.0321	0.0057	0.0378	0.0340	0.0095	0.0057	0.0246
S14	0.0076	0.0567	0	0.0227	0.0095	0.0567	0.0662	0.0718	0.0567	0.0529	0.0473
S15	0.0113	0.0208	0.0113	0	0.0227	0.0132	0.0113	0.0340	0.0095	0.0057	0.0057
S16	0.0473	0.0340	0.0605	0.0718	0	0.0359	0.0567	0.0397	0.0227	0.0340	0.0284
S17	0.0151	0.0265	0.0548	0.0189	0.0076	0	0.0340	0.0510	0.0340	0.0246	0.0529
S18	0.0227	0.0359	0.0227	0.0189	0.0302	0.0378	0	0.0397	0.0208	0.0076	0.0095
S19	0.0132	0.0208	0.0397	0.0151	0.0284	0.0397	0.0681	0	0.0227	0.0378	0.0246
S20	0.0038	0.0132	0.0227	0.0057	0.0246	0.0151	0.0113	0.0227	0	0.0246	0.0151
S21	0.0038	0.0284	0.0076	0.0095	0.0076	0.0227	0.0321	0.0284	0.0378	0	0.0340
S22	0.0170	0.0227	0.0189	0.0397	0.0321	0.0284	0.0397	0.0246	0.0454	0.0359	0

and

Table 4. Total influence matrix.

Factor	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11
S1	0.0626	0.1131	0.1037	0.0848	0.0689	0.0761	0.0825	0.1072	0.0679	0.1125	0.1199
S2	0.0876	0.0402	0.0916	0.0651	0.0513	0.0593	0.0370	0.0702	0.0464	0.1044	0.0720
S3	0.1091	0.0938	0.0374	0.0657	0.0512	0.0572	0.0482	0.0519	0.0542	0.1012	0.0849
S4	0.0449	0.0317	0.0345	0.0337	0.0480	0.0564	0.0340	0.0688	0.0493	0.0467	0.0521
S5	0.0584	0.0556	0.0474	0.0988	0.0404	0.0814	0.0545	0.0629	0.0480	0.0666	0.0648
S6	0.1152	0.0808	0.0720	0.1434	0.1278	0.0696	0.0884	0.1328	0.1134	0.1076	0.1171
S7	0.0638	0.0430	0.0444	0.0597	0.0390	0.0513	0.0208	0.0589	0.0916	0.0526	0.0485
S8	0.0924	0.0516	0.0559	0.0498	0.0573	0.0686	0.0379	0.0372	0.0615	0.0534	0.0548
S9	0.1060	0.0596	0.0656	0.0605	0.0574	0.0643	0.0634	0.0521	0.0376	0.0677	0.0834
S10	0.1154	0.1114	0.0834	0.0782	0.0719	0.0890	0.0449	0.1161	0.0643	0.0597	0.1045
S11	0.1138	0.0647	0.0653	0.0621	0.0610	0.0543	0.0317	0.0594	0.0531	0.0841	0.0460
S12	0.0478	0.0349	0.0340	0.0718	0.0545	0.0666	0.0227	0.0517	0.0319	0.0597	0.0446
S13	0.0396	0.0364	0.0307	0.0509	0.0529	0.0445	0.0228	0.0300	0.0467	0.0390	0.0472
S14	0.1196	0.0786	0.0731	0.1139	0.0928	0.0782	0.0413	0.0737	0.0645	0.0803	0.0882
S15	0.0739	0.0695	0.0584	0.0438	0.0384	0.0542	0.0302	0.0555	0.0395	0.1020	0.0893
S16	0.1157	0.1031	0.0952	0.1286	0.1318	0.1209	0.0842	0.1050	0.0877	0.1231	0.1324
S17	0.0543	0.0420	0.0593	0.0835	0.0542	0.0700	0.0339	0.0624	0.0729	0.0670	0.0907
S18	0.0518	0.0358	0.0356	0.0785	0.0664	0.0642	0.0451	0.0728	0.0676	0.0527	0.0654
S19	0.0751	0.0584	0.0678	0.0749	0.0806	0.0721	0.0404	0.0797	0.0785	0.0924	0.0840
S20	0.0517	0.0382	0.0326	0.0532	0.0496	0.0641	0.0219	0.0504	0.0391	0.0354	0.0543
S21	0.0678	0.0435	0.0507	0.0767	0.0758	0.0769	0.0341	0.0721	0.0496	0.0784	0.0609
S22	0.0761	0.0453	0.0528	0.0836	0.0582	0.0797	0.0358	0.0572	0.0672	0.0686	0.0851
Factor	S12	S13	S14	S15	S16	S17	S18	S19	S20	S21	S22
S1	0.0476	0.0615	0.0743	0.1106	0.0747	0.0620	0.0715	0.0774	0.0487	0.0502	0.0604
S2	0.0371	0.0622	0.0587	0.0981	0.0664	0.0560	0.0588	0.0908	0.0514	0.0640	0.0507
S3	0.0364	0.0545	0.0576	0.0831	0.0647	0.0498	0.0681	0.0680	0.0423	0.0464	0.0405
S4	0.0329	0.0419	0.0704	0.0550	0.0516	0.0485	0.0610	0.0550	0.0487	0.0372	0.0469
S5	0.0827	0.0590	0.0949	0.0807	0.0656	0.0807	0.0541	0.0627	0.0915	0.0562	0.0629
S6	0.1175	0.1123	0.1175	0.1360	0.1261	0.1152	0.0946	0.1057	0.1027	0.0885	0.0885
S7	0.0435	0.0423	0.0717	0.0510	0.0406	0.0522	0.0450	0.0607	0.0326	0.0430	0.0356
S8	0.0407	0.0376	0.0729	0.0540	0.0692	0.0572	0.0724	0.0874	0.0414	0.0347	0.0403
S9	0.0429	0.0590	0.0877	0.0559	0.0452	0.0626	0.0941	0.1028	0.0621	0.0483	0.0573
S10	0.0547	0.0569	0.0655	0.1146	0.1026	0.0684	0.0805	0.0957	0.0625	0.0518	0.0668
S11	0.0506	0.0760	0.0681	0.0436	0.0585	0.0897	0.0651	0.0828	0.0439	0.0404	0.0536
S12	0.0219	0.0353	0.0514	0.0598	0.0449	0.0510	0.0503	0.0650	0.0337	0.0401	0.0466
S13	0.0250	0.0227	0.0331	0.0368	0.0548	0.0310	0.0648	0.0622	0.0317	0.0354	0.0445
S14	0.0443	0.1015	0.0551	0.0778	0.0590	0.1056	0.1221	0.1305	0.1016	0.0943	0.0902
S15	0.0339	0.0486	0.0437	0.0365	0.0541	0.0442	0.0457	0.0712	0.0348	0.0304	0.0317
S16	0.0941	0.0921	0.1270	0.1400	0.0619	0.1000	0.1243	0.1163	0.0792	0.0847	0.0817
S17	0.0428	0.0627	0.0948	0.0591	0.0450	0.0409	0.0795	0.0979	0.0695	0.0575	0.0851
S18	0.0484	0.0663	0.0617	0.0550	0.0621	0.0719	0.0401	0.0812	0.0514	0.0469	0.0397
S19	0.0458	0.0610	0.0859	0.0631	0.0693	0.0831	0.1153	0.0545	0.0624	0.0813	0.0618
S20	0.0246	0.0378	0.0512	0.0353	0.0492	0.0420	0.0412	0.0537	0.0245	0.0533	0.0378
S21	0.0524	0.0614	0.0571	0.0782	0.0473	0.0597	0.0831	0.0726	0.0798	0.0307	0.0683
S22	0.0462	0.0584	0.0611	0.0814	0.0689	0.0670	0.0820	0.0714	0.0787	0.0665	0.0333

, respectively.

Calculate the influence degree Di, the reception degree Gi, the centrality Mi, and the causality degree Ri of each influencing factor of the fire in sequence according to Formulas (3)–(6). The results are summarized in

Table 5. Results of DEMATEL analysis.

Influencing Factor	Influence Degree (Di)	Reception Degree (Gi)	Centrality (Mi)	Causality Degree (Ri)	Centrality Ranking	Factor Attribute
S1	1.7379	1.7427	3.4806	−0.0048	3	Resultant Factor
S2	1.4192	1.3313	2.7505	0.0879	13	Causal Factor
S3	1.3662	1.2914	2.6577	0.0748	16	Causal Factor
S4	1.0492	1.6611	2.7103	−0.6119	15	Resultant Factor
S5	1.4699	1.4292	2.8991	0.0407	8	Causal Factor
S6	2.3726	1.5189	3.8914	0.8537	1	Causal Factor
S7	1.0919	0.9558	2.0477	0.1362	22	Causal Factor
S8	1.2283	1.5280	2.7563	−0.2997	12	Resultant Factor
S9	1.4356	1.3326	2.7682	0.1030	11	Causal Factor
S10	1.7589	1.6549	3.4138	0.1040	5	Causal Factor
S11	1.3678	1.6900	3.0579	−0.3222	7	Resultant Factor
S12	1.0198	1.0658	2.0857	−0.0460	21	Resultant Factor
S13	0.8825	1.3111	2.1936	−0.4285	20	Resultant Factor
S14	1.8862	1.5614	3.4476	0.3249	4	Causal Factor
S15	1.1295	1.6054	2.7350	−0.4759	14	Resultant Factor
S16	2.3289	1.3819	3.7108	0.9471	2	Causal Factor
S17	1.4250	1.4386	2.8637	−0.0136	10	Resultant Factor
S18	1.2606	1.6133	2.8739	−0.3528	9	Resultant Factor
S19	1.5875	1.7655	3.3530	−0.1780	6	Resultant Factor
S20	0.9410	1.2752	2.2162	−0.3342	19	Resultant Factor
S21	1.3771	1.1818	2.5589	0.1953	18	Causal Factor
S22	1.4245	1.2242	2.6488	0.2003	17	Causal Factor

. Based on the calculation results in Table 5, a causal relationship diagram of the influencing factors of fire accidents in subway stations is drawn, with the X-axis representing centrality and the Y-axis representing causality, as shown in Figure 2.

3.2. Establishing the Hierarchical Model

The reachability matrix is established according to Formulas (7) and (8), as listed in

Table 6. Reachability matrix.

Factor	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11	S12	S13	S14	S15	S16	S17	S18	S19	S20	S21	S22
S1	1	1	1	0	0	0	0	1	0	1	1	0	0	0	1	0	0	0	0	0	0	0
S2	0	1	1	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	1	0	0	0
S3	1	1	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
S4	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
S5	0	0	0	1	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	1	0	0
S6	1	0	0	1	1	1	0	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
S7	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
S8	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
S9	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1	1	0	0	0
S10	1	1	0	0	0	0	0	1	0	1	1	0	0	0	1	1	0	0	1	0	0	0
S11	1	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
S12	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0
S13	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
S14	1	0	0	1	1	0	0	0	0	0	0	0	1	1	0	0	1	1	1	1	1	1
S15	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0
S16	1	1	1	1	1	1	0	1	0	1	1	1	1	1	1	1	1	1	1	0	0	0
S17	0	0	0	0	0	0	0	0	0	0	1	0	0	1	0	0	1	0	1	0	0	0
S18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
S19	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	1	0	0	0
S20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
S21	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
S22	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1

.

The reachability set L(Si) and prior set P(Si) of the influencing factors are determined using formulas (9) and (10) based on the reachability matrix. The levels of the factors are then divided using formula (11), as listed in

Table 7. Hierarchy analysis calculation results.

Factor	L(Si)	P(Si)	Q(Si)
S1	(1, 2, 3, 8, 10, 11, 15)	(1, 3, 6, 8, 9, 10, 11, 14, 16)	(1, 3, 8, 10, 11)
S2	(2, 3, 10, 15, 19)	(1, 2, 3, 10, 16)	(2, 3, 10)
S3	(1, 2, 3, 10)	(1, 2, 3, 16)	(1, 2, 3)
S4	(4)	(4, 5, 6, 14, 16)	(4)
S5	(4, 5, 14, 20)	(5, 6, 14, 16)	(5, 14)
S6	(1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)	(6, 16)	(6, 16)
S7	(7, 9)	(7)	(7)
S8	(1, 8)	(1, 6, 8, 10, 16)	(1, 8)
S9	(1, 9, 18, 19)	(6, 7, 9)	(9)
S10	(1, 2, 8, 10, 11, 15, 16, 19)	(1, 2, 3, 6, 10, 15, 16, 19)	(1, 2, 10, 15, 16, 19)
S11	(1, 11)	(1, 6, 10, 11, 16, 17)	(1, 11)
S12	(12)	(6, 12, 16)	(12)
S13	(13)	(6, 13, 14, 16)	(13)
S14	(1, 4, 5, 13, 14, 17, 18, 19, 20, 21, 22)	(5, 6, 14, 16, 17)	(5, 14, 17)
S15	(10, 15)	(1, 2, 6, 10, 15, 16)	(10, 15)
S16	(1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)	(6, 10, 16)	(6, 10, 16)
S17	(11, 14, 17, 19)	(6, 14, 16, 17)	(14, 17)
S18	(18)	(6, 9, 14, 16, 18, 19)	(18)
S19	(10, 18, 19)	(2, 6, 9, 10, 14, 16, 17, 19)	(10, 19)
S20	(20)	(5, 6, 14, 20)	(20)
S21	(21)	(14, 21)	(21)
S22	(22)	(14, 22)	(22)

. A hierarchical model is established as shown in Figure 3.

3.3. Analysis of the Mechanism of Factor Influence

3.3.1. Centrality Analysis

Factors located in the first quadrant of the centrality–causality diagram exhibit both high causality and high centrality, indicating that they are key drivers in the evolution of subway station fire risks [24]. According to the results, the five most critical influencing factors are S6—Fire Safety Education and Training, S16—Completeness of Fire Management Rules and Regulations, S1—Fire Smoke Detection and Firefighting Capability, S10—Operational Status of Monitoring Equipment, and S14—Effectiveness of Emergency Plans. These elements collectively form the core of a comprehensive fire risk defense system that integrates human, technical, and managerial components.

Fire Safety Education and Training (S6) provides the foundational support by enhancing the professional competence of subway staff and improving passengers’ fire safety awareness and emergency response capabilities. Staff training should cover essential areas such as the operation of fire protection equipment, initial fire suppression, and evacuation guidance, reinforced through regular drills. For passengers, safety education can be delivered via station broadcasts, visual displays, emergency signage, and other communication channels. Maintaining training records and conducting periodic evaluations ensure that training efforts result in real-world emergency readiness, embedding a prevention-oriented safety culture throughout the system [25].

Completeness of Fire Management Rules and Regulations (S16) serves as the institutional framework that ensures consistency and accountability in fire safety management. Through the establishment of a grid-based responsibility system, it provides clear operational guidelines covering routine inspections, emergency drills, performance assessments, and personnel responsibilities. Integrating digital management platforms further enhances traceability and supports intelligent early-warning capabilities, reinforcing systemic resilience.

Fire Smoke Detection and Firefighting Capability (S1) and Operational Status of Monitoring Equipment (S10) are technically vital for early risk detection and real-time information acquisition. Their effectiveness directly determines the accuracy and timeliness of fire warnings and the quality of initial response actions. Malfunctioning or poorly calibrated equipment may result in delayed alerts or false negatives, jeopardizing both passenger safety and emergency procedures.

Effectiveness of Emergency Plans (S14) acts as the strategic link that connects risk identification with actionable response. Well-developed emergency plans include clearly defined response thresholds, resource allocations, personnel assignments, and communication protocols. During incidents, standardized command structures and intelligent decision-support tools enable rapid and efficient emergency handling, minimizing casualties and losses.

In summary, the joint optimization of S6, S16, S1, S10, and S14 is essential to building a robust, multi-layered defense mechanism against subway station fires, ensuring proactive risk reduction and efficient emergency response.

3.3.2. Causality Analysis

As shown in Table 5, a total of eleven factors—such as S2 (Rolling Stock Equipment System), S3 (Power Supply Equipment System), S5 (Staff Emergency Response Skills), and S6 (Fire Safety Education and Training)—are classified as causal factors, meaning they actively influence the behavior or state of other components within the fire risk system. Among these, S16 (Completeness of Fire Management Rules and Regulations) exhibits the highest causality degree, signifying its dominant role in triggering downstream effects and shaping system-wide fire safety performance.

In contrast, factors including S4 (Passenger Fire Safety Awareness), S8 (Adverse Environmental Elements Inside and Outside the Station), S11 (Effectiveness of Early Warning Systems), S12 (Staff Security Inspection Competence), and S13 (Emergency Supplies Support Capability) are identified as resultant factors, which are predominantly shaped by changes in other variables. Their states are reflective of systemic responses to shifts in causal drivers, and they represent the observable consequences of upstream weaknesses. This distinction highlights the dynamic interplay between cause and effect in subway fire risk propagation and reinforces the need to prioritize root causes for effective prevention strategies.

3.3.3. ISM Results Analysis

The Interpretive Structural Modeling (ISM) analysis reveals a multi-level hierarchical structure among the influencing factors of subway station fire incidents, offering valuable insights into the underlying logic of fire risk propagation. According to the model, a total of 22 factors are arranged across six hierarchical levels, where a higher level signifies deeper systemic influence and broader impact scope. These levels can be grouped into three categories: fundamental causes, intermediate causes, and direct (surface) causes. At the top of the hierarchy, Level 6 (L6) includes S16 (Completeness of Fire Management Rules and Regulations), S6 (Fire Safety Education and Training), and S7 (Architectural Fire Protection Design). These are identified as fundamental influencing factors, as they shape the behavior of numerous downstream components and establish the foundation for the entire fire safety framework in subway systems.

In contrast, Levels 2 through 5 (L2–L5) consist of intermediate factors that serve as critical connectors in the fire risk transmission chain. They mediate the effects of deep-rooted causes and influence how risks manifest and escalate. At the bottom, Level 1 (L1) comprises direct causes—factors that directly lead to fire incidents, such as equipment failures or insufficient emergency responses. Although these are the most immediately observable, they are often symptoms of systemic deficiencies rooted in the upper levels. This layered structure emphasizes the importance of adopting a top-down fire risk management approach, targeting core weaknesses at the institutional and design levels while reinforcing operational readiness and response capabilities at the front line.

4. Analysis of Causative Link Path

4.1. Transmission Path Analysis Starting from S6

Starting from the key causative factor S6 (Fire Safety Education and Training), the causative paths that affect fire accidents in subway stations are sought. There are a total of 26 causative chains, as shown in Figure 4. Based on the hierarchical structure and centrality value, the influence, degree of being affected, centrality, and ranking of different risk transmission paths are listed, as shown in

Table 8. Analysis of the conduction path of S6.

No.	Path	Influence Degree		Reception Degree		Centrality
		Value	Rank	Value	Rank	Value	Rank
1	S6 → S5 → S4	4.7928	24	4.4524	22	9.2451	23
2	S6 → S5 → S20	4.6645	25	4.0534	25	8.7179	25
3	S6 → S9 → S1 → S2 → S12	7.7882	18	6.7654	19	14.5535	17
4	S6 → S9 → S1 → S2 → S10 → S8	9.7471	10	8.8282	12	18.5753	10
5	S6 → S9 → S1 → S2 → S10 → S11	9.8836	8	10.8836	1	11.8836	20
6	S6 → S9 → S1 → S2 → S10 → S15	9.6508	12	10.5488	2	11.5488	21
7	S6 → S9 → S1 → S2 → S19 → S18	9.5488	14	9.0485	8	18.5973	9
8	S6 → S9 → S1 → S3 → S10 → S8	9.7048	11	8.7517	14	18.4565	11
9	S6 → S9 → S1 → S3 → S10 → S11	9.8413	9	8.9309	11	18.7722	8
10	S6 → S9 → S1 → S3 → S10 → S15	9.6085	13	8.7895	13	18.398	12
11	S6 → S9 → S1 → S3 → S13	7.6103	19	6.971	18	14.5812	16
12	S6 → S14 → S1 → S2 → S12	8.2184	16	6.9891	17	15.2074	15
13	S6 → S14 → S1 → S2 → S10 → S8	10.1773	3	9.0519	7	19.2292	4
14	S6 → S14 → S1 → S2 → S10 → S11	10.3138	1	9.2311	4	19.5449	1
15	S6 → S14 → S1 → S2 → S10 → S15	10.081	5	9.0897	6	19.1707	5
16	S6 → S14 → S1 → S2 → S19 → S18	9.979	7	9.2722	3	19.2512	3
17	S6 → S14 → S5 → S4	6.6301	21	5.9639	21	12.5939	19
18	S6 → S14 → S5 → S20	4.1771	26	4.0999	24	8.2771	26
19	S6 → S14 → S1 → S3 → S13	8.0405	17	7.1947	16	15.2351	14
20	S6 → S14 → S1 → S3 → S10 → S8	10.135	4	8.9754	10	19.1104	6
21	S6 → S14 → S1 → S3 → S10 → S11	10.2715	2	9.1546	5	19.4261	2
22	S6 → S14 → S1 → S3 → S10 → S15	10.0387	6	9.0132	9	19.0519	7
23	S6 → S14 → S17 → S11	6.9001	20	6.039	20	12.939	18
24	S6 → S14 → S17 → S19 → S18	8.2975	15	7.6676	15	15.965	13
25	S6 → S14 → S21	5.1275	23	3.9728	26	9.1002	24
26	S6 → S14 → S22	5.557	22	4.1653	23	9.7222	22

.

The causal chain with the highest degree of influence and centrality is Fire Safety Education and Training (S6) → Effectiveness of Emergency Plans (S14) → Fire Smoke Detection and Firefighting Capability (S1) → Rolling Stock Equipment System (S2) → Operational Status of Monitoring Equipment (S10) → Effectiveness of Early Warning Systems (S11).

The most severely affected causal chain is Fire Safety Education and Training (S6) → Emergency Evacuation Design (S9) → Fire Smoke Detection and Firefighting Capability (S1) → Rolling Stock Equipment System (S2) → Operational Status of Monitoring Equipment (S10) → Effectiveness of Early Warning Systems (S11).

Fire Safety Education and Training (S6) is an important foundation of the entire metro fire safety system. Through conducting fire safety education and training for subway staff and passengers, their demands and behavioral characteristics for evacuation have become clearer. Based on effective fire safety education and training, Effectiveness of Emergency Plans (S14) has become a key link in the cause-causing chain. A complete and effective emergency response plan should fully take into account factors such as the spatial layout of subway stations, the characteristics of personnel flow, and the conditions of equipment and facilities and formulate detailed response strategies for different types of fire scenarios. It is not only necessary to clarify the responsibilities and divisions of labor of each department and personnel in fire emergency response but also to plan evacuation routes and determine rescue resource allocation plans. When conducting Emergency Evacuation Design (S9), the width and direction of evacuation passages, the setting of evacuation signs, and the formulation of evacuation plans can be considered more specifically. Emergency evacuation design determines key elements such as the routes, time, and space for personnel evacuation. This requires the Fire Smoke Detection and Firefighting Capability (S1) to accurately monitor the spread of smoke in these areas, so as to provide accurate information support for evacuation. The temperature sensors, smoke sensors and other components in the Rolling Stock Equipment System (S2) can provide real-time data for fire smoke monitoring, while communication devices can promptly transmit these monitoring data to the fire control center to enable timely response measures to be taken [26]. Operational status of monitoring equipment (S10) directly determines the effectiveness of the early warning system (S11). Accurate and reliable monitoring equipment can obtain fire-related information in real time, such as temperature and smoke concentration, and promptly transmit this information to the early warning system. The early warning system analyzes and judges the received information. When the set threshold is reached, it promptly issues an alarm to remind the staff and passengers to take corresponding countermeasures.

4.2. Transmission Path Analysis Starting from S7

Using S7 (Architectural Fire Protection Design) as the starting point, nine major risk transmission chains were identified, as depicted in Figure 5. These chains illustrate how design-related factors influence downstream fire safety performance. The calculated influence degree, reception degree, and centrality of each chain are detailed in

Table 9. Analysis of the conduction path of S7.

No.	Path	Influence Degree		Reception Degree		Centrality
		Value	Rank	Value	Rank	Value	Rank
1	S7 → S9 → S1 → S2 → S12	6.5143	8	6.2291	9	12.7434	9
2	S7 → S9 → S1 → S2 → S10 → S8	8.4732	3	8.2919	5	16.7652	4
3	S7 → S9 → S1 → S2 → S10 → S11	8.6097	1	8.4711	2	17.0809	1
4	S7 → S9 → S1 → S2 → S10 → S15	8.3769	5	8.3297	4	16.7067	5
5	S7 → S9 → S1 → S2 → S19 → S18	8.2749	7	8.5122	1	16.7872	3
6	S7 → S9 → S1 → S3 → S10 → S8	8.4309	4	8.2154	7	16.6464	6
7	S7 → S9 → S1 → S3 → S10 → S11	8.5674	2	8.3946	3	16.9621	2
8	S7 → S9 → S1 → S3 → S10 → S15	8.3346	6	8.2532	6	16.5879	7
9	S7 → S9 → S1 → S3 → S13	6.3364	9	6.4347	8	12.7711	8

.

Among them, the chain with the highest overall influence and centrality is S7 → S9 (Emergency Evacuation Design) → S1 (Fire Smoke Detection and Firefighting Capability) → S2 (Rolling Stock Equipment System) → S10 (Operational Status of Monitoring Equipment) → S11 (Effectiveness of Early Warning Systems).

The chain with the highest reception degree is S7 → S9 → S1 → S2 → S19 (Emergency Repair and Rescue Capability) → S18 (Medical Response Capability).

These two chains reflect how fire protection design at the architectural level sets off a series of technical and emergency response processes that are crucial to fire risk mitigation in subway environments.

Architectural Fire Protection Design (S7) serves as a structural safeguard that limits fire spread and enables compartmentalized protection. A well-designed system ensures that, during a fire event, independent fire zones can effectively contain the hazard, allowing safe routes and buffer spaces for evacuation. This physical foundation directly supports Emergency Evacuation Design (S9), which determines critical parameters such as corridor width, evacuation flow direction, signage placement, and the logic of escape routes. For these designs to be operationally effective, S1 (Fire Smoke Detection and Firefighting Capability) must function reliably by accurately sensing smoke density, temperature, and spread rate in real time, providing essential input for both evacuation and suppression decisions.

Further down the chain, S10 (Operational Status of Monitoring Equipment) plays a vital role by collecting and transmitting fire-related data—including smoke concentration and thermal conditions—to the control system. The accuracy and responsiveness of S11 (Effectiveness of Early Warning Systems) are directly dependent on this real-time input. Malfunctions or delays in monitoring may lead to untimely or incorrect alerts, undermining emergency response efficiency. In the chain involving S19 (Emergency Repair and Rescue Capability) and S18 (Medical Response Capability), the connection highlights the post-fire recovery phase. Timely rescue operations facilitate access to affected areas, helping emergency responders reach and treat injured individuals swiftly, thereby improving survival outcomes and reducing the severity of fire-related consequences.

4.3. Transmission Path Analysis Starting from S16

With S16 (Completeness of Fire Management Rules and Regulations) as the starting point, the analysis identifies fifteen key causative chains of fire risk propagation in subway stations, as illustrated in Figure 6. The influence degree, reception degree, and centrality of these chains are presented in

Table 10. Analysis of the conduction path of S16.

No	Path	Influence Degree		Reception Degree		Centrality
		Value	Rank	Value	Rank	Value	Rank
1	S16 → S14 → S5 → S4	6.5875	12	5.848	12	12.4355	12
2	S16 → S14 → S5 → S20	6.4592	13	5.449	13	11.9083	13
3	S16 → S14 → S21	5.1275	15	3.9728	15	9.1002	15
4	S16 → S14 → S22	5.5144	14	4.0494	14	9.5638	14
5	S16 → S14 → S1 → S2 → S12	8.1758	9	6.8732	10	15.049	10
6	S16 → S14 → S1 → S2 → S10 → S11	10.2712	1	9.1152	2	19.3865	1
7	S16 → S14 → S1 → S2 → S10 → S15	10.0384	5	8.9738	4	19.0123	5
8	S16 → S14 → S1 → S2 → S10 → S8	10.1347	3	8.936	5	19.0708	4
9	S16 → S14 → S1 → S2 → S19 → S18	9.9364	7	9.1563	1	19.0928	3
10	S16 → S14 → S1 → S3 → S10 → S11	10.2289	2	9.0387	3	19.2677	2
11	S16 → S14 → S1 → S3 → S10 → S8	10.0924	4	8.8595	7	18.952	6
12	S16 → S14 → S1 → S3 → S10 → S15	9.9961	6	8.8973	6	18.8935	7
13	S16 → S14 → S1 → S3 → S13	7.9979	10	7.0788	9	15.0767	9
14	S16 → S14 → S17 → S11	6.8575	11	5.9231	11	12.7806	11
15	S16 → S14 → S17 → S19 → S18	8.2549	8	7.5517	8	15.8066	8

.

Among them, the chain with the highest influence and centrality is S16 → S14 (Effectiveness of Emergency Plans) → S1 (Fire Smoke Detection and Firefighting Capability) → S2 (Rolling Stock Equipment System) → S10 (Operational Status of Monitoring Equipment) → S11 (Effectiveness of Early Warning Systems).

The chain with the highest reception degree is S16 → S14 → S1 → S2 → S19 (Emergency Repair and Rescue Capability) → S18 (Medical Response Capability).

These two chains reveal how fire safety regulations serve as the upstream initiator of multi-stage fire response processes and system readiness.

A well-established fire management regulatory system (S16) forms the institutional cornerstone of subway safety. It defines standardized procedures for routine inspections of fire protection facilities, sets clear requirements for staff training, and delineates organizational responsibilities. This regulatory framework provides structured support for the development of S14 (Emergency Plans) that are not only scientifically grounded but also operationally feasible. Effective emergency plans, in turn, enhance the performance of S1 (Fire Smoke Detection and Firefighting Capability) by ensuring that critical systems and personnel responses are well-coordinated under emergency conditions [27].

Downstream, the Rolling Stock Equipment System (S2) is crucial not only for safe rail operations but also for its integration with fire detection and response capabilities. A well-functioning S1 ensures that fire threats are detected early enough to protect rolling stock and minimize service disruptions. Furthermore, S10 (Operational Status of Monitoring Equipment) serves as the critical interface between detection and early warning. Its reliability directly impacts S11 (Effectiveness of Early Warning Systems), determining whether accurate, timely alerts can be issued to activate emergency protocols. Any delay or error at this stage may compromise response efficiency and system resilience.

4.4. Discussion of Comparative Insights from Transmission Paths of S6, S7, and S16

The representative transmission paths originating from S6 (Fire Safety Education and Training), S7 (Architectural Fire Protection Design), and S16 (Completeness of Fire Management Rules and Regulations) illustrate distinct yet complementary strategic perspectives for enhancing fire safety in subway stations. Each path reflects a different system layer—human, spatial, and institutional—contributing uniquely to fire risk mitigation.

• S6 Path: Human-Centered Activation

Starting from S6, the path with the highest influence and centrality degree is identified as S6 → S14 → S1 → S2 → S10 → S11, while the path with the highest reception degree is S6 → S9 → S1 → S2 → S10 → S11.

The path with the highest influence and centrality degree underscores the pivotal role of personnel preparedness. Fire safety education and training act as the behavioral catalyst, initiating improvements in emergency planning (S14), enhancing detection and response capabilities (S1), and ultimately strengthening early warning effectiveness (S11). It illustrates a bottom-up mobilization logic, where enhanced awareness and operational readiness among staff and passengers drive the robustness of the entire safety system.

Accordingly, fire safety education and training should be integrated into the qualification certification and promotion assessment systems for subway personnel to enhance their practical emergency response capabilities. Specific measures include implementing mandatory training modules based on typical fire scenarios, with content regularly updated to reflect emerging technologies and risk conditions; linking certification renewal and promotion evaluations to individuals’ proficiency in fire emergency handling; and promoting position-specific joint emergency drills to strengthen interdepartmental coordination and response synergy.

2.

S7 Path: Structural Safeguard Foundation

Starting from S7, the path with the highest influence and centrality degree is identified as S7 → S9 → S1 → S2 → S10 → S11, while the path with the highest reception degree is S7 → S9 → S1 → S2 → S19 → S18.

The path with the highest influence and centrality degree reflects a design-centric approach to fire resilience. Architectural fire protection planning and rational Emergency Evacuation Design (S9) provide the spatial foundation necessary for effective firefighting operations, monitoring (S10), and safe evacuation. It exemplifies a hardware-oriented pathway, emphasizing how physical layout and spatial compartmentalization shape downstream system reliability.

Therefore, during the initial planning stage of building fire protection design, efforts should be made to strengthen fire and smoke compartmentation, enhance the fire resistance rating of fire separation facilities, properly install fire separation devices, and reduce the failure rate of smoke control systems to effectively prevent high-loss risk fire incidents [28]. In the later operation and maintenance stage, it is recommended to establish a post-occupancy evaluation mechanism, making use of data from routine drills, minor incidents, and near misses to continuously optimize key design elements.

3.

S16 Path: Institutional Control Backbone

Starting from S16, the path with the highest influence and centrality degree is identified as S16 → S14 → S1 → S2 → S10 → S11, while the path with the highest reception degree is S16 → S14 → S1 → S2 → S19 → S18.

Rooted in governance and regulation, the path with the highest influence and centrality degree represents a top-down management model. The completeness of fire management rules and regulations initiates coordinated improvements in planning (S14), system readiness (S1, S2), and technical responsiveness (S10, S11). It emphasizes the institutional layer as the backbone of system-wide fire safety control, ensuring accountability, procedural standardization, and operational discipline.

Along this risk transmission path, it is essential that urban rail transit operations ensure regular revision and updating of fire safety regulations in response to emerging technologies, evolving risks, and actual operational conditions. For example, annual third-party fire risk audits should be conducted, covering all subway stations to identify and rectify potential hazards in a timely and systematic manner.

Although these paths originate from different domains—people, structure, and policy—they almost ultimately converge on S11 (Effectiveness of Early Warning Systems). This convergence highlights early warning performance as the critical endpoint of a successful fire safety strategy. The results emphasize the necessity of an integrated “people–system–structure” approach, where education and training, spatial design, and institutional control reinforce one another to enhance fire resilience in complex urban transit environments.

5. Conclusions

This study integrates the PSR (Pressure–State–Response) model with the DEMATEL and ISM methods to systematically identify, classify, and analyze the influencing factors of subway station fire safety. A total of 22 secondary indicators were constructed across the three PSR dimensions, providing a structured and dynamic analytical framework. By incorporating centrality values and causal relationships derived from DEMATEL, the study quantitatively evaluated factor importance and identified key causative chains through risk transmission path analysis.

The results reveal that subway fire incidents are shaped by complex and interrelated factors, with S6 (Fire Safety Education and Training), S16 (Completeness of Fire Management Rules and Regulations), and S7 (Architectural Fire Protection Design) serving as fundamental initiators within the ISM hierarchy. Six critical transmission paths were identified, showing how human, managerial, and structural elements propagate through technical systems—such as S1 (Fire Smoke Detection and Firefighting Capability), S2 (Rolling Stock Equipment System), and S10 (Operational Status of Monitoring Equipment)—to ultimately impact S11 (Effectiveness of Early Warning Systems) and emergency outcomes.

These findings demonstrate the layered and systemic nature of subway fire risk evolution. They provide theoretical support and practical direction for risk mitigation strategies. Enhancing staff training, improving emergency planning, refining architectural design, and strengthening fire safety regulations are essential to building a resilient, proactive, and integrated fire safety system in urban rail transit environments.