Research on the Fire Resilience Assessment of Ancient Architectural Complexes Based on the AHP-CRITIC Method

Abstract

Ancient architectural complexes are an important part of human cultural heritage, carrying a wealth of historical and cultural information. However, fire safety issues in these complexes are becoming increasingly prominent, and it is urgent to assess and enhance their fire resilience to support sustainable development. This paper takes ancient architectural complexes as the research object and establishes a fire resilience evaluation indicator system for ancient architectural complexes, which includes 25 third-level indicators categorized under architectural characteristics, facility factors, management factors, and social factors. Then, this paper combines the AHP method and the CRITIC method to determine the weight of each indicator. The results show that architectural features and facility factors are key level 2 indicators affecting the fire resilience of ancient architectural complexes. The fire resistance rate, building materials, automatic alarm system, etc., are key level 3 indicators influencing the fire resilience of ancient architectural complexes. It is suggested that efforts should be made to enhance the fire resilience of ancient architectural complexes by improving the fire resistance rate, strengthening smart early warning systems, and intensifying the ensuring of firefighting responses. This paper provides valuable insights and recommendations for effectively preventing fire disasters in ancient architectural complexes, thereby supporting their sustainable management and long-term conservation.

1. Introduction

Ancient architectural complexes are the treasures of human culture, reflecting profound historical heritage and distinctive styles. They play a significant role in promoting excellent national cultures and strengthening cultural confidence. However, due to historical limitations, ancient architectural complexes are often densely packed with narrow streets, and are mostly made of wood. Especially in the southern regions of China such as Jiangxi, Hunan, and Guangdong, where timber resources are abundant, various buildings of different scales were often constructed using wood and bricks. Additionally, the dense clustering of buildings was common due to the presence of clan communities. In the event of a fire, this poses significant challenges for evacuation of personnel and firefighting rescue efforts. These ancient architectural complexes face unprecedentedly complex uncertainties and potential fire risks.

For instance, on 11 January 2014, a fire broke out in Dokuzong, Yunnan Province, China, with a burnt and demolished house area of 59,900 square meters and a direct economic loss of CNY 89.84 million. On 10 December 2017, a fire led to the destruction of the Nine Dragons Temple, the “tallest wooden pagoda in Asia”, located in Chengdu, Sichuan, China, with a fire area of more than 800 square meters. On 15 April 2019, a major fire broke out at Notre Dame de Paris [1,2,3], located in Paris, France, resulting in the collapse of the spire and the complete destruction of the middle and rear wooden roofs. The frequent occurrence of fires in ancient architectural complexes in recent years illustrates the need for fire prevention and resilience enhancement in ancient architectural complexes.

Fire prevention and control should start from a systematic perspective, and resilience is a good and systematic viewpoint. The United Nations Office for Disaster Risk Reduction (UNISDR) proposed the concept of resilience from the perspective of the disaster prevention field, defining resilience as the ability of a system or community at risk to resist, absorb, adapt to, and quickly recover from hazards, with protection and recovery being its important basic functions [4]. Guay [5] defines resilience as a holistic approach including communities, society, and systems, focusing not only on resisting the effects of a disaster, but also how the community will cope and recover from it. Mayunga [6] quantifies community disaster resilience by studying social, economic, physical, human, and natural components. In order to quantitatively assess the fire resilience of historical neighborhoods, Yan [7] and others used the Pressure–State–Response (PSR) model to screen and construct a resilience assessment system consisting of 36 indicators from the external environment, inherent risks, components, and other elements. Li [8] took large commercial complexes as their research object, analyzed the factors affecting fire protection resilience, and established an evaluation index system based on the framework of vulnerability, disaster adaptability, and resilience. Guo [9] put forward the concept of building resilient cities and explored the connotation of resilient cities from three aspects: the ability to mitigate the impact of disasters, the ability to adapt to disasters, and the ability of the system to recover after disasters.

In terms of the methodological quantitative assessment of fires, scholars have conducted a wide range of research. Ma [10] used fuzzy hierarchical analysis to determine the building fire resilience level by quantitative analysis of the resilience index system. Fu [11] applied the entropy weight method and the theory of object element topology to achieve an objective evaluation of the fire resilience level of high-rise buildings. You [12] proposed an object–element model for the fire risk evaluation of ancient architectural complexes based on the object–element analysis method to achieve a quantitative evaluation of the fire risk of ancient building groups. Xu [13] proposed the application of the fire sub-risk index method to construct a fire risk assessment index system for ancient architectural complexes, using hierarchical analysis to determine the index weights. Li [14] and Zou [15] et al. also adopted different quantitative methods to study the fire resilience of buildings.

Currently, domestic and foreign research on resilience mainly focuses on city resilience [16,17], building resilience assessments [18,19], etc.; an insufficient amount of study has focused on ancient architectural complexes, so the current research on ancient architectural complexes still has some shortcomings. On the one hand, the existing research lacks the fire safety assessment of ancient architectural complexes from the perspective of resilience. Furthermore, most of them choose a single indicator assignment method, resulting in a lack of objectivity in the indicators. On the other hand, the selection of indicators is not scientific and comprehensive enough.

Based on the perspective of resilience evolution, this paper proposes a set of evaluation indicator systems applicable to the fire resilience of ancient architectural complexes. Then, it combines the analytic hierarchy process (AHP) and the Criteria Importance Through Intercriteria Correlation (CRITIC) method to determine the comprehensive weight of all indicators. After that, this paper evaluates the overall resilience of the ancient building group, and finally accurately derives the key indicators affecting the fire toughness of the ancient building group. This paper provides a theoretical basis and fire prevention reference for effectively improving the fire resilience of ancient architectural complexes. The detailed research flowchart of this paper is shown as Figure 1 below.

2. Fire Resilience Framework for Ancient Architectural Complexes

2.1. Concept of Fire Resilience

At present, there is no clear definition of the resilience of ancient architectural complexes in the academic community. Referring to the definition of resilience proposed by UNISDR and combined with the three development stages of the resilience theory [20], it is believed that the resilience of ancient architectural complexes should consider three aspects. Firstly, maintenance and resistance to fire should be considered. This focuses on whether the ancient architectural complex can return to its pre-disaster state after a disaster. Secondly, consideration should be given to the maximum degree of shock it can absorb before it enters a new state. This emphasizes the maximum magnitude of disturbance that can be absorbed by the ancient complex at the next equilibrium instant. Thirdly, the adaptability and dynamic evolution of the system should be considered. This emphasizes the ability of ancient architectural complexes to absorb, react, learn, and optimize, and focuses on the ability to recover and adjust.

In summary, the fire resilience of ancient architectural complexes is defined as follows. When an ancient architectural complex is threatened by fire or is perturbed by multiple fire factors, its systems can absorb and resist risk, maintain, and restore the fire-safe stable state, which includes the protection of the inhabitants, buildings, and artifacts from fire, or has the ability to respond quickly and efficiently and recover quickly from an unavoidable fire. It enables basic functions to remain operational, aiming to minimize overall losses. After a disaster, it can adjust quickly, learn from past experiences, and optimize its systems to compensate for deficiencies.

2.2. Structural Characteristics of Fire Resilience in Ancient Building Complexes

To understand the fire resilience of ancient architectural complexes on a deeper level, its structural characteristics are concluded and analyzed [20,21,22]. Fire resilience of ancient architectural complexes is further decomposed into five aspects as follows.

(1)

Robustness. This is expressed as the ability of ancient architecture complexes to absorb fire disturbances. That is, the ability to maintain the system in a safe state to the maximum extent possible after a fire. For ancient architectural complexes, robustness can be demonstrated by improving the fire resistance of building materials and enhancing structural stability. For example, applying modern fire-resistant coatings to wooden structures can improve the building’s fire resistance rating.

(2)

Redundancy. This is expressed as the way ancient architecture complexes respond to fire disturbances. The key functional facilities in the system of the ancient building complex should have a backup module, when the original module suffers damage, the backup module can ensure the system maintains normal operation, speed up the recovery in time, and relieve the pressure in space. Ancient architectural complexes can enhance redundancy by incorporating modern fire protection facilities, such as automatic sprinkler systems and backup water sources, to ensure the effective supplementation and replacement of the primary fire protection systems during a fire.

(3)

Efficiency. This is expressed as the ability of ancient architecture complexes to recover from fires. This demonstrates the complex’s ability to respond quickly to fire and rescue during and after a fire to minimize system losses. Improving the fire safety efficiency of ancient architectural complexes can involve enhancing emergency medical facilities, training fire personnel, and optimizing fire emergency response procedures.

(4)

Intelligence. This is expressed as the capability of the ancient architectural complex system to identify problems, ensure rational deployment of resources, determine the priority of action, optimize decision-making, and maximize the effectiveness of resources under limited resources. Intelligence can be enhanced by introducing advanced fire monitoring and early warning systems. For example, installing smoke detectors and temperature sensors to monitor building conditions in real-time and respond quickly.

(5)

Adaptivity. This is demonstrated by the ability to learn from past disaster incidents and improve adaptive capacity to disasters. The adaptability of ancient architectural complexes to future fires can be enhanced by conducting regular fire drills and post-disaster evaluations, and by continuously updating and improving fire management strategies.

2.3. Mechanisms of Fire Resilience in Ancient Architectural Complexes

The mechanism of fire resilience in ancient architectural complexes is reflected in the whole process, namely maintaining stability before the incident, absorbing and resisting during the incident, and restoring and optimizing after the incident. Its mechanism is shown in Figure 2 as follows.

As presented in Figure 2, the fire resilience of ancient building complexes is reflected in the whole process of pre-disaster maintenance, disaster absorption and response, and post-disaster recovery and optimization.

Before the fire disaster, ancient building complexes mainly relies on their own system of architectural features, fire protection facilities, and other aspects of the joint role to prevent fires themselves. This is so the various parts of the function can be maintained in a safe state. When they catch fire, the robustness of ancient building complexes helps to absorb the impact of fire when they do not reach their load-bearing thresholds. When the system exceeds adaptivity, it requires an emergency response from the building’s automatic fire suppression system and outside rescue forces. After the fire disaster, the ancient building complex system optimizes the system’s fire response process by recovering or reconstructing it, and learning from its experience, thus enhancing the system’s self-adaptability.

3. Fire Resilience Evaluation Indicator Systems of Ancient Architectural Complexes

3.1. Principle of Evaluation Indicator Selection

In this paper, the evaluation indicators of fire-safe resilience were elected by the following principles.

(1)

Scientific. Indicators were established according to scientific standards; indicator analysis avoided the influence of subjective factors. Indicators were established under the guidance of national laws and regulations to ensure their objectivity.

(2)

Comprehensive. Indicator selection was based on the holistic nature of the ancient building complexes; this paper comprehensively integrated the various indicators related to fire safety, and reflected the factors that may cause fires in the complexes from all aspects.

(3)

Independent. The indicators selected were independent of each other, and there was no crossover between them. Each indicator has its own meaning, ensuring that the indicators are broad and comprehensive.

(4)

Operative. The selected indicators were concise and easy to implement, and the quantifiable and accessible nature of the indicator data were considered in the specific analyses, to facilitate subsequent scoring by experts and make the evaluation results more objective and accurate.

3.2. Evaluation Indicators

According to the fire resilience of ancient architectural complexes and indicator selection principle, this paper proposed the evaluation indicators for the fire resilience evaluation of ancient architectural complexes, combining the “Code for Fire Protection Design of Buildings” (GB55037-2022), the “Fire Protection Law of the People’s Republic of China” (2021), and expert opinion. Additionally, the indicator system considered the fire resilience and the practicalities of ancient architectural complexes.

This paper established a three-level evaluation index system for the fire resilience of ancient architectural complexes, as shown in

Table 1. Evaluation index system of fire resilience of ancient architectural complexes.

Level 1 Indicators (A)	Level 2 Indicators (B)	Level 3 Indicators (C)	Resilience Category	Indicator Attributes
Overall fire resilience of ancient architectural complexes (x $A$)	Architectural Features ($B_1$)	Building Age ($C_1$)	Robustness	−
		Fire Resistance Rate ($C_2$)	Robustness	+
		Building Density ($C_3$)	Robustness	+
		Fire Separation Distance ($C_4$)	Robustness	+
		Smoke Control and Exhaust Capacity ($C_5$)	Redundancy	+
		Building Materials ($C_6$)	Robustness	+
		Building Height ($C_7$)	Robustness	−
	Facility Factors ($B_2$)	Automatic Alarm System ($C_8$)	Intelligence	+
		Evacuation Sign ($C_9$)	Intelligence	+
		Emergency Lighting Systems ($C_{10}$)	Robustness	+
		Transportation Network ($C_{11}$)	Redundancy	+
		Sprinkler System ($C_{12}$)	Redundancy	+
		Medical Facility ($C_{13}$)	Efficiency	+
	Management Factors ($B_3$)	Fire Prevention Inspection and Rectification ($C_{14}$)	Adaptivity	+
		Emergency Planning and Improvement ($C_{15}$)	Adaptivity	+
		Fire Code System Implementation ($C_{16}$)	Intelligence	+
		Firefighting and Rescue Response Capability ($C_{17}$)	Efficiency	+
		Multisectoral Decision-Making Connectivity ($C_{18}$)	Intelligence	+
		Daily Fire Safety Training ($C_{19}$)	Adaptivity	+
		Firefighting Workforce Development ($C_{20}$)	Efficiency	+
		Government Funding of Disaster Prevention ($C_{21}$)	Intelligence	+
	Society Factors ($B_4$)	Residents’ Fire Safety Awareness ($C_{22}$)	Efficiency	+
		Tourism Development ($C_{23}$)	Robustness	−
		Fire Insurance Coverage ($C_{24}$)	Intelligence	+
		Individual Firefighting and Self-Rescue Capabilities ($C_{25}$)	Adaptivity	+

. In level 1, the resilience of ancient architectural complexes is the only indicator; it can also be seen as the target level. Level 2 contains four sub-indicators; they are architectural features, facility factors, management factors, and societal factors. This means that fire resilience is supported by architectural features, facility factors, management factors, and societal factors. Furthermore, architectural features, facility factors, management factors, and societal factors were divided into seven, six, eight, and four sub-indicators, correspondingly. An evaluation system containing 25 indicators was established and is numbered in Table 1.

As can be seen in Table 1, fire resilience is influenced by architectural features, facility factors, management factors, and societal factors. In terms of architectural features, this starts with the properties of the building itself. This affects resilience a lot. For instance, the older the building, the higher its value, which in turn leads to greater fire disaster vulnerability. Many ancient architectures were built of wood, and thus they are poorly fire resistant. In terms of facility factors, this starts with external items and materials. Items including automatic alarm systems, sprinkler systems, fire extinguishers, fire-fighting water sources, etc., are significant items. Management factors are primarily concerned with the management and regulation of behavioral activities for disaster prevention and mitigation. Societal factors focus on the external environment as it relates to people.

From the perspective of resilience analysis, the evaluation index can be divided into five groups according to Section 2.2, as shown in Figure 3. This indicates that the building age, the fire resistance rate, the building density, the fire separation distance, the building materials, the emergency lighting systems, and tourism development support robustness. The smoke control and exhaust capacity, the transportation network, and a sprinkler system support redundancy. Medical facilities, the firefighting and rescue response capability, firefighting workforce development, and residents’ fire safety awareness support the efficiency. Fire prevention inspections and rectification, emergency planning and improvement, government funding of disaster prevention, and individual firefighting and self-rescue capabilities support adaptivity.

3.3. Evaluation Indicator Description

To deepen the understanding of the Level 3 indicators, this section provides a detailed explanation of their definitions, interpretations, associated resilience categories, and factors to consider during evaluation.

Building Age (${\mathit{C}}_{\mathbf{1}}$). This refers to the time when the building was completed. Building codes and standards vary by era; newly constructed buildings typically adhere to more stringent fire safety regulations and standards. Additionally, building materials tend to have reduced fire resistance over time due to deterioration. Older buildings generally exhibit lower robustness when faced with a fire. In the assessment, consideration is primarily given to building regulations and standards, as well as maintenance and renovation records.

Fire Resistance Rate (${\mathit{C}}_{\mathbf{2}}$). This refers to the length of time that building materials and structures can maintain their load-bearing capacity and integrity during a fire. Buildings with a high fire resistance rating can sustain structural stability for a longer period during a fire, providing more time for evacuation and firefighting. Buildings with a higher fire resistance rating are better able to withstand fire damage, thus enhancing their robustness. In the assessment, consideration is primarily given to building materials, structural design, and fire resistance test results.

Building Density (${\mathit{C}}_{\mathbf{3}}$). This refers to the degree of concentration of buildings within a specific area. Excessively high building density can increase the difficulty of firefighting, potentially triggering chain reactions and enlarging the scale of a fire. High-density buildings may facilitate faster fire spread and reduce robustness. In the assessment, considerations primarily include neighboring buildings, fire access routes, and fire separation measures.

Fire Separation Distance (${\mathit{C}}_{\mathbf{4}}$). This refers to the minimum distance requirements between different buildings. An adequate fire separation distance can effectively prevent a fire from spreading from one building to another, thereby reducing the risk of fire propagation and enhancing the robustness of the building complex. In the assessment, considerations primarily include building planning, the surrounding environment, and urban planning.

Smoke Control and Exhaust Capacity (${\mathit{C}}_{\mathbf{5}}$). This refers to the ability of a building’s smoke control system to effectively remove smoke and toxic gases during a fire. Without an effective smoke control system, smoke can quickly spread, increasing the difficulty of escape and the risk of casualties. Backup systems and system zoning for smoke control are examples of redundancy. In the assessment, considerations primarily include the design of the smoke control system, system maintenance, and operational effectiveness.

Building Materials (${\mathit{C}}_{\mathbf{6}}$). This refers to the various materials used in the construction of a building, including those used in walls, floors, roofs, and other components. Fire-resistant materials such as concrete and steel can enhance the building’s fire resistance, while flammable materials like wood and certain synthetic materials may accelerate the spread of fire, increasing fire hazards. Flammable materials can reduce the building’s robustness. In the assessment, considerations primarily include the fire performance of materials, material sources and quality, and the installation of materials.

Building Height (${\mathit{C}}_{\mathbf{7}}$). This refers to the height from one floor slab to the next. In high-rise buildings, the greater height presents significant challenges for evacuation and rescue during a fire. High-rise buildings face higher fire risks and require greater robustness in their structure and fire prevention measures. In the assessment, considerations primarily include evacuation design, firefighting facilities, and rescue capabilities.

Automatic Alarm System (${\mathit{C}}_{\mathbf{8}}$). This refers to a fire detection and alarm device that automatically detects signs of a fire through sensors and sends alerts to building occupants and fire departments. Timely fire alarms can quickly notify people to evacuate and initiate firefighting measures. This falls under intelligent detection and response, reflecting smart capabilities. Key considerations include the types and layout of detectors, system testing and maintenance, and alarm signals.

Evacuation Signs (${\mathit{C}}_{\mathbf{9}}$). These are signs that guide people on how to safely evacuate, including escape route maps and exit signs. Clear evacuation signs help individuals quickly find safe exits during a fire. Intelligent designs such as dynamic signs and smart adjustments of indicator paths reflect advanced functionality. In the assessment, considerations primarily include the placement of signs, their brightness and clarity, and compliance with regulations.

Emergency Lighting Systems (${\mathit{C}}_{\mathbf{10}}$). It refers to a system that provides illumination when the main power source fails, ensuring necessary lighting during a fire or other emergencies to help people find safe exits and evacuation paths. Ensuring the visibility of evacuation routes and safety exits is crucial for enhancing the building’s robustness. In the assessment, key considerations include the coverage area of the lighting, battery life and maintenance, and the intensity of the illumination.

Transportation Network (${\mathit{C}}_{\mathbf{11}}$). This refers to the layout of roads, passageways, and traffic facilities within and around a building, affecting the accessibility for firefighting vehicles and personnel. Backup routes and passageway distribution in the network reflect redundancy. The assessment primarily considers road width and layout, traffic flow, and signage.

Sprinkler System (${\mathit{C}}_{\mathbf{12}}$). This describes an automated fire suppression system that uses sprinklers to spray water over the fire area to extinguish flames or cool building materials to prevent fire spread. The system includes multiple sprinklers, backup water sources, and independent water supply systems, reflecting redundancy. The assessment focuses on system design, the water source and pressure, and system maintenance.

Medical Facilities (${\mathit{C}}_{\mathbf{13}}$). This includes hospitals, first aid stations, and emergency medical equipment used for treating injuries sustained during a fire. Adequate medical facilities provide timely first aid and treatment. The efficient provision of emergency medical resources and services enhances overall rescue effectiveness, reflecting efficiency. The assessment considers first aid equipment, medical support, and training and drills.

Fire Prevention Inspection and Rectification (${\mathit{C}}_{\mathbf{14}}$). This refers to regular inspections of buildings and their facilities to identify and address potential fire hazards, reducing fire risk and ensuring compliance with fire safety standards. Continuous improvement and feedback updates reflect adaptability. The assessment primarily considers inspection frequency, issue documentation, and correction effectiveness.

Emergency Planning and Improvement (${\mathit{C}}_{\mathbf{15}}$). This refers to emergency response plans for situations like fires, with the level of detail and update frequency of these plans. Well-developed plans can incorporate lessons learned and dynamically adjust to new conditions and risks, reflecting adaptability. The assessment includes the planning of content, updates, and drills.

Fire Code System Implementation (${\mathit{C}}_{\mathbf{16}}$). This refers to whether buildings adhere to national and local fire safety laws, regulations, and standards. This directly impacts the fire safety of the building, ensuring the scientific and effective implementation of fire safety measures, reflecting intelligent fire supervision. The assessment focuses on compliance with standards, the enforcement of regulations, and compliance checks.

Firefighting and Rescue Response Capability (${\mathit{C}}_{\mathbf{17}}$). This refers to the ability of fire departments and rescue personnel to swiftly and effectively conduct firefighting and rescue operations. A strong response capability can quickly control fires and minimize damage to people and property. Effective response reflects efficiency. The assessment includes the response time, equipment and resources, and personnel training.

Multisectoral Decision-Making Connectivity (${\mathit{C}}_{\mathbf{18}}$). This refers to the ability of various relevant departments (such as fire, medical, police, and administrative) to share information and coordinate decisions during a fire. Good interdepartmental connectivity improves emergency response efficiency and effectiveness. Intelligent communication platforms and information sharing reflect intelligence. The assessment focuses on coordination mechanisms, information sharing, and joint drills.

Daily Fire Safety Training (${\mathit{C}}_{\mathbf{19}}$). This refers to regular fire safety knowledge training for building occupants and residents. Regular training improves fire prevention awareness and emergency response skills. Skill enhancement, technology updates, and experience absorption reflect adaptability. The assessment includes the training content, frequency, and effectiveness.

Firefighting Workforce Development (${\mathit{C}}_{\mathbf{20}}$). This refers to the organizational structure, personnel quality, equipment, and training of the firefighting team. A well-trained and well-equipped firefighting team can respond more effectively to fires and emergencies. Investments in team training and equipment maintenance reflect efficiency. The assessment considers personnel training and qualifications, equipment and facilities, and organizational structure.

Government Funding of Disaster Prevention (${\mathit{C}}_{\mathbf{21}}$). This refers to the government’s funding for disaster prevention and firefighting, including infrastructure, equipment procurement, and personnel training. Sufficient funding enhances disaster and fire prevention capabilities, improves facilities, and strengthens overall the fire response ability, reflecting intelligence. The assessment includes funding usage, budget planning, and allocation.

Residents’ Fire Safety Awareness (${\mathit{C}}_{\mathbf{22}}$). This refers to residents’ awareness and attention to fire risks, prevention measures, emergency response, and self-rescue skills. High fire safety awareness encourages effective fire prevention and emergency actions, reducing fire risk and improving self-protection capabilities. Enhancing fire safety awareness improves residents’ self-protection and reduces response burdens, reflecting efficiency. The assessment includes knowledge dissemination, training and publicity, and self-assessment.

Tourism Development (${\mathit{C}}_{\mathbf{23}}$). This refers to the scale of the tourism industry, visitor flow, the distribution of tourism facilities, and the impact on historical buildings. During peak tourism periods, high visitor density can increase fire risk. Buildings in high-tourism areas require greater robustness. The assessment includes visitor density, fire prevention measures in tourism facilities, and the emergency response.

Fire Insurance Coverage (${\mathit{C}}_{\mathbf{24}}$). This refers to the proportion of buildings or assets insured against fire, including the scope and level of coverage. Higher fire insurance coverage helps a complex quickly obtain financial compensation after a fire and encourages more standardized fire risk management. Insurance coverage enhances risk analysis and prediction through commercial institutions, reflecting intelligence. The assessment includes the insurance coverage rate, the insurance scope, and claims records.

Individual Firefighting and Self-Rescue Capabilities (${\mathit{C}}_{\mathbf{25}}$). This refers to an individual’s ability to perform initial firefighting, escape, and self-rescue during a fire. Improved self-rescue capability can reduce fire spread and increase survival chances. Enhanced self-rescue ability reflects adaptability. The assessment includes self-rescue knowledge and skills, training and drills, and practical application ability.

4. Methods

In this paper, the combination of AHP and CRITIC was used to determine the indicator weights. The AHP method was used to calculate the subjective weights of indicators at all levels, then the CRITIC [23,24] method was used to calculate the objective weights, and the subjective issues in the evaluation process were corrected. The weights calculated by the two methods were weighted and averaged to obtain the comprehensive weights, so as to obtain the comprehensive weights of the indicators. The AHP-CRITIC method is flexible, objective, and professional.

4.1. AHP Method

(1)

Judgement matrix

The judgment matrix originated from the comparison matrix of various indicators. In this paper, the scalar method was adopted to make the comparison matrix $A={(a_{ij})}_{m\times n}$. The meaning of the scales and interpretations are presented in

Table 2. Scale and interpretations.

Scales	Interpretations
1	Factors i and j are equally important
3	Factor i is slightly more important than j
5	Factor i is significantly more important than j
7	Factor i is strongly more important than j
9	Factor i is extremely more important than j
2, 4, 6, 8	Intermediate values of the above scales

, where $a_{ij}$ represents the relative importance of indicator $i$ to indicator $j$.

(2)

Weight calculation

Based on the judgement matrix, this paper applied the “square root method” to calculate the weights of indicators, as shown in Equation (1):

$$W^{\prime }={\displaystyle \frac{\overline{w_i}}{{\displaystyle \sum _{i=1}^n\overline{w_i}}}}$$

(1)

where $W^{\prime }$ represents the weight obtained by the AHP method, $\overline{w_i}=n\sqrt{{\displaystyle \prod _{j=1}^n{x}_{ij}}}$, and n is the order of the matrix.

In this paper, the consistency test of the weights was performed, and the calculation process was omitted.

4.2. CRITIC Method

The CRITIC method is a multi-factor decision-making method that determines the weight of a factor by analyzing the correlation between factors. The CRITIC method considers the importance of the factors and the degree of conflict between factors in order to assign weights to each factor.

(1)

Indicator standardization

Indicators have different attributes and data types; therefore, indicators need to be standardized before calculation. Data were standardized by the extreme variance method. For the positive indicators listed in Table 1, they work better at higher values, and they were standardized as Equation (2).

$$z_{ij}^{+}={\displaystyle \frac{x_{ij}-\min x_j}{\max x_j-\min x_j}}\hspace{0.33em}i=1,2,\dots ,m;\hspace{0.33em}j=1,2,\dots ,n$$

(2)

For the negative indicators listed in Table 1, they work worse at higher values, and they were standardized as Equation (3).

$$z_{ij}^{-}={\displaystyle \frac{\max x_j-x_{ij}}{\max x_j-\min x_j}}\hspace{0.33em}i=1,2,\dots ,m;\hspace{0.33em}j=1,2,\dots ,n$$

(3)

(2)

Weight calculation

The weight calculated by the CRITIC method contains two factors, contrast factor ${\sigma }_j$ and conflict factors $r_{ij}$. The contrast factor ${\sigma }_j$ was calculated by Equation (4).

$${\sigma }_j=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^m\left(x_{ij}-\overline{x_j}\right)}}{m-1}}}$$

(4)

where m represents the amount of data for an indicator.

The conflict factors $r_{ij}$ was calculated by Equation (5).

$$r_{ij}={\displaystyle \frac{{\displaystyle \sum _{i=1}^m\left(x_i-\overline{x_i}\right)\left(x_{j-}\overline{x_j}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^m{\left(x_i-\overline{x_i}\right)}^2{\displaystyle \sum _{i=1}^m{\left(x_j-\overline{x_j}\right)}^2}}}}}$$

(5)

The weight was calculated by Equation (6) [25,26].

$$W^{″}={\displaystyle \frac{{\sigma }_j{\displaystyle \sum _{i=1}^m\left(1-r_{ij}\right)}}{{\displaystyle \sum _{j=1}^n{\sigma }_j\left({\displaystyle \sum _{i=1}^m\left(1-r_{ij}\right)}\right)}}}$$

(6)

where $W^{″}$ represents the weight obtained by the CRITIC method, and n represents the number of indicators.

4.3. Combined Weights

The weights obtained by the AHP method were more subjective and did not fully reflect objectivity. In order to reduce the influence of subjectivity, the subjective and objective preference coefficients were introduced, and the weights obtained by the AHP method and the CRITIC method were combined by the linear weighting method to obtain the combined weights, which are calculated by Equation (7):

$$W=\alpha W^{\prime }+\left(1-\alpha \right)W^{″}\hspace{0.33em}\hspace{0.33em}0\le \alpha \le 1$$

(7)

where $W$ represents the combined weights, and $\alpha$ represents the subjective and objective preference coefficients; in this paper, the value is taken as 0.5.

4.4. Evaluation of Resilience

According to the weight calculation, therefore, the resilience can be calculated through Equation (8).

$$R=W\times C$$

where $R$ represents the matrix of resilience, and $C$ represents the matrix of indicator values.

5. Results and Analysis

5.1. Results of Weighting

All kinds of weights were gained from Equations (1)–(7). For the basic data of indicators, they were obtained in two ways. Quantifiable indicators were obtained and assessed according to laws and regulations. For instance, the fire separation distance and building density were evaluated according to fire safety regulations. Non-quantifiable indicators were evaluated by expert scoring. A total of 10 experts were invited to score in this paper, including specialists in firefighting and rescue, ancient architecture, and scholars. Weights were obtained and presented in

Table 3. Weights of evaluation index for fire resilience of ancient architectural complexes.

Level 1 Indicators (A)	Level 2 Indicators (B)	${\mathit{W}}_{\mathit{B}}^{\prime }$	${\mathit{W}}_{\mathit{B}}^{″}$	Level 3 Indicators (C)	${\mathit{W}}_{\mathit{C}}^{\prime }$	${\mathit{W}}_{\mathit{C}}^{″}$	Combined Weights W.
Overall resilience evaluation indicator system ($A$)	Architectural Features ($B_1$)	0.5497	0.2990	$C_1$	0.0151	0.0544	0.0348
				$C_2$	0.2149	0.0439	0.1294
				$C_3$	0.0522	0.0421	0.0472
				$C_4$	0.0321	0.0347	0.0334
				$C_5$	0.0899	0.0339	0.0619
				$C_6$	0.1288	0.0372	0.0830
				$C_7$	0.0167	0.0528	0.0348
	Facility Factors ($B_2$)	0.2715	0.2349	$C_8$	0.1256	0.0339	0.0798
				$C_9$	0.0124	0.0340	0.0232
				$C_{10}$	0.0086	0.0253	0.0170
				$C_{11}$	0.0303	0.0440	0.0372
				$C_{12}$	0.0653	0.0413	0.0533
				$C_{13}$	0.0292	0.0564	0.0428
	Management Factors ($B_3$)	0.1160	0.2968	$C_{14}$	0.0271	0.0311	0.0291
				$C_{15}$	0.0124	0.0301	0.0213
				$C_{16}$	0.0069	0.0440	0.0255
				$C_{17}$	0.0376	0.0388	0.0382
				$C_{18}$	0.0030	0.0357	0.0194
				$C_{19}$	0.0217	0.0413	0.0315
				$C_{20}$	0.0023	0.0381	0.0202
				$C_{21}$	0.0050	0.0377	0.0214
	Society Factors ($B_4$)	0.0627	0.1962	$C_{22}$	0.0170	0.0450	0.0310
				$C_{23}$	0.0048	0.0551	0.0300
				$C_{24}$	0.0077	0.0291	0.0184
				$C_{25}$	0.0334	0.040	0.0367

.

5.2. Weights of Level 2 Indicators

The weights of level 2 indicators are shown in Table 3. The weights gained by the AHP method for architectural features ($B_1$), facility factors ($B_2$), management factors ($B_3$), and societal factors ($B_4$) are 0.5497, 0.2715, 0.1160, and 0.0627, correspondingly. This indicates that architectural features (0.5497) and facility factors (0.2715) are far more important than management factors (0.1160) and societal factors (0.0627) from a subjective perspective. Architectural features and facility factors are intrinsic characteristics possessed by the ancient building complex itself, which is the material basis of the complex. It is suggested that the material basis played a decisive role in resisting and coping with fire risk. In contrast, managemental and societal factors were relatively minor.

The weights gained by the CRITIC method for architectural features ($B_1$), facility factors ($B_2$), management factors ($B_3$), and societal factors ($B_4$) are 0.2990, 0.2349, 0.2968, and 0.1962 correspondingly. This is quite different from the weights gained from the AHP method. They are comparatively balanced between weights. This indicates that architectural features (0.2990) and management factors (0.2968) are relatively more important than facility factors (0.2349) and societal factors (0.1962). This suggested that architectural features and management factors are dominant factors of the resilience of ancient architectural complexes.

By comparing the two sets of weights, it can be found that AHP-decided weights are more in favor of the material basis of ancient architectural complexes, and CRITIC-decided weights are more in favor of architectural features and management factors. None of the weights determined by a single method are comprehensive, therefore the combined weights are necessary.

AHP-CRITIC combined weights are calculated according to Equation (7) and are presented in Figure 4. This reveals that the combined weights of architectural features ($B_1$), facility factors ($B_2$), management factors ($B_3$), and societal factors ($B_4$) are 0.4244, 0.2532, 0.2046, and 0.1295. Their influence on resilience declines in that order. Among all these factors, architectural features have the greatest impact, and societal factors have the smallest impact. Facility factors weights are slightly more important than management factors. Therefore, the enhancement of fire resilience of ancient architectural complexes should focus on strengthening the construction of the physical level of ancient architectural complexes.

5.3. Weights of Level 3 Indicators

The weights of the level 3 indicators are presented in Table 3 and Figure 5. As can be seen in Figure 5, the fire resistance rate, the building material, the automatic alarm system, the smoke control and exhaust capacity, the sprinkler system, the building density, the medical facilities, the firefighting and rescue response capacity, the individual firefighting and self-rescue capacity, and the transportation network are outstanding indicators. Their weights are 0.1294, 0.0830, 0.0798, 0.0619, 0.0533, 0.0472, 0.0428, 0.0382, 0.0372, and 0.0367, correspondingly. Among all these outstanding indicators, 8 out of 10 came from architectural features and facility factors. The fire resistance rate is the most influential architectural feature, the automatic alarm system is the most influential facility factor, the firefighting and rescue response capacity is the most influential management factor, and the transportation network is the most influential management factor. Therefore, for the fire safety protection of ancient architectural complexes, the above outstanding factors should be strengthened to effectively improve the fire resilience of ancient architectural complexes.

5.4. Resilience Category Analysis

Fire resilience was divided into five categories in Section 2.2, and the weights of each category are calculated and presented in Figure 6. It is important to note that the weight of the resilience category was calculated by adding up the corresponding level 3 indicators as a list, which is classified in Table 1. As shown in Figure 6, the weights of robustness, redundancy, efficiency, intelligence, and adaptivity are 0.409, 0.1524, 0.1322, 0.1875, and 0.1186, respectively.

It turns out that redundancy is the most important resilience category, followed by intelligence. This indicates that strengthening the ability of ancient architecture complexes to absorb fire disturbances and maintain a safe state are the most significant resilience-building aspects. This highlights the priority of fire disaster prevention. Furthermore, intelligence plays a secondary important role in fire resilience. This suggests that it is important to identify problems, deploy resources rationally, determine action priority, and optimize decision-making. This emphasizes the significance of the fire disaster response. Additionally, enhancing redundancy, efficiency, and adaptivity are also important in strengthening the fire resilience of ancient architectural complexes.

6. Fire Resilience Enhancement Advice

The above analysis proves that architectural features and facility factors are two prior level 2 indicators. The fire resistance rate, the building material, the automatic alarm system, etc., indicators are 10 outstanding level 3 indicators. Robustness and intelligence are two important resilience categories. Considering that most of ancient architectural complexes are wooden structures and are old in age, this paper proposes some targeted and practical fire resilience enhancement advice as follows.

6.1. Improve Resistance Rate of Ancient Architectural Complexes

The above analysis shows that architectural features are one of the most influential level 2 indicators. The fire resistance rate, the building material, the smoke control and exhaust capacity, and the building density are top-ranking sub-indicators. Of these sub-indicators, some indicators cannot be improved, like the building density and the building material, for historical and cultural reasons. Therefore, upgrading the fire resistance rate is the most effective method.

The improvement of the fire resistance rate of ancient architectural complexes can be achieved by applying fire-resistant coatings to some of the major wooden structures. Replacement measures can be taken for some of the building components that have fallen into disrepair by replacing them with more fire-resistant materials. In order to improve the fire resistance level of the cultural relics and ancient architectural complexes, it is necessary to strengthen the renovation of the firewall, and the flammable materials present in the cultural relics and ancient architectural complexes should be improved by taking separate measures.

6.2. Strengthen Fire Monitoring, Warning, and Smart Firefighting

This shows that the facility factor is one of the most influential level 2 indicators. The automatic alarm system, the sprinkler system, medical facilities, and the transportation network are top-ranking sub-indicators. In this area, fire warning and firefighting are vital. It is recommended to install smoke detectors, temperature sensors, and video monitoring systems to enhance monitoring and early warning capabilities for fire hazards, which are beneficial for shifting the risk control point. Due to the flammability of ancient architectural complexes and the rapid development of fire conditions, it is necessary to deploy fire monitoring and early warning systems as well as automatic fire-extinguishing devices in key protected ancient architectural complexes to reduce the response time.

6.3. Strengthen the Ensuring of the Firefighting Response

When a fire breaks out, the firefighting capacity is the most important component. The ensuring of the firefighting response plays an important role. Firstly, it is essential to enhance the firefighting capabilities of professional fire brigades, as they are the main force in extinguishing fires. Secondly, the self-rescue abilities of ordinary people and employees should be improved. Additionally, the funding, equipment, and supplies for fire rescue must be ensured to guarantee the effectiveness of firefighting capabilities. Finally, fire extinguishing drills must be strengthened to ensure the efficiency of firefighting operations.

7. Case Study

7.1. A Basic Situation of an Ancient Architectural Complex

This paper evaluated the fire resilience of an ancient architectural complex. The researched architectural complex is in Jiangxi Province, covering an area of about 10 km², with a history of about a thousand years, and is inhabited by nearly 3000 villagers. The ancient architectural complex has a construction area of 10 km², with 69 ancient ancestral halls and residential buildings, and has 10 provincially protected buildings. The complex is circular and runs north–south, measuring approximately 1 km from east to west, and 0.5 km from north to south. The main body of the building is a mixed brick and wood structure, and the walls of ancient building rooms are generally wood-frame structures. An aerial view of the ancient architectural complex is shown in Figure 7.

This paper evaluated the fire resilience of the ancient architectural complex by indicators listed in Table 1, and indicators and resilience are evaluated in accordance with

Table 4. Classification criteria of indicators and resilience.

Grade	Interpretations
1	The object is in a very bad state
2	The object is in a bad state
3	The object is in a moderate state
4	The object is in a good state
5	The object is in a very good state

. The investigation results are shown in

Table 5. Scores of indicators of fire resilience of ancient architectural complexes.

Indicators	Average Scores	Indicators	Average Scores	Indicators	Average Scores	Indicators	Average Scores
C1	2.4	C8	1.9	C15	3.8	C22	3.5
C2	2.1	C9	2.1	C16	3.1	C23	2.8
C3	3.3	C10	3.4	C17	3.2	C24	2.3
C4	2.0	C11	3.5	C18	2.9	C25	2.6
C5	2.4	C12	4.2	C19	2.5
C6	3.3	C13	3.0	C20	3.4
C7	4.2	C14	3.5	C21	4.2

as follows.

7.2. Fire Resilience Evaluation and Analysis

According to Equation (8) and Table 5, the overall resilience value, namely 3.01, of the ancient architectural complex was calculated. It turns out that the resilience of the ancient architectural complex is in a moderate state. The in-depth analysis according to Table 4 reveals that the building height, the sprinkler system, and government funding for disaster prevention were in a good state. Indicators containing the fire separation distance, the automatic alarm system, evacuation signs, etc., were in a bad state. As for outstanding level 3 indicators, they were in a moderate state.

In terms of the level 2 indicators, the completion rates of them are calculated and presented in Figure 8. The completion rate here is represented by the ratio of the indicator score to the full score. It is shown in Figure 8 that the completion rates of architectural features, facilities factors, management factors, and societal factors are 59.43%, 58.48%, 65.51%, and 56.90%, respectively. The completion rates of these indicators are relatively close, which indicates that these indicators are relatively balanced. However, this reveals that both of the level 2 indicators are at a moderate level, and they need to be improved immediately.

The completion rates of various resilience categories are displayed in Figure 9. It is shown that the completion rates of robustness indicators, redundancy indicators, efficiency indicators, intelligence indicators, and adaptivity indicators are 58.05%, 74.15%, 64.75%, 4984%, and 60.00%. The completion rates of various resilience categories are moderate overall, and need to be significantly strengthened. Additionally, it is worth noting that the intelligence indicators are the worst, which indicates a need for significant enhancement.

In summary, the analysis reveals that the ancient architectural complex located in Jiangxi province has moderate fire resilience overall. The development of the indicators is relatively balanced, but the intelligence indicators are underdeveloped. It is recommended to strengthen the fire resistance rate, upgrade the automatic alarm system, and conduct other measurements to improve the resilience of the ancient architectural complex.

8. Conclusions

This paper studied the conceptual and structural characteristics of fire resilience, proposed an evaluation indicator system, and then obtained the key factors affecting the resilience of ancient architectural complexes. This method was applied to an ancient architectural complex. Therefore, conclusions can be drawn as follows.

(1)

This paper studied the concept of fire resilience of ancient architectural complexes and proposed measuring robustness, redundancy, efficiency, intelligence, and adaptivity structural characteristics of fire resilience.

(2)

This paper established an evaluation indicators system of fire resilience for ancient architectural complexes, which includes 25 third-level indicators categorized under architectural characteristics, facility factors, management factors, and societal factors.

(3)

This paper determined indicator weights using the AHP-CRITIC method, and figured out the most important level 2 indicators, level 3 indicators, and resilience categories.

(4)

This paper gave suggestions to enhance the fire resilience of ancient architectural complexes from the perspective of the fire resistance rate, smart firefighting, and the ensuring of the firefighting response.

This paper did not consider the impact of the environment and surrounding layout on the fire resilience of historic building complexes. A reflection on how certain measures might affect the heritage value of the buildings may require further research.