Exploring the Mutual Influence Relationships of International Airport Resilience Factors from the Perspective of Aviation Safety: Using Fermatean Fuzzy DEMATEL Approach

Abstract

International airports are responding to the threat of climate change and various man-made hazards by proposing impact protection measures. Airport managers and risk controllers should develop a comprehensive risk assessment model to measure the mutual influence relationships of resilience factors. In this paper, the problem of treating resilience factors as independent ones in previous studies is overcome. In this study, we not only develop a framework for assessing resilience factors in international airports based on an aviation safety perspective, but also develop the Fermatean fuzzy decision-making trial and evaluation laboratory (FF-DEMATEL) to identify the mutual influence relationships of resilience factors. Fermatean fuzzy sets are incorporated in DEMATEL to reflect information incompleteness and uncertainty. The critical resilience factors of international airports were identified through real-case analysis. In terms of importance, the results show that rescue capability is a core capability that is important for airport resilience. In addition, “security management system (SeMS) integrity”, “education and training of ground staff on airport safety awareness”, “first aid mechanism for the injured”, and “adequate maintenance equipment for rapid restoration tasks” are identified as key factors that are given more weights. On the other hand, in terms of influence strength, the detection capability has the highest total influence and significantly influenced the other resilience capabilities. Finally, the influential network relation map (INRM) is utilized to assist decisionmakers in swiftly comprehending the impact of factors and formulating viable strategies to enhance airport resilience. This enables airport managers and risk controllers to make informed decisions and allocate resources efficiently.

1. Introduction

On 11 September 2001, a series of suicide terrorist attacks in the United States caused a major shutdown of the U.S. airport operation, resulting in significant economic losses, traffic congestion and gridlock, and health and environmental problems [1,2]. This incident also prompted the U.S. government to recognize the importance of infrastructure risk and resilience assessment. In transportation, airports are the primary infrastructure for air transportation, and they serve as hubs of transportation among countries around the world. There have been many man-made accidents and natural disasters that have caused airport failures, leading to serious problems such as restricted entry and exit of the country, flight delays, and passenger panic [3]. Choi et al. [4] show that international airports are critical to the social and economic development of countries and regions and are key drivers in the global supply chain, and in turn, enhance various economic benefits in other industries. Therefore, air transportation has become a key infrastructure that affects globalization and cultural and economic exchanges.

In the face of climate change and man-made hazards, ensuring airport resilience is of utmost importance. Unpredictable internal events or external attacks with unknown vulnerabilities can lead to disruptions in the air transportation system and significantly impact airport operations. However, if airport risk management measures are proactively planned and resilience is enhanced, the negative impacts following such events can be mitigated [5]. Therefore, it is crucial for airport managers to utilize a resilience assessment model to develop comprehensive protection strategies and contingency measures. This approach not only improves emergency management capabilities but also facilitates efficient reconstruction planning, aiming to enhance facility resilience, minimize the likelihood of air transportation system disruptions, and expedite the airport’s return to normal operations [6].

Huang et al. [2] proposed a complete framework for airport resilience assessment in which they divided airport resilience capabilities into four stages, including detection capability, resistance capability, rescue capability, and recovery capability, which can be subdivided into a number of resilience factors. The Bayesian best worst method (Bayesian BWM) was used to determine the optimal group weights of these resilience factors. However, Huang et al. [2] assume that the resilience factors are independent. In reality, these factors should highly influence each other, especially within each stage. Unfortunately, no studies have explored the mutual influence relationship of these factors, and few studies have examined the issue of airport resilience from an aviation safety perspective.

To fill these research gaps, this study proposes a framework for assessing international airport resilience factors based on an aviation safety perspective and develops the Fermatean fuzzy decision-making trial and evaluation laboratory (FF-DEMATEL) to identify the mutual influence relationships of resilience factors. This study provides a comprehensive view of airport security, aiding in decision making and strategies to enhance its effectiveness in uncertainty and interconnected environment. Here, Fermatean fuzzy sets (FFs) are used to interpret the ambiguity and uncertainty of expert semantics, especially in the presence of information omissions and incompleteness. FFs, compared to intuitionistic and Pythagorean fuzzy sets, encompasses a broader range of fuzzy information [7,8]. On the other hand, DEMATEL is one of the most effective methods to identify the mutual influence relationships among factors in MCDM. Since airport resilience factors are mutually constrained, soft computing models are needed to explore which factors mainly affect others, and which factors are easily affected by other factors. The proposed FF-DEMATEL combines FFs and DEMATEL to determine the indirect and direct influence relationships among the resilience factors. This model overcomes the limitations of original DEMATEL by addressing the issue of information uncertainty. Finally, the influential network relation map (INRM) is used to help decisionmakers quickly understand the influence of factors on each other, so as to formulate feasible strategies to improve airport resilience. Based on the aforementioned advantages of FF-DEMATEL, this study adopts this technique as a tool for data analysis.

The research gaps and contributions of this study are described below.

i.

The international airport resilience assessment framework proposed in this study is novel, especially from the perspective of aviation safety.

ii.

This study improves the shortcoming of Huang et al. [2]’s study, which assumed that the resilience factors are independent.

iii.

Incorporating FFs into DEMATEL in this study not only reflects information uncertainty, but also covers a wider range of missing information.

iv.

This study uses Taiwan’s Taoyuan International Airport as an analysis case, and the research process can be replicated in other international airports.

v.

Decisionmakers or risk managers can use the INRM and factor–influence relationships to develop risk management strategies to enhance the resilience of international airports.

The remaining sections of this study are organized as follows: Section 2 reviews the relevant studies on airport resilience assessment. Section 3 introduces the proposed airport resilience assessment framework and the resilience factors. Section 4 presents the implementation procedures and equations of FF-DEMATEL. Section 5 presents a case study and illustrates the results of the analysis. Finally, Section 6 discusses and draws conclusions and recommendations for future research.

2. Literature Review on Airport Resilience

In the past, cost–benefit analysis (CBA) has been one of the most popular tools for risk assessment. However, CBA analysis is not effective in accurately estimating current airport security costs, so Stewart and Mueller [9] believe that more simulation experiments are needed to explore the interdependencies that exist in airport security. In addition to CBA, past studies have developed theoretical frameworks to discuss airport resilience; for example, Zhou and Chen [10] explored the condition of airports in China after being affected by severe weather events. They developed a new indicator framework to measure the level of airport resilience to assess the speed of recovery of airline services from a disruptive event. The study showed that airport resilience is affected by weather conditions, airport capacity, and alternatives. Bao and Zhang [6] measured the resilience of Beijing Capital International Airport to emergency events. The study developed a system to measure the resilience of large airports to emergencies, identifying how vulnerability and contingency affect operational resilience so that airport managers can take appropriate measures to respond to emergencies. Janić [5] explored the resilience of air cargo networks (e.g., FedEx Express) after being disrupted by large-scale events. The study proposes a methodology for estimating the resilience of air cargo networks and selects the best response strategies to improve the resilience of air cargo and its ability to withstand large internal and external disruptive events. The results of the study indicate that inventory costs are the most influential factor in the resilience of air cargo networks.

Qin et al. [11] explored air cargo congestion due to disaster events. They proposed a two-stage optimization approach to coordinate aircraft takeoff and landing plans with cargo ramp aircraft parking arrangements to improve rescue efficiency and reduce the ongoing impact of disasters. The study identifies runway and storage integration management as the most critical factors for improving mission fleet turnaround. Rezaee and Yousefi [12] applied multiple criteria decision-making (MCDM) methodology to investigate airport operational performance and risk management at Urmia International Airport in Iran. They consider the causal relationships among risks and the negative impact on airport operational performance after risk events. Wang et al. [13] explored the unmanned aerial systems (UAS) intrusion at Singapore Airport. They propose a probabilistic conflict prediction with Monte Carlo simulations to predict the potential collision routes of drones, which can help flight safety personnel quickly identify potential threats during drone incursions and pass it on to the pilots to take mitigation measures as soon as possible, effectively reducing flying risks. More research on airport resilience is summarized in

Table 1. Relevant studies on airport resilience assessment.

Author	Research Content	Methodology
Janić [14]	The study assesses how the air transportation network at U.S. airports is affected by events and how quickly the impact is reduced and normal operations are restored. The study found that the resilience of airports after an event is the ability to maintain operations.	A novel approach to estimating the resilience, vulnerability, and cost of aviation networks.
Zhou and Chen [10]	The study explores what factors affect airport resilience after severe weather events in Chinese airports. The study indicates that airport resilience is related to weather conditions, airport capacity, and alternatives.	A new indicator to measure the level of airport resilience, calculating the speed of recovery of airline services from disruptive events.
Yanjun et al. [15]	The study assesses the robustness of China’s air transportation systems after disruptive events through simulations, specifically taking into account structural and dynamic aspects of the airports to measure the resilience of the airports. The study shows that the size and intensity of disruptions at airports have a direct impact on the severity of system degradation and recovery time.	An agent-based model to assess the operational resilience of airline networks.
Clark et al. [16]	The study analyzes the criticality and resilience of the U.S. National Airspace System’s airport network following natural disasters, human factors, and cyberattacks to improve management vulnerabilities. The study shows that identifying system deficiencies can improve system robustness and resiliency.	A method to analyze the functional relationship of airports.
Zhao et al. [17]	The study explores the economic and technical analysis of hydrogen energy systems, photovoltaic energy, battery storage systems, aircraft electric auxiliary power units, and electric vehicles in the airport electrification energy system to investigate the advantages of hydrogen energy for power outage resilience.	A mixed-integer linear programming optimization method based on life cycle theory.
Bao and Zhang [6]	The study explores the resilience of the Beijing Capital International Airport (BCIA) to measure which factors affect airport resilience. The study indicates that total vulnerability and resilience are primarily influenced by the land sector, and that overall emergency response capacity is also decisive for airport resilience.	A system of indicators to measure the resilience of large airports to emergencies.
Wong et al. [18]	The study explores the impact of disruptive events (e.g., severe weather, human factors, and force majeure) on individual airline operational resilience at four U.S. airports to provide new insights into network theory. The results show that all three methods are effective in identifying airline resilience differences among airlines.	Data-driven analysis, Mahalanobis distance, network analysis, and hybrid data-driven network analysis.
Kisiel [19]	The study explores the A320 single-aisle aircraft at EPA Flughafen (EPWR) and examines the sensitivity and flexibility of boarding strategies to the number of priority passengers in order to improve boarding efficiency. The findings suggest that a random passenger boarding strategy could be used to optimize the passenger boarding process.	The concept and structure of a simulation model that calculates passenger boarding times based on the number of priority passengers.
Janić [5]	The study focuses on assessing the resilience of the air cargo network (FedEx Express, U.S.) to quickly return to operational capacity after a large-scale disruptive event (the northeast blizzard). The study identifies resilience as the ability of an airport to maintain planning during and after a disruptive event.	A methodology for estimating the resilience of an airline cargo transport network.
Gössling [20]	The study draws attention to the long-term problems of air transportation through the COVID-19 crisis, and the potential risks to society from aviation development, including excessive CO2 emissions, rapid spread of disease, and airline overcapacity, among other problems. The study suggests that the optimal flexibility of the airline system should be based on the question of how much air transportation is needed, that an ideal airline system is one that takes into account social risks, and that its costs are part of the price of air travel.	Qualitative research.
Zhou et al. [21]	The study finds that the number of disrupted links (global airport connections) caused by COVID-19 is very high, so the number of links is important in measuring the vulnerability of air transport networks. The study takes a practical approach to the vulnerability of the global air transport network to different levels of airport disruptions and finds that the key to connectivity is primarily in bridging different airports rather than among core airports in the global air transport network.	A novel hierarchically weighted network efficiency indicator to measure air transportation network connectivity.
Qin et al. [11]	The study illustrates how to improve the resilience of airport rescue in order to achieve the best rescue results and reduce the ongoing impact of disasters that require air support and are prone to air transport congestion. The study points out that the arrival and departure times of each flight are planned according to the respective cargo transportation needs, and runway resources are limited, so integrated runway and storage management to achieve appropriate resource allocation is the key to improving aircraft turnover.	Development of a two-stage optimization method.
Mottahedi et al. [22]	The study uses a combination of expert judgment and fuzzy set theory in an underground coal mine main wind turbine system to understand the factors affecting resilience for effective resilience management. The study assesses the factors affecting resilience through reliability, maintainability, organizational resilience, and equipment health management indices, which were used by managers to improve or optimize operational strategies to increase the overall resilience of the organization.	A practical index-based approach to facilitate the process of estimating system flexibility while taking into account influencing factors.
Sreenath et al. [23]	The study evaluates the potential risks of solar PV (photovoltaics) at airports and minimized them to achieve maximum economic benefits. The study identifies the most serious risks as interference with the communication system, bird strikes at PV sites, and electrical hazards to the PV system, and implemented mitigation measures from the most serious risks to achieve the maximum shallowness of the solar PV installation.	HIRA (hazard identification and risk assessment) methodology.
Valotto et al. [24]	The study analyzes road dust in the vicinity of Venice International Airport to identify the most polluted sites and to understand the risk assessment of human exposure, dermal exposure, and inhalation pathways. The study identifies streets as the most polluted areas and road dust as an important source of atmospheric particulate matter through resuspension.	The statistical methods EF (the enrichment factors), PLI (pollution load index), CA (cluster analysis), and PCA (principal component analysis) were used to identify the most polluted sites in the monitoring area, and then the inverse distance weighted (IDW) method was used to study the spatial variation of PLI in the monitoring area.
Huang et al. [2]	The study illustrates a comprehensive airport resilience measure, using Taiwan’s airports as an example, to assess four dimensions (detection capability, resilience, rescue capability, and recovery capability) as a basis for decision making by operations-related managers. The results of the study include pre-risk detection capability to post-risk recovery capability, which helps to strengthen the vulnerability of airports.	Bayesian BWM and modified PROMETHEE.
Janssen et al. [25]	The study analyzes IEDs (improvised explosive devices), and different efficiency performance indicators in the aviation sector, and identified the influence relationships among security risks and efficiency indicators. The study finds that reducing the number of passengers prior to screening, reducing security risks, efficiency measures, and maximizing passenger dispersion in available space can reduce the post-incident impact of airports.	It develops new research methods combining agent-based security risk assessment methods and typical agent-based methods to analyze operational efficiency.
Wang et al. [26]	The study explores the potential for recreational UAS (unmanned aerial systems) intrusion into Singapore airport airspace and post-collision event effects. The study assesses and simulates UAS flight paths, collision risks, and the worst-case scenario that would allow Singapore Airport to experience an emergency without the need to immediately close the airport to maintain flight safety and operations.	3D Monte Carlo UAS location distribution model.
Wang et al. [13]	The study analyzes UAS (unmanned aerial systems) intrusions at Singapore airports to help traffic controllers quickly identify UAS that pose a threat and communicate the message to pilots to take mitigation measures as soon as possible. The study finds that defining safe flight operations could improve flight path planning in the future by taking into account more real-world events and models.	A probabilistic collision prediction collision route based on the well-known optimal rapidly-exploring random tree (RRT) using Monte Carlo and sensors to generate acceptable collision prediction routes.
Rezaee and Yousefi [12]	The study was conducted to optimize risk management priorities at the Urmia International Airport in Iran by identifying airport risk priorities, considering the causal relationships among risks and the performance of airport operations after the impact of an event. This enables airport management to effectively plan control measures to improve safety and system performance.	MCDM, data envelopment analysis (DEA) model, FCM method, SBDEA method.

.

Upon reviewing previous literature, it is evident that while many studies have delved into the resilience and security aspects of airports, few have employed the MCDM method to evaluate the mutual influences among airport resilience factors. Additionally, most existing research focuses on specific regions or events, lacking a universally applicable, comprehensive framework for airport resilience assessment. This study addresses these gaps by introducing a holistic risk assessment model that not only thoroughly investigates various resilience factors but also delves into their interdependencies. By integrating the FF-DEMATEL method, our research not only captures the uncertainties of the information but also generates influence weights, thereby ranking these resilience factors. This provides airport managers with a clearer and more practical guideline for decision making.

3. Proposed Airport Resilience Factors

This study invited risk managers and senior aviation police executives from international airports to form a decision-making group. To gather the experts, we initially conducted a comprehensive review of the industry and identified potential candidates based on their professional background and years of experience. The approach for selecting experts follows the methods of past research [27,28]. We then approached these candidates through formal invitations, explaining the purpose and importance of their participation in the study. We emphasized the significance of their expertise in evaluating resilience factors and their contribution to enhancing airport safety and preparedness.

The members of the decision-making group were all experienced in aviation safety duties for many years and had been in supervisory positions for more than five years. All members’ backgrounds are described in

Table 2. Background information of the 17 experts.

No.	Department	Job Title	Work Experience (Years)	Education
1	Aviation Police Bureau	Deputy Captain	5–10	Master
2	Civil Aeronautics Administration	Senior Specialist	More than 10	Master
3	Aviation Police Bureau	Major	More than 10	Master
4	National Immigration Agency	Inspector	More than 10	Master
5	Aviation Police Bureau	Captain of Section	5–10	Bachelor
6	National Immigration Agency	Senior Executive Officer	More than 10	Master
7	Civil Aeronautics Administration	Specialist	5–10	Master
8	Aviation Police Bureau	Commander	More than 10	Bachelor
9	Central Police University	Doctoral Candidate	More than 10	Master
10	Aviation Police Bureau	Commander	More than 10	Master
11	Aviation Police Bureau	Police Officer	More than 10	Bachelor
12	Aviation Police Bureau	Section Assistant	More than 10	Master
13	UPS	FSC	More than 10	Bachelor
14	Aviation Police Bureau	Section Assistant	2–3	Master
15	Aviation Police Bureau	Subsection Chief	More than 10	Master
16	Taoyuan International Airport Corporation	Senior Executive Officer	5–10	Master
17	Aviation Police Bureau	Sub-Lieutenant	More than 10	Bachelor

, and they were involved in identifying resilience factors, assessing factor influence, and developing management implications in this study.

The airport resilience factors were initially constructed by reviewing a large amount of the literature [2,4,5,6,10,29,30,31,32,33,34,35,36,37,38,39,40,41]. The resilience factors mentioned in these references serve as references for establishing the airport resilience assessment framework in this study. After more than five meetings, the unimportant resilience factors were eliminated, and the key important factors were retained. All selected resilience factors have received support from the aforementioned literature.

According to the resilience concept proposed by Huang et al. [2], the factors were further categorized into four categories, including detection capability (R₁), resistance capability (R₂), rescue capability (R₃), and recovery capability (R₄). R₁ refers to the ability to detect and predict the occurrence of an incident before the risk occurs, which can be composed of F₁ to F₅. R₂ refers to the ability to effectively suppress the severity of the hazard when the risk occurs, which can be composed of F₆ to F₁₀. R₃ refers to the ability to detect and predict the occurrence of an incident after the risk occurs, which can be composed of F₁₁ to F₁₆. R₄ refers to the ability to resume airport operations after the occurrence of the risk for a certain period of time, and can be composed of F₁₇ to F₂₂. All factors align with the resilience objectives of international airports. The definition of each resilience factor is shown in

Table 3. Proposed airport resilience factors.

Capability Code	Capability	Resilience Factor Code	Resilience Factor
R1	Detection capability	F1	Work environment planning and management, and personnel security awareness and alertness.
		F2	Security management system (SeMS) integrity.
		F3	Reliability of the airport’s video surveillance and epidemic prevention system.
		F4	Detection and handling of unauthorized drone activity.
		F5	Threat identification capability of the airport’s cyber security system.
R2	Resistance capability	F6	Emergency response procedures in case of discovering flammable or explosive substances.
		F7	Education and training of ground staff on airport safety awareness.
		F8	Architectural structure and earthquake prevention measures of airport terminal buildings.
		F9	Proper intrusion prevention measures for airport perimeters.
		F10	Airport cyber security system protection measures.
R3	Rescue capability	F11	Sufficiency of firefighting resources inside and outside the airport.
		F12	Stability of communication systems among various departments of the airport.
		F13	Adequate emergency evacuation measures and clear escape instructions.
		F14	First aid mechanism for the injured.
		F15	Drafting of emergency response plans and procedures for disaster relief.
		F16	Medical resources around the outside of the airport.
R4	Recovery capability	F17	Airport staff morale for post-disaster reconstruction.
		F18	Repair and maintenance planning of the internal facilities of the terminal.
		F19	Recovery command center established to coordinate the allocation of people, supplies, and resources.
		F20	Airport runway restoration operations in a timely manner.
		F21	Standby power generation equipment to ensure that the power system is not disrupted.
		F22	Adequate maintenance equipment for rapid restoration tasks.

.

4. FF-DEMATEL Approach

MCDM is undeniably a highly effective decision-making tool that has garnered widespread acclaim in various fields. Its distinct advantage lies in its capacity to handle complex decision problems where multiple criteria, often conflicting, need to be considered simultaneously [42]. DEMATEL is a technique for identifying the mutual influence relationships among factors in MCDM [8,28]. It is mainly used in qualitative assessment systems. It requires experts to determine the strength of the influence of each factor or inter-factor and convert it into a quantifiable value to obtain the INRM. This technique has been widely used in various decision-making problems of influence assessment. In this study, FFs are incorporated into the DEMATEL algorithm to retain more potential or uncertain or missing information. Since the assessment framework developed in Section 3 is a hierarchical structure with two levels, capability and factory, five DEMATEL interviews and calculations are required. The detailed FF-DEMATEL concept and calculation procedure are described below.

Step 1. 

Establish an Expert Decision-Making Group

Experts with expertise in airport resilience assessment were formed into a decision-making group. Expert k can be denoted as E_k, where k = 1, 2,…, K.

Step 2. 

Confirm the Factors of Airport Resilience

It is confirmed that all experts agree on the resilience factors compiled in Section 3. The factor j can be denoted as C_j, where j = 1, 2,…, n. The influence data among the factors can be obtained from

Table 4. Linguistic term of FFs [8].

Linguistic Term	FF Number
Influence Level	Membership (μ)	Non-Membership (v)
Nearly Influence (NI)	0.06	0.99
Low Influence (L)	0.11	0.99
Relatively Low Influence (RL)	0.27	0.98
Moderate Influence (M)	0.44	0.95
Moderately High Influence (MH)	0.56	0.90
High Influence (H)	0.69	0.82
Very High Influence (VH)	0.81	0.67
Extremely High Influence (EH)	0.92	0.51
Completely Influence (CI)	1.00	0.00

.

Step 3. 

Establish the FFs Direct Relationship Matrix

Experts need to make pairwise comparisons of n factors to obtain the mutual influence strength. In simple terms, expert k judges the direct influence strength of factor i on factor j according to Table 4 to form the FFs direct relationship matrix ${\mathit{X}}^{\left(k\right)}$, as shown in Equation (1).

$$\begin{gathered} {\mathit{X}}^{\left(k\right)}=\left[\begin{array}{cccc}\left({\mu }_F\left(x_{11}^{\left(k\right)}\right),v_F\left(x_{11}^{\left(k\right)}\right)\right)& \left({\mu }_F\left(x_{12}^{\left(k\right)}\right),v_F\left(x_{12}^{\left(k\right)}\right)\right)& \cdots & \left({\mu }_F\left(x_{1n}^{\left(k\right)}\right),v_F\left(x_{1n}^{\left(k\right)}\right)\right)\\ \left({\mu }_F\left(x_{21}^{\left(k\right)}\right),v_F\left(x_{21}^{\left(k\right)}\right)\right)& \left({\mu }_F\left(x_{22}^{\left(k\right)}\right),v_F\left(x_{22}^{\left(k\right)}\right)\right)& \cdots & \left({\mu }_F\left(x_{2n}^{\left(k\right)}\right),v_F\left(x_{2n}^{\left(k\right)}\right)\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({\mu }_F\left(x_{n1}^{\left(k\right)}\right),v_F\left(x_{n1}^{\left(k\right)}\right)\right)& \left({\mu }_F\left(x_{n2}^{\left(k\right)}\right),v_F\left(x_{n2}^{\left(k\right)}\right)\right)& \cdots & \left({\mu }_F\left(x_{nn}^{\left(k\right)}\right),v_F\left(x_{nn}^{\left(k\right)}\right)\right)\end{array}\right] \\ i=j=1, 2,\dots , n; k=1, 2,\dots , K, \end{gathered}$$

(1)

where ${\mu }_F\left(x_{ij}^{\left(k\right)}\right)$ and $v_F\left(x_{ij}^{\left(k\right)}\right)$ are the membership (μ) and non-membership (v) of the assessment of x events, in which $0\le {\mu }_F\left(x_{ij}^{\left(k\right)}\right)\le 1$ and $0\le v_F\left(x_{ij}^{\left(k\right)}\right)\le 1$, and FFs direct relationship matrix ${\mathit{X}}^{\left(k\right)}$’s diagonal elements of the matrix must be zero, i.e., $\left({\mu }_F\left(x_{ii}^{\left(k\right)}\right),v_F\left(x_{ii}^{\left(k\right)}\right)\right)$ = 0.

On the other hand, the sum of the cubes of membership and non-membership of FFs will be between 0 and 1, i.e., $0\le {\left({\mu }_F\left(x_{ij}^{\left(k\right)}\right)\right)}^3+{\left(v_F\left(x_{ij}^{\left(k\right)}\right)\right)}^3\le 1$. According to the definition of FFs [42], the degree of uncertainty of Expert k can be calculated from Equation (2).

$${\pi }_F\left(x_{ij}^{\left(k\right)}\right)=\sqrt[3]{1-{\left({\mu }_F\left(x_{ij}^{\left(k\right)}\right)\right)}^3-{\left(v_F\left(x_{ij}^{\left(k\right)}\right)\right)}^3},0\le {\pi }_F\left(x_{ij}^{\left(k\right)}\right)\le 1.$$

(2)

Step 4. 

Use the Arithmetic Mean to Aggregate the Judgments of Multiple Experts to Construct the Average FFs Direct Relationship Matrix

Most of the integration of expert assessment information is done by averaging, so the average FF direct relationship matrix A is used, as shown in Equation (3).

$$\mathit{A}=\left[\begin{array}{cccc}\left({\mu }_F\left(a_{11}^{}\right),v_F\left(a_{11}^{}\right)\right)& \left({\mu }_F\left(a_{12}^{}\right),v_F\left(a_{12}^{}\right)\right)& \cdots & \left({\mu }_F\left(a_{1n}^{}\right),v_F\left(a_{1n}^{}\right)\right)\\ \left({\mu }_F\left(a_{21}^{}\right),v_F\left(a_{21}^{}\right)\right)& \left({\mu }_F\left(a_{22}^{}\right),v_F\left(a_{22}^{}\right)\right)& \cdots & \left({\mu }_F\left(a_{2n}^{}\right),v_F\left(a_{2n}^{}\right)\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({\mu }_F\left(a_{n1}^{}\right),v_F\left(a_{n1}^{}\right)\right)& \left({\mu }_F\left(a_{n2}^{}\right),v_F\left(a_{n2}^{}\right)\right)& \cdots & \left({\mu }_F\left(a_{nn}^{}\right),v_F\left(a_{nn}^{}\right)\right)\end{array}\right], i=j=1, 2,\dots , n.$$

(3)

where $\left({\mu }_F\left(a_{ij}^{}\right),v_F\left(a_{ij}^{}\right)\right)=\frac{1}{k}{\displaystyle \sum _{k=1}^K\left({\mu }_F\left(x_{ij}^{\left(k\right)}\right),v_F\left(x_{ij}^{\left(k\right)}\right)\right)}$.

Step 5. 

Calculate the Average FFs Score Function and the Degree of Uncertainty of the Integration of Experts

According to the basic calculation rules of the FFs score function [42], the average FFs score function can be derived, as shown in Equation (4).

$$scoref\left({\mu }_F\left(a_{ij}^{}\right),v_F\left(a_{ij}^{}\right)\right)={\left({\mu }_F\left(a_{ij}^{}\right)\right)}^3-{\left(v_F\left(a_{ij}^{}\right)\right)}^3,-1\le scoref\left({\mu }_F\left(a_{ij}^{}\right),v_F\left(a_{ij}^{}\right)\right)\le 1.$$

(4)

However, the score function is a function between −1 and 1. It needs to use Equation (5) to make the range converge to between 0 and 1, which can be called the FF defuzzification function ($\phi$).

$${\phi }_{ij}=1+scoref\left({\mu }_F\left(a_{ij}^{}\right),v_F\left(a_{ij}^{}\right)\right),0\le {\phi }_{ij}\le 1.$$

(5)

Through Equations (4) and (5), the average FFs direct relationship matrix can be transformed into the group relationship matrix, as shown in Equation (6).

$$\mathsf{\phi }=\left[\begin{array}{cccc}{\phi }_{11}& {\phi }_{12}& \cdots & {\phi }_{1n}\\ {\phi }_{21}& {\phi }_{22}& \cdots & {\phi }_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\phi }_{n1}& {\phi }_{n2}& \cdots & {\phi }_{nn}\end{array}\right], i=j=1, 2,\dots , n.$$

(6)

In addition, the uncertainty of the group can be determined by Equation (7) [43].

$$\partial {\pi }_F\left(x_{ij}^{}\right)=\sqrt[3]{1-{\mu }_F{\left(a_{ij}^{}\right)}^3-v_F{\left(a_{ij}^{}\right)}^3},0\le \partial {\pi }_F\left(a_{ij}^{}\right)\le 1.$$

(7)

Step 6. 

Obtain the Normalized Group Relationship Matrix

Next, the influence relationships among the factors are identified by simply following the conventional DEMATEL operation. In this step, the normalized group relationship matrix is obtained by performing the normalization procedure, as shown in Equation (8).

$$\mathsf{\gamma }=\left[\begin{array}{cccc}\epsilon \cdot {\phi }_{11}& \epsilon \cdot {\phi }_{12}& \cdots & \epsilon \cdot {\phi }_{1n}\\ \epsilon \cdot {\phi }_{21}& \epsilon \cdot {\phi }_{22}& \cdots & \epsilon \cdot {\phi }_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ \epsilon \cdot {\phi }_{n1}& \epsilon \cdot {\phi }_{n2}& \cdots & \epsilon \cdot {\phi }_{nn}\end{array}\right], i=j=1, 2,\dots , n.$$

(8)

where $\epsilon =\frac{1}{\max \left\{{\displaystyle \sum _{j=1}^n{\phi }_{ij},{\displaystyle \sum _{i=1}^n{\phi }_{ij}}}\right\}}$.

Step 7. 

Generate the Total Group Influence Matrix

The mutual influence relationships among factors may be direct or indirect. In order to ensure that all potential influence relationships are taken into account, the matrix is multiplied and summed up, as shown in Equation (9). The total group influence matrix is presented as shown in Equation (10).

$$\begin{array}{l}\mathit{T}=\mathsf{\gamma }+{\mathsf{\gamma }}^2+{\mathsf{\gamma }}^3+\cdots {\mathsf{\gamma }}^{\infty }=\mathsf{\gamma }\left(\mathit{I}+\mathsf{\gamma }+{\mathsf{\gamma }}^2+{\mathsf{\gamma }}^3+\cdots +{\mathsf{\gamma }}^{\infty -1}\right)\\ =\mathsf{\gamma }\left(\mathit{I}-{\mathsf{\gamma }}^{\infty }\right){\left(\mathit{I}-\mathsf{\gamma }\right)}^{-1}=\mathsf{\gamma }{\left(\mathit{I}-\mathsf{\gamma }\right)}^{-1}\end{array}$$

(9)

where ${\mathsf{\gamma }}^{\infty }={[0]}_{n\times n}$, and I is the identity matrix.

$$\mathit{T}=\left[\begin{array}{cccc}{t}_{11}& t_{12}& \cdots & t_{1n}\\ t_{21}& t_{22}& \cdots & t_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ t_{n1}& t_{n2}& \cdots & t_{nn}\end{array}\right], i=j=1, 2,\dots , n.$$

(10)

Step 8. 

Obtain Factor Influence Weights and Constructing INRM

The element t_ij of the total group influence matrix can be interpreted as the sum of the direct and indirect influence of factor i on factor j. Therefore, the degree of influence for factor i (r_i) can be obtained from Equation (11). Similarly, the degree of being influenced (s_i) for factor i is given by Equation (12).

$$r_i=t_{11}+t_{12}+\cdots t_{1n}={\displaystyle \sum _{j=1}^n{t}_{ij}}$$

(11)

$$s_i=t_{11}+t_{21}+\cdots t_{n1}={\left[{\displaystyle \sum _{i=1}^n{t}_{ij}}\right]}^{Transpose}$$

(12)

According to Equations (11) and (12), the total influence of factor i, including r_i and s_i, can be defined as r_i + s_i. The influence weight of factor i in this assessment system is obtained through Equation (13).

$$w_i=\frac{r_i+s_i}{{\displaystyle \sum _{i=1}^n\left(r_i+s_i\right)}}$$

(13)

On the other hand, r_i − s_i reflects the net effect of factor i. When r_i − s_i is greater than 0, it means that factor i significantly influences other factors. Conversely, when r_i − s_i is less than 0, it means that factor i is significantly influenced by other factors. By using r_i + s_i and r_i − s_i as the horizontal and vertical axes of INRM, the relative positions of each factor can be plotted. In this paper, the directions of the arrows are used to describe the mutual influence relationship among the factors.

5. Data Analysis

This section presents an introduction to the applied case study and the results of the FF-DEMATEL analysis. Finally, management implications are provided.

5.1. Case Description

According to the report “Critical Infrastructure Security Protection Plan” released by the Office of Homeland Security, Executive Yuan in May 2018, it is stated that airports are one of the important CIs in Taiwan. According to the information of “Civil Aviation Airport Facilities and Energy” published by the Civil Aeronautics Administration of the Ministry of Transportation in May 2019, it is stated that Taiwan Taoyuan International Airport ranks first among 17 civil airports in Taiwan in terms of data such as passenger/cargo capacity, average daily traffic, and fire protection level. Therefore, this paper uses Taiwan Taoyuan International Airport as the main analysis case to explore the mutual influence relationships among airport disaster resilience factors and suggestions for improvement.

First, each expert in the decision-making group completed the FF-DEMATEL questionnaire, the contents of which were explained in detail to the experts, and the experts spent approximately one week completing the questionnaire. The result of the first expert’s questionnaire is shown in

Table 5. Information of FF-DEMATEL filled by the first expert.

	R1	R2	R3	R4
R1	0	L	L	L
R2	EH	0	EH	H
R3	L	L	0	EH
R4	L	L	L	0
	F1	F2	F3	F4	F5
F1	0	EH	H	H	EH
F2	L	0	L	M	M
F3	L	EH	0	NI	NI
F4	L	EH	NI	0	NI
F5	M	EH	NI	NI	0
	F6	F7	F8	F9	F10
F6	0	L	NI	NI	NI
F7	EH	0	NI	NI	H
F8	NI	NI	0	NI	NI
F9	NI	NI	NI	0	NI
F10	NI	L	NI	NI	0
	F11	F12	F13	F14	F15	F16
F11	0	M	EH	EH	EH	EH
F12	NI	0	EH	EH	L	NI
F13	L	M	0	NI	L	NI
F14	EH	H	NI	0	H	EH
F15	EH	L	EH	EH	0	L
F16	L	NI	NI	H	EH	0
	F17	F18	F19	F20	F21	F22
F17	0	NI	EH	L	NI	NI
F18	NI	0	NI	H	EH	EH
F19	L	L	0	EH	EH	EH
F20	NI	L	NI	0	NI	L
F21	NI	L	NI	L	0	H
F22	NI	L	L	EH	L	0

.

5.2. Calculating the Influence Weights of the Resilience Factors through FF-DEMATEL

According to the content filled in by the first expert in Table 5, the FFs direct relationship matrix (Equation (1)) can be formed. Through Equation (2), each expert’s degree of uncertainty in the assessment is obtained. Since there are multiple experts filling out the questionnaire, the data of multiple experts are integrated according to Equation (3), as shown in

Table 6. The average FF direct relationship matrix A.

	R1	R2	R3	R4
R1	(0.000, 0.000)	(0.784, 0.481)	(0.782, 0.544)	(0.367, 0.863)
R2	(0.505, 0.764)	(0.000, 0.000)	(0.632, 0.788)	(0.499, 0.791)
R3	(0.297, 0.919)	(0.356, 0.924)	(0.000, 0.000)	(0.848, 0.429)
R4	(0.351, 0.912)	(0.377, 0.918)	(0.517, 0.745)	(0.000, 0.000)
	F1	F2	F3	F4	F5
F1	(0.000, 0.000)	(0.911, 0.406)	(0.675, 0.731)	(0.681, 0.776)	(0.682, 0.775)
F2	(0.821, 0.479)	(0.000, 0.000)	(0.709, 0.636)	(0.536, 0.852)	(0.705, 0.695)
F3	(0.679, 0.678)	(0.664, 0.685)	(0.000, 0.000)	(0.463, 0.871)	(0.391, 0.919)
F4	(0.488, 0.848)	(0.615, 0.774)	(0.404, 0.909)	(0.000, 0.000)	(0.304, 0.941)
F5	(0.652, 0.802)	(0.792, 0.620)	(0.548, 0.787)	(0.406, 0.924)	(0.000, 0.000)
	F6	F7	F8	F9	F10
F6	(0.000, 0.000)	(0.806, 0.486)	(0.547, 0.728)	(0.329, 0.907)	(0.282, 0.919)
F7	(0.876, 0.416)	(0.000, 0.000)	(0.446, 0.758)	(0.738, 0.534)	(0.701, 0.658)
F8	(0.578, 0.784)	(0.452, 0.866)	(0.000, 0.000)	(0.468, 0.847)	(0.282, 0.925)
F9	(0.268, 0.915)	(0.582, 0.762)	(0.265, 0.909)	(0.000, 0.000)	(0.329, 0.922)
F10	(0.267, 0.933)	(0.663, 0.591)	(0.238, 0.938)	(0.443, 0.857)	(0.000, 0.000)
	F11	F12	F13	F14	F15	F16
F11	(0.000, 0.000)	(0.484, 0.846)	(0.868, 0.446)	(0.869, 0.451)	(0.869, 0.456)	(0.609, 0.666)
F12	(0.635, 0.655)	(0.000, 0.000)	(0.765, 0.668)	(0.814, 0.531)	(0.754, 0.600)	(0.596, 0.719)
F13	(0.558, 0.739)	(0.582, 0.738)	(0.000, 0.000)	(0.832, 0.461)	(0.808, 0.497)	(0.413, 0.879)
F14	(0.760, 0.512)	(0.693, 0.589)	(0.607, 0.698)	(0.000, 0.000)	(0.835, 0.454)	(0.794, 0.426)
F15	(0.752, 0.663)	(0.601, 0.645)	(0.844, 0.514)	(0.852, 0.437)	(0.000, 0.000)	(0.597, 0.690)
F16	(0.494, 0.819)	(0.496, 0.841)	(0.504, 0.836)	(0.906, 0.364)	(0.816, 0.546)	(0.000, 0.000)
	F17	F18	F19	F20	F21	F22
F17	(0.000, 0.000)	(0.282, 0.932)	(0.777, 0.532)	(0.629, 0.655)	(0.553, 0.762)	(0.835, 0.492)
F18	(0.641, 0.676)	(0.000, 0.000)	(0.651, 0.652)	(0.525, 0.784)	(0.880, 0.417)	(0.858, 0.496)
F19	(0.863, 0.435)	(0.619, 0.789)	(0.000, 0.000)	(0.684, 0.756)	(0.811, 0.516)	(0.871, 0.478)
F20	(0.685, 0.604)	(0.376, 0.928)	(0.548, 0.812)	(0.000, 0.000)	(0.362, 0.892)	(0.601, 0.722)
F21	(0.695, 0.589)	(0.731, 0.661)	(0.821, 0.500)	(0.596, 0.754)	(0.000, 0.000)	(0.874, 0.382)
F22	(0.859, 0.430)	(0.745, 0.642)	(0.653, 0.705)	(0.854, 0.458)	(0.713, 0.642)	(0.000, 0.000)

. Through Equations (4) and (5), the FF score function is defuzzified to obtain the FF defuzzification function, as shown in

Table 7. FF defuzzification function.

	R1	R2	R3	R4
R1	0.000	0.592	0.579	0.352
R2	0.421	0.000	0.441	0.408
R3	0.312	0.314	0.000	0.633
R4	0.321	0.320	0.431	0.000
	F1	F2	F3	F4	F5
F1	0.000	0.672	0.479	0.462	0.463
F2	0.611	0.000	0.525	0.384	0.504
F3	0.500	0.493	0.000	0.360	0.321
F4	0.376	0.442	0.328	0.000	0.299
F5	0.440	0.565	0.419	0.319	0.000
	F6	F7	F8	F9	F10
F6	0.000	0.602	0.445	0.322	0.312
F7	0.650	0.000	0.413	0.562	0.515
F8	0.428	0.361	0.000	0.374	0.308
F9	0.313	0.439	0.317	0.000	0.313
F10	0.302	0.521	0.297	0.364	0.000
	F11	F12	F13	F14	F15	F16
F11	0.000	0.377	0.641	0.641	0.640	0.483
F12	0.494	0.000	0.537	0.597	0.553	0.460
F13	0.443	0.449	0.000	0.619	0.601	0.348
F14	0.576	0.532	0.471	0.000	0.622	0.606
F15	0.533	0.487	0.616	0.634	0.000	0.471
F16	0.393	0.382	0.386	0.674	0.595	0.000
	F17	F18	F19	F20	F21	F22
F17	0.000	0.303	0.580	0.492	0.432	0.616
F18	0.489	0.000	0.500	0.416	0.652	0.627
F19	0.640	0.437	0.000	0.472	0.599	0.638
F20	0.525	0.313	0.407	0.000	0.335	0.460
F21	0.533	0.526	0.607	0.446	0.000	0.653
F22	0.638	0.537	0.482	0.632	0.524	0.000

.

Next, the results of the FF-DEMATEL analysis are obtained by performing the calculations as in the general form of DEMATEL (e.g., Equations (6)–(13)), as shown in

Table 8. The results of FF-DEMATEL.

	r	s	r + s	r − s	Local Weight	Rank
R1	5.795	4.284	10.078	1.511	0.252	2
R2	5.002	4.753	9.755	0.249	0.244	4
R3	4.852	5.502	10.354	−0.650	0.259	1
R4	4.350	5.460	9.811	−1.110	0.245	3
F1	7.723	7.308	15.031	0.415	0.220	2
F2	7.579	7.980	15.559	−0.401	0.227	1
F3	6.496	6.752	13.248	−0.256	0.193	3
F4	5.708	5.963	11.671	−0.255	0.170	5
F5	6.730	6.234	12.964	0.496	0.189	4
F6	3.475	3.471	6.946	0.005	0.208	2
F7	4.154	3.807	7.961	0.347	0.239	1
F8	3.035	3.055	6.090	−0.019	0.183	5
F9	2.909	3.329	6.238	−0.420	0.187	3
F10	3.111	3.022	6.133	0.088	0.184	4
F11	5.372	4.828	10.200	0.545	0.165	3
F12	5.140	4.465	9.605	0.675	0.156	5
F13	4.849	5.155	10.004	−0.306	0.162	4
F14	5.410	5.979	11.390	−0.569	0.184	1
F15	5.303	5.745	11.049	−0.442	0.179	2
F16	4.795	4.698	9.493	0.096	0.154	6
F17	6.013	6.891	12.904	−0.878	0.169	4
F18	6.624	5.354	11.978	1.270	0.157	5
F19	6.795	6.342	13.137	0.453	0.172	2
F20	5.153	6.141	11.294	−0.988	0.148	6
F21	6.779	6.223	13.003	0.556	0.170	3
F22	6.778	7.191	13.969	−0.414	0.183	1

. Here, since the perspectives we examine the resilience factors can be divided into four dimensions, the local weight within each dimension is used as the ranking index. R₃ is the perspective with the highest weight, and the weight obtained is 0.259. Under R₁, the weights are ranked as F₂$\succ$F₁$\succ$F₃$\succ$F₅$\succ$F₄. Under R₂, the weights are ranked as F₇$\succ$F₆$\succ$F₉$\succ$F₁₀$\succ$F₈. Under R₃, the weights are ranked as F₁₄$\succ$F₁₅$\succ$F₁₁$\succ$F₁₃$\succ$F₁₂$\succ$F₁₆. Under R₄, the weights are ranked as F₂₂$\succ$F₁₉$\succ$F₂₁$\succ$F₁₇$\succ$F₁₈$\succ$F₂₀. Figure 1 provides an overview of the relative importance of all the factors. In general, the top five ranked factors are F₇, F₂, F₁, F₆, and F₃. This analysis result aligns with the objective of this study. The factor weights take into account their mutual influence, rather than assuming independence.

We can plot the INRM by using “r + s” as the horizontal axis and “r − s” as the vertical axis, as in Figure 2. The larger the “r + s” of a factor means that it cannot be ignored in the assessment system, and the larger the “r − s” means the stronger the influence of the factor. The resulting INRM provides decisionmakers with a quick way to know which factors are influential and which factors are susceptible to the influence of others. The specific management implications and discussion are presented in Section 5.3.

5.3. Management Implications

Through INRM (Figure 2), the mutual influence relationships among different levels and local parts can be obtained, and the management implications can be divided into the following five points, which are described as follows:

(i)

For capability level, detection capability (R₁) can significantly affect resistance capability (R₂), rescue capability (R₃), and recovery capability (R₄). On the other hand, R₃ with a weight of 0.259 has the highest weight.

Taoyuan International Airport is classified as a “Class I national critical infrastructure” and is a representative critical infrastructure for air transportation hubs in Taiwan. In addition to the operation and management of the air terminals, the core business of Taoyuan Airport is the prevention and rescue of airport disasters and aviation safety incidents, emergency care, 24/7 dynamic monitoring, and the handling of abnormal events. In terms of detection capability, the staff is normally assigned to airport inspection and management, ground safety control, and management and maintenance of air terminal land, facilities, and hardware and software to ensure the normal operation of the nation’s most important public air transportation. It is clear that in practice, detection capability significantly affects other capabilities. Therefore, the ability to detect and predict incidents before they occur is of paramount importance [44].

If the airport is paralyzed, not only will its international image be seriously affected, but also the negative impact on the citizens will be huge. Therefore, among the protection principles of this infrastructure, early detection becomes increasingly important and should be the primary goal. In the mid-term, the buildings should be repaired or reinforced from the point of view of preventing the recurrence of disasters. After the situation is cleared, experts and scholars should be invited to participate in the final reconstruction and restoration of the site, including safety assessment, reinforcement, and other emergency construction proposals.

(ii)

Within detection capability (R₁): work environment planning and management, and personnel security awareness and alertness (F₁) and threat identification capability of the airport’s network security system (F₅) significantly affect SeMS integrity (F₂) and reliability of the airport’s video surveillance and epidemic prevention system (F₃).

Taoyuan Airport is a major hub for domestic and international passengers and air cargo, with the highest flight density in the country. Therefore, the airport has a high demand and stability for network communications, which in turn affects the stability of the operation of various industries and trades and has a ripple effect on the overall economy. In the areas of work environment planning and management, personnel security awareness and alertness (F₁), and threat identification capability of the airport’s cyber security system (F₅), the airport network security management system policy regulates and manages the four components of personnel, application systems, hardware equipment, and network facilities that affect aviation safety and passenger privacy. The airport cyber security management system has taken into consideration the interdependence of systems and equipment. For example, critical information and communication systems need to rely on a stable power supply, and access control systems and air conditioning systems need to maintain a physical environment for operation. Therefore, when the airport cyber security system identifies external threats, it will affect the overall operation of the airport, so the results are significant. In particular, with the COVID-19 epidemic affecting the whole world, Taoyuan Airport serves all international passengers, so it is necessary to maintain the highest level of alertness for disease control and requires a protective network of the Department of Disease Control and surrounding medical institutions [45].

A country’s border of entry and exit is its international airports, so it is very important to be able to make policy and detection actions immediately when the front line detects uncertain possible risks, to avoid external threats entering the country, which will affect the internal life of the people and changes in the social environment.

(iii)

Within resistance capability (R₂), education and training of ground staff on airport safety awareness (F₇) can have a significant influence on four items at the level of resilience factors: Emergency response procedures in case of discovering flammable or explosive substances (F₆), architectural structure and earthquake prevention measures of airport terminal buildings (F₈), proper intrusion prevention measures for airport perimeters (F₉), and airport cyber security system protection measures (F₁₀).

Improving security efficiency is a key factor in strengthening defenses to avoid human error. The education and training of ground staff on airport safety awareness are implemented to effectively suppress the degree of risk at the moment of occurrence. When the ground staff inspect the airport and find suspicious people, they need to make a security notification to airport police, which can enhance the airport’s prevention ability and reduce the chance of major accidents.

The following three points can be used to strengthen personnel education and training [46]: (1) Personnel education, training, drills, and hazard identification for complex incidents should be enhanced, so that maintenance personnel and manufacturers can effectively and quickly respond to incidents. The training includes emergency reporting, responsibility area implementation, security awareness, all-out defense mobilization, civil aviation laws and regulations, disaster prevention technician education, evacuation and disaster refuge, escape assembly, construction notification, etc., to strengthen the airport staff’s ability to respond to reporting and awareness of responsibilities. (2) Airport security culture should be promoted: Everyone is responsible for airport security, so all staff security should be implemented. The concept of responsibility zone should be combined to implement the detection and reporting of abnormal people and things in the zone, such as observation of suspicious people and identification of unattended luggage, and to establish the security reporting culture of “see something, say something” and “see it, hear it, report it”. (3) Various drills and tests should be executed: related training, reporting, behavior detection, and the effectiveness of drills should be examined.

(iv)

Within rescue capability (R₃), sufficiency of firefighting resources inside and outside the airport (F₁₁) and stability of communication systems among various departments of the airport (F₁₂) significantly affect the following two factors: first aid mechanism for the injured (F₁₄) and drafting of emergency response plans and procedures for disaster relief (F₁₅).

The protection objective of Taoyuan Airport is to ensure the safety of infrastructure and assets to Taiwan’s vital air transportation, economy, and public confidence. When a critical facility fails, others may be affected as well. Therefore, when a major incident occurs at Taoyuan Airport, resulting in casualties and failure of airport facilities, external resources may not be able to arrive in time, which may have a significant influence on the incident at hand. Therefore, the airport should take the lead to simulate various disaster relief situations and draw up relevant contingency plans to enable the airport to obtain the golden rescue period internally. Therefore, F₁₁ and F₁₂ will have a significant influence on F₁₄ and F₁₅. It is also important to have a pre- and post-incident process plan in place before a risky incident occurs. The airport should take a cross-departmental manner to revise and construct plans and procedures that combine airport resources and manpower to maintain normal airport operations under any circumstances.

The core function of Taoyuan Airport is to correspond to, identify, and support the internal necessary assets for the continuous operation of various core functional businesses, mainly in three categories: terminal physical maintenance operations, information and communication, and key personnel. Information and communication related personnel should implement the agent system and have personnel stationed 24 h a day. Important servers, network equipment, etc. should implement data backup and a dual backup structure to establish an internal essential asset dependency network. The key external resources of Taoyuan Airport include electricity, water supply, gas supply, transportation, fuel, and information and communication. Therefore, the stability of the horizontal connection of the communication system among the various departments of the airport would enable the resources and response to be effective [47].

(v)

Within recovery capability (R₄), repair and maintenance planning of the internal facilities of the terminal (F₁₈), recovery command center established to coordinate the allocation of people, materials, and resources (F₁₉), and standby power generation equipment to ensure that the power system is not disrupted (F₂₁) are three factors that significantly affect the other factors.

The airport involves many agencies and public and private entities, and the laws and regulations under which they operate are different. Under the existing laws and localism, each entity has its own plan and contingency procedures to follow, which may lead to blind spots or delays in communication and coordination under a complex disaster. Therefore, under the framework of Taiwan’s critical infrastructure, Taoyuan Airport should adopt the concept of a “large airport” jointly owned by all stakeholders as the protection plan and strategy, and regularly develop and revise the relevant plans in a cross-departmental manner to maintain normal airport operations in various situations.

It can be observed that the most serious impact on hard warfare, personnel, and information and communication systems is the power interruption when overall external critical resources are interrupted. Therefore, it is important to have emergency generators to provide power for emergency needs such as lighting, firefighting, emergency telephones, and traffic monitoring in case of power failure, and to conduct regular maintenance [48]. The aviation industry is a highly internationalized industry, and the construction and management of airside facilities and equipment must comply with the International Civil Aviation Organization (ICAO) regulations, and in the event of an aviation accident, the rescue and fire-fighting standards must also comply with the relevant operational regulations.

MCDM has been widely used in identifying the interrelationships among factors [49]. However, when evaluating complex and uncertain environments, it becomes challenging for experts to express their judgments accurately using crisp values. To address this issue, various fuzzy theories have been integrated with conventional DEMATEL methods to account for uncertainty. However, these fuzzy theories often overlook the experts’ confidence level in the evaluation values. In contrast, the FF-DEMATEL approach incorporates two fuzzy parameters, membership (μ) and non-membership (v), to address this limitation. This allows us to not only assess the reliability of the decision-making group in the evaluation but also calculate 2-tuple numbers to retain all information. Moreover, FF-DEMATEL facilitates the generation of influential criteria weights and their prioritization.

Table 9. Comparison of the three DEMATEL methods.

	Data Type	Information Uncertainty	Considers Both Certainty and Uncertainty	Reflects the Accuracy of Expert Opinions
DEMATEL	Crisp	No	No	Low
Fuzzy DEMATEL	Triangular fuzzy numbers	Yes	No	Medium
FF-DEMATEL	2-tuple numbers	Yes	Yes	High

provides a summary of the distinctions between conventional DEMATEL, general fuzzy DEMATEL, and FF-DEMATEL methods.

6. Conclusions

Past studies have suggested factors to assess airport resilience. However, most of the research methods consider the factors as independent (e.g., AHP, BWM, Bayesian BWM), and such assumptions violate the real situation. On the other hand, few papers have conducted data analysis through the MCDM concept. In order to bridge the gap with previous studies, this study proposes a framework for assessing the resilience factor of international airports based on the aviation safety perspective. In terms of methodology, FF-DEMATEL is developed in this study to identify the mutual influence relationships of the resilience factors. In particular, FFs are used to interpret the ambiguity and uncertainty of expert semantics, which cover a broader range of fuzzy information. In this study, it is assumed that there are interconnections among the airport resilience factors, and through the analysis, it can be known which factors mainly affect others and which factors are easily affected by other factors. The results of this study can be briefly described as follows:

(i)

“Detection capability (R₁)” significantly affects “resistance capability (R₂),” “rescue capability (R₃),” and “recovery capability (R₄).”

(ii)

In the detection capability (R₁) perspective, “work environment planning and management, personnel security awareness and alertness (F₁),” and “threat identification capability of the airport’s cyber security system (F₅)” significantly affect “SeMS integrity (F₂)” and “reliability of the airport’s video surveillance and epidemic prevention system (F₃).”

(iii)

In the resistance capability (R₂) perspective, “education and training of ground staff on airport safety awareness (F₇)” is particularly important.

(iv)

In the rescue capability (R₃) perspective, “sufficiency of firefighting resources inside and outside the airport (F₁₁)” and “stability of communication systems among various departments of the airport (F₁₂)” significantly affect “first aid mechanism for the injured (F₁₄)” and “drafting of emergency response plans and procedures for disaster relief (F₁₅).”

(v)

In the recovery capability (R₄) perspective, “repair and maintenance planning of the internal facilities of the terminal (F₁₈),” “recovery command center established to coordinate the allocation of people, supplies, and resources (F₁₉)” and “standby power generation equipment to ensure that the power system is not disrupted (F₂₁)” significantly affect the other factors.

In conclusion, this paper presents a novel framework for assessing the resilience of international airports, especially from an aviation safety perspective. At the same time, we improve the shortcomings of past studies, which assumed that the resilience factors are independent. This paper also incorporates FFs into DEMATEL to reflect information uncertainty and to cover a wider range of missing information. Finally, using the Taoyuan International Airport in Taiwan as a case study, the study process can be replicated for other international airports in the future. Decisionmakers or risk managers can use INRM and factor influence weights to develop risk management strategies to improve the resilience of international airports.

This study contributes to facilitating the implementation of resilience assessments in other international airports. Different airports can adapt the evaluation framework according to their specific backgrounds and conditions. We propose that international airports develop improvement strategies based on four aspects: detection, resistance, rescue, and recovery, to ensure comprehensive response capabilities when faced with identifiable and unpredictable risks. These strategies can be tailored to the unique circumstances of each airport to enhance their overall resilience. However, this study has several limitations, including the lack of measurement of airport resilience capabilities, not considering other fuzzy methods, and not determining the optimal number of experts. In future research, it would be beneficial to investigate multiple international airports and conduct on-site visits to assess their performance using the proposed evaluation framework. This approach would allow for identifying and improving the weaknesses of each airport to enhance their resilience. In the methodology section, incorporating a broader range of performance evaluation methods (e.g., TOPSIS, VIKOR, PROMETHEE, COPRAS) for comparison would enhance the reliability and robustness of the evaluation model. Furthermore, future research could consider adding other fuzzy sets for evaluation to identify the most suitable fuzzy theories for a given case, such as intuitionistic [50], Pythagorean [51], picture [52], hesitant [53], neutrosophic [54], plithogenic [55], hypersoft fuzzy sets [56], etc.