An Evaluation Model for the Firefighting and Rescue Capability of Cultural Relic Building Complexes in Forest Areas

Abstract

Previous evaluation models for cultural relic buildings in relation to fire risk fail to consider the necessity for effective firefighting and rescue capabilities in complex forest environments. This paper incorporates variables, including those pertaining to forest fires and climatic conditions, into the assessment index system. The hierarchical analysis method and the local punishment-incentive variable weighting method are employed to introduce a compensation coefficient score. A model for the evaluation of firefighting and rescue capability in a continuous area of cultural relic buildings in conjunction with the surrounding forest environment has been developed. The firefighting and rescue capability of the Yuelu Mountain scenic spot was evaluated at 73.91 (level III) using the fixed weight method and 69.52 (level IV) using the variable weight method. The variable weight method proved to be a more accurate approach for evaluating the status and importance of dynamic targets, thus enabling a more precise evaluation of the comprehensive evaluation area. The evaluation results inform the formulation of targeted improvement measures for enhancing the firefighting and rescue capabilities of cultural relic buildings.

1. Introduction

Cultural relic buildings are of immense cultural and historical significance, serving to represent the political, economic, artistic, and religious aspects of ancient societies. They are invaluable national heritage sites, which serve to represent the cultural and historical legacy of these societies. As of 2020, the number of cultural relic buildings in China exceeded 260,000. The distribution of cultural relic buildings is shaped by a complex interplay of natural and social factors, with the majority situated in low mountain forest environments. This has resulted in the formation of a continuous area of cultural relic buildings within forest environments. To illustrate, there are more than 60 cultural relic buildings at Lushan Mountain (6 m–1443 m above sea level), in region 80 at Wutai Mountain (624 m–3061 m above sea level), and over 10 at Qingcheng Mountain (718 m–1222 m above sea level). The cultural relic buildings are of an early construction age, with the majority constructed from wood or brick. They are located in a continuous area within a forested environment. The area is prone to firefighting and rescue difficulties, with firefighting and rescue equipment being difficult or even unable to approach. Consequently, cultural relic buildings are at an extremely high risk of fire and possess irrecoverable characteristics. Figure 1 illustrates the number of forest fires in China from 2010 to 2019 [1]. The phenomenon of global warming has resulted in a notable increase in the frequency of forest fires, which has served to exacerbate the existing problem of firefighting and rescue operations in cultural relic buildings. A review of statistical data from the period between 2009 and 2019 indicates that a total of 392 fires occurred in cultural relic buildings within the country. To illustrate, a fire in Baojing ancient village on 25 January 2014 came perilously close to destroying the entire village. A fire in Dukezong ancient town in Shangri-La on 10 January 2014 impacted 335 households and 242 houses. Figure 2 illustrates the typical characteristics of fires in cultural relic buildings in recent years. Moreover, the incidence of forest fires is rising as a consequence of global warming, which in turn has a deleterious impact on carbon storage and climate balance. This creates a vicious circle [2,3,4], which must be addressed through the protection of cultural relic buildings in forests in conjunction with an assessment of the risk of forest fires [5,6].

A great deal of research has been conducted by scholars from both domestic and foreign institutions on the subject of fire safety assessment of cultural relic buildings. Wu et al. [7] developed an index system comprising three aspects: cultural relic value sensitivity, village fire hazard, and evacuation accessibility. A hybrid intelligence model was constructed on an ANP and using a Bayesian algorithm. Zhang et al. [8,9] proposed a CFD-based framework for the fire risk assessment of contiguous wood-structured villages in western Hunan. This framework encompasses the study of a number of different aspects, including village layout, street layout, residential materials, structural forms, energy patterns, fire habits, and other pertinent factors. Chen et al. [10] proposed a Bayesian network combination construction method for the fire risk assessment of historical buildings, which integrates static indicators such as building parameters and cultural significance with dynamic indicators such as environmental factors. Lee et al. [11] employed big data analysis and remote sensing technology to facilitate the development of the AHP structure with items and factors. Subsequently, they proceeded to assess the severity of building fires in 17 villages, including the Taishan District, New Taipei City, Taiwan. Yuan et al. [12] evaluated the fire safety of Dangjia Village in Shaanxi Province by calculating the scalar product of the weights and grades of parameters, including brick wall integrity, wood column integrity and moisture content, and fire service accessibility. Palazzi et al. [13] employed the fire risk index method to assess the fire risk of 443 unreinforced masonry buildings situated within the Yungay historical center in Santiago, Chile. Hu et al. [14] proposed a semi-quantitative evaluation method for buildings based on a fire risk index and a Bayesian network.

The majority of current research on cultural relic buildings is focused on the risk of fire, with relatively little research conducted on the subject of firefighting and rescue capability. To enhance the firefighting and rescue capability of cultural relic buildings in forest settings, this study innovatively integrates forest fire, climatic conditions, and other influencing factors into the evaluation system, thereby establishing a firefighting and rescue capability evaluation method for individual cultural relic buildings in conjunction with forest fires. On this basis, the local penalty-incentive variable weight method is introduced to establish a firefighting and rescue capability evaluation method and an evaluation level of cultural relic buildings in contiguous areas for forest environments. In conclusion, this paper presents an evaluation of the firefighting and rescue capability of the Yuelu Mountain scenic spot, and subsequently proposes measures to enhance this capability based on the evaluation results.

2. Evaluation of Individual Cultural Relic Buildings

2.1. Evaluation Model

The analytic hierarchy process (AHP), initially proposed by Satty in the 1970s, is a method of applying network system theory and multi-objective comprehensive evaluation. AHP integrates both qualitative and quantitative analysis. It has a wide range of applications. In terms of applications in cultural relic buildings, Li et al. [15] established a residential fire risk assessment system, combining the triangular fuzzy analytic hierarchy process (FAHP) and entropy weight method, to evaluate the Hexinwu building group in Guangdong province. Xu et al. [16] proposed a fire risk assessment method for ancient buildings based on AHP and applied it to a typical family hotel in the ancient city of Feng Huang. Yan et al. [17] employed integrated the analytic hierarchy process (AHP) and principal component analysis (PCA) to assess and analyze cultural relic buildings. In terms of applications in forest fires, Coban et al. [18] employed the analytic hierarchy process to assess the fire risk of the forests susceptible to primary fires in the Bucak forest in Turkey. In a similar vein, Gianluigi Busico et al. [19] proposed a forest fire risk assessment method based on a geographic information system and the analytic hierarchy process. In terms of applications in other fields, Mi et al. [20] proposed a fire risk assessment method for residential buildings that incorporates fuzzy theory, evidential reasoning theory, and expected utility. This method employs a fuzzy analytic hierarchy process to analyze the fire risk index system for residential buildings. Wang et al. [21] established evaluation indexes and identified potential fire-causing factors to conduct a qualitative and quantitative analysis of a typical large-scale commercial complex. The AHP has previously been applied to cultural relic buildings and forest fires. This allows for the integration of forest fire and climatic conditions into the index system, as well as the establishment of a firefighting and rescue capability evaluation model for cultural relic buildings in conjunction with forest fires.

2.1.1. Establishment of the Index System

A review of the literature and case studies reveals the following fire safety problems in cultural relic buildings, as illustrated in Figure 3. Firstly, the fire resistance level of building materials is low. Secondly, there is a greater accumulation of combustible substances within the building. Thirdly, the fire separation between adjacent buildings is inadequate. Fourthly, the complex location of the building makes it difficult to rescue. Finally, the firefighting facilities are not optimal. The aforementioned factors will have varying effects on the firefighting and rescue capabilities of cultural heritage buildings.

The evaluation index system for the firefighting and rescue capability of cultural relic buildings is shown in Table 1. The indicators are classified into four intermediate layers according to the location of the cultural relic buildings, the characteristics of the buildings, the location of the fire station, and the rescue force.

2.1.2. Index Weight Coefficient

To construct a scientific and reasonable evaluation index system for the firefighting and rescue capability of cultural relic buildings, four types of experts in related fields were invited to evaluate the cumulative weight of the index. The evaluation team comprised firefighting and rescue personnel, university scientific research personnel, building designers, and building managers (see Table 2). By the differing categories of personnel, the evaluation results were weighted by varying ratios, as shown in Equation (1).

(1)${\omega }_i=k_1{\displaystyle \frac{\sum _{i=1}^{n_1}{\omega }_{1,j}}{n_1}}+k_2{\displaystyle \frac{\sum _{i=1}^{n_2}{\omega }_{2,j}}{n_2}}+k_3{\displaystyle \frac{\sum _{i=1}^{n_3}{\omega }_{3,j}}{n_3}}+k_4{\displaystyle \frac{\sum _{i=1}^{n_4}{\omega }_{4,j}}{n_4}}$

where ${\omega }_i$ is the weight of the ith index; ${\omega }_{1,j}$ is the weight assigned to the index by the jth category 1 expert; $n_1$ is the number of category 1 experts; and $k_1$ is the weighting factor for category 1 experts. The explanatory notes for the remaining three categories of experts can be obtained in the same way.

The 1–9 scale method was used to assign $a_{ij}$, $a_{ii}=1$, $a_{ij}=1/a_{ji}$ (i, j = 1, 2, 3…n). The evaluation criteria presented in Table 3 were used to make a pairwise comparison of the indicators at each level, resulting in the evaluation matrix A. For example, if A₁ is considered to be slightly more important than A₂, then $a_{12}=3$. Conversely, if A₃ is identified as being significantly more important than A₂, then $a_{23}=1/5$, as shown in Equations (2) and (3). The intermediate layer index judgment matrix generated by an expert is shown in B below.

(2)$\mathrm{A}=\left[\begin{array}{ccccc}{a}_{11}& a_{12}& a_{13}& \cdots & a_{1\mathrm{n}}\\ a_{21}& a_{22}& a_{23}& \cdots & a_{2\mathrm{n}}\\ a_{31}& a_{32}& a_{33}& \cdots & a_{3\mathrm{n}}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ a_{\mathrm{n}1}& a_{\mathrm{n}2}& a_{\mathrm{n}3}& \cdots & a_{\mathrm{nn}}\end{array}\right]$

(3)$\mathrm{B}=\left[\begin{array}{cccc}1& 1/5& 1/3& 3\\ 5& 1& 1& 5\\ 3& 1& 1& 7\\ 1/3& 1/5& 1/7& 1\end{array}\right]$

The square root method is used to determine the relative weight of each index. According to Equation (4), and normalizimg the vector to obtain the corresponding weights of the external firefighting and rescue force, the internal firefighting and rescue force, the internal influencing factors, and the forest influencing factors in the B matrix can be calculated as 0.1248, 0.4173, 0.3995, and 0.0583, respectively.

(4)${\overline{\omega }}_m=\sqrt[n]{\prod _{j=1}^n{a}_{ij}}$

To ascertain the degree of coordination between the relative importance of each index, it is necessary to check the consistency of the matrix using Equation (5). The consistency ratio of the evaluation matrix is defined as CR (consistency ratio). If the consistency ratio is less than 0.1, it can be concluded that the degree of inconsistency of the matrix is within an acceptable range, and that the matrix has satisfactory consistency and passes the consistency test. The judgment matrix of the middle layer, with a consistency ratio of 0.0389, meets the consistency requirement.

(5)$\mathrm{CR}=\mathrm{C}\mathrm{I}/\mathrm{R}\mathrm{I}$

where CI is the consistency index, $\mathrm{CI}={\displaystyle \frac{{\lambda }_{\mathit{max}}-n}{n-1}}$. ${\lambda }_{\mathit{max}}$ is the largest eigenvalue of the judgment matrix. RI is the random consistency index.

Similarly, the weight of the index layer corresponding to the index B_ij in its middle layer A_i can be calculated according to the process of constructing the evaluation matrix, calculating the weight, and checking the consistency. The weight of the index layer corresponding to the evaluation target can be calculated by multiplying the weight of the middle layer and the weight of the index layer, as shown in Equation (6).

(6)${\omega }_{{\mathrm{B}}_{ij}}={\omega }_{{\mathrm{A}}_i}\times {\omega }_{{\mathrm{B}}_j}$

where ${\omega }_{{\mathrm{A}}_i}$ is the weight of the intermediate layer A_i in which B_ij is in the decision target. ${\omega }_{{\mathrm{B}}_j}$ is the weight of B_ij in its intermediate layer A_i.

2.1.3. Indicator Scoring Standard

Detailed scoring criteria have been developed for each indicator. Due to space limitations, the arrival time of fire and rescue personnel (B₁₁) and the forest fire separation zone (B₄₁) have been presented as examples. Concerning indicator B₁₁, the arrival time of fire and rescue personnel, if the time is less than five minutes, the score is 100. If the response time exceeds 15 min, the score is reduced to 60 points. If the response time exceeds 30 min, the score is 0 [22]. For other times, the interpolation method is used to derive the requisite value, as shown in Equation (7).

(7)$P_{11}=\left\{\begin{array}{c} 100 0\le t\le 300\\ -(1/15)t+120 300<t\le 1800\\ 0 1800<t\end{array}\right.$

For B₄₁, if the width of the forest fire separation zone meets the requirements of the specification, the target is 30 m and the score is 100. If the width of the forest fire separation zone essentially meets the requirements, the target is 15 m and the score is 60. If the required specifications are not met, the target is set to 0 m, the score is 0, and the remaining widths are calculated using the interpolation method, as shown in Equation (8).

(8)$P_{41}=\left\{ \begin{array}{c} 4d 0\le d\le 15\\ (8/3)d+20 15<d\le 30\\ 100 30<d\end{array}\right.$

2.1.4. Determining the Evaluation Level

The firefighting and rescue capability evaluation score for a single cultural relic building is calculated using Equation (9).

(9)$S=\sum _{\mathrm{i}=1}^n{\mathsf{\omega }}_i{P}_i$

where $S$ is the firefighting and rescue capability score of cultural relic buildings. $n$ is the number of indicators. ${\mathsf{\omega }}_i$ is the cumulative weight of the ith index and the value interval is (0, 1). $P_i$ is the evaluation score of the ith index and the value interval is [0, 100].

By the correlation between fire risk score and risk level [16], the firefighting and rescue capability score of an individual cultural relic building is in alignment with the fire and rescue capability level of the qualitative evaluation, as illustrated in Table 4.

2.2. Case Evaluation of Single Cultural Relic Building

2.2.1. Case Overview of Single Cultural Relic Building

A comprehensive investigation has been carried out on a representative cultural relic building located within the Yuelu Mountain Scenic Area, Changsha City, China. The results of the investigation indicate that the wall is constructed of brick and wood, the column is made of brick and concrete, and the beam is wooden. The width of the road leading to the building is 4 m and the estimated time for the external fire brigade to arrive is approximately 7 min. There is a rocky lake situated 850 m from the building, which could be used as an external water source. The building is situated close to a forest, which is home to a multitude of ancient and renowned trees, including camphor and maple. The building is equipped with fire extinguishers, hydrants, and a miniature fire station. Staff receive fire training, fire drills are organized, and regular fire inspections are carried out.

2.2.2. Evaluation Results

The weighting coefficients corresponding to each index, together with the results of the expert assessment, are presented in Figure 4. The score for this cultural relic building is calculated to be 72.73, which corresponds to a medium level of firefighting and rescue capability.

3. Regional Evaluation of Cultural Relic Building Complexes

3.1. Regional Evaluation Model

3.1.1. Variable Weight Theory

It is recommended that the firefighting and rescue capability of the cultural heritage building complexes in the region be considered in light of the firefighting and rescue capability of the individual cultural relic buildings and regional influencing factors [23,24]. Firstly, the presence of contiguous forest environments increases the probability of forest fires and the severity of their consequences. Secondly, the presence of complex terrain and elevation differences serves to extend the response time of external firefighting resources. Finally, the presence of tourists also introduces an element of uncertainty about the risk of fire and the difficulty of firefighting and rescue operations.

In the fixed weight evaluation model, the weight values of the static indicators are fixed and unchanging. The regional evaluation results are frequently a simple weighted average of the results of each evaluation unit, which is not an optimal approach for the open and dynamic research object of scenic spots [25]. The firefighting and rescue capability of regional cultural relic buildings shows a “barrel effect”, whereby the evaluation results depend on the individual cultural relic buildings with worse evaluation conditions. The variable weight synthesis theory is employed to introduce a local penalty-incentive mechanism to calculate the evaluation coefficient of the firefighting and rescue capability of the target region. This addresses the limitations of a fixed weight evaluation system, which is unable to accurately reflect the dynamic state of the target and to provide a comprehensive evaluation of the regional firefighting and rescue capability. The variable weight evaluation theory considers the relative importance of the basic indicators and the horizontal configuration of the indicators in the target decision, as shown in Equation (10).

(10)$\omega {\displaystyle (x_i)}={\displaystyle \frac{{\omega }_{x_i}^{\left(0\right)}f\left(x_i\right)}{\sum _{i=1}^n{\omega }_{x_i}^{\left(0\right)}f\left(x_i\right)}}$

where $\omega \left(x_i\right)$ is the variable weight of the evaluation unit $x_i$. ${\omega }_{x_i}^{\left(0\right)}$ is the fixed weight of the evaluation unit $x_i$, $f\left(x_i\right)$ is a local penalty-incentive state variable weight function, and n is the number of evaluation units.

The local penalty-incentive variable weight function is as shown in Equation (11).

(11)$f{\displaystyle (x_i)}=\left\{\begin{array}{cc}{\displaystyle \frac{c_2-c_1}{\lambda -\mu }}\ln {\displaystyle \frac{\mu }{x_i}}+c_2& 0<x_i\le \mu \\ -{\displaystyle \frac{c_2-c_1}{\lambda -\mu }}{x}_i+{\displaystyle \frac{c_2\lambda -c_1\mu }{\lambda -\mu }}& \mu <x_i\le \lambda \\ C+{\displaystyle \frac{c_2-c_1}{2(\lambda -\mu )(\alpha -\lambda )}}{(\alpha -x_i)}^2& \lambda <x_i\le \alpha \\ C& \alpha <x_i\le \beta \\ K\left(1-\beta \right)\ln {\displaystyle \frac{1-\beta }{1-x_i}}+C& \beta <x_i\le 1\end{array}\right.$

where $C, c_1, c_2$ is the evaluation strategy, $0<C<c_1<c_2<1$. $\mu$ is the upper limit of the extra strong penalty and $(0,\mu ]$ is the extra strong penalty interval. $\lambda$ is the upper limit of the strong penalty and $(\mu ,\lambda ]$ is the strong penalty interval. $\alpha$ is the penalty level and $(\lambda ,\alpha )$ is the initial penalty interval. $\beta$ is the incentive level, $[\alpha ,\beta ]$ is the qualified interval, and ($\beta ,1)$ is the excitation interval. $K$ is the adjustment coefficient.

3.1.2. Determining the Variable Weights

The actual state of regional firefighting and rescue capability has a “barrel effect”, which depends on the evaluation of the state of the poorer monoliths, so it is necessary to set the function of the penalty amplitude as much larger than the incentive amplitude parameter. In this paper, we reference the monolithic cultural relic buildings firefighting and rescue capability evaluation level (excellent, good, medium, fair, poor) to determine the penalty-incentive interval. And, according to the actual research situation in Yuelu Mountain, combined with the curve of the penalty variable weight state vector function (see Figure 5a), we discussed the evaluation strategy and the value of the adjustment coefficient with the experts and tentatively set $\mu =0.6, \lambda =0.7, \alpha =0.8, \beta =0.9, C=0.6, c_1=0.7, c_2=0.9, K=2, x_i=S_i/100$, as shown in Equation (12).

Its feasibility is verified. In the region of extra-strong penalty stage $(0,\mu ]$, the heaviest penalty needs to be applied to the weights of extreme deterioration indicator factors. At this time, the influence of $\mu$ on the state variable weight vector $f\left(x_i\right)$ is shown in Figure 5b, which shows that when the firefighting and rescue capability is poor, in the case of $x_i=(0~0.7)$, the influence on $f\left(x_i\right)$ is not great when $\mu <0.6$. Meanwhile, when $\mu >0.6$, this will lead to the punishment being too serious, so $\mu$ taking 0.6 is more appropriate. In the incentivized phase ($\beta ,1)$ region, the unit with “excellent” firefighting and rescue capability should be rewarded. At this time, the impact of $\beta$ on the state variable weight vector $f\left(x_i\right)$ is shown in Figure 5c: when the single unit score is high, in the case of $x_i=(0.8~1)$, when $\beta$ is between $0.8 \mathrm{and} 0.9,$ the value of $f\left(x_i\right)$ still shows a large impact. Considering that this paper mainly deals with the more dangerous evaluation indexes, and that the good evaluation indexes do not have too many requirements, it is appropriate to choose 0.9. The above process, to a certain extent, can reduce the potential subjectivity and increase the scientific rationality, so that the firefighting and rescue capacity of a low single unit obtains a higher weight.

(12)$f{\displaystyle (x_i)}=\left\{\begin{array}{cc}2\ln {\displaystyle \frac{0.6}{x_i}}+0.9& 0<x_i\le 0.6\\ -2x_i+2.1& 0.6<x_i\le 0.7\\ 0.6+10{(0.8-x_i)}^2& 0.7<x_i\le 0.8\\ 0.6& 0.8<x_i\le 0.9\\ 0.2\ln {\displaystyle \frac{0.1}{1-x_i}}+0.6& 0.9<x_i\le 1\end{array}\right.$

3.1.3. Compensation Score and Evaluation Level

The protection level of individual cultural relic buildings can be categorized into three distinct units: the national key cultural relic protection unit, the provincial cultural relic protection unit, and the municipal cultural relic protection unit. A field study has revealed that the fire management level of national key cultural relic protection units is considerably superior to that of provincial cultural relic protection units, while the fire management level of municipal cultural relic protection units is characterized by significant shortcomings. Consequently, the compensation coefficient $h$ has been incorporated into the score of each cultural relic building, thereby enabling a more precise reflection of the regional firefighting and rescue capability. The compensation coefficient is $h=1.3$ for national key cultural relic protection units, $h=1.1$ for Hunan provincial cultural relic protection units, and $h=0.9$ for Changsha city cultural relic protection units, as shown in Equation (13).

(13)$S_i^{\prime }=h{S}_i{\displaystyle \frac{\sum _{i=1}^n{S}_i}{\sum _{i=1}^n{hS}_i}}$

Given the variable weight and compensation value of each monomer of the regional cultural relic buildings, the variable weight compensation value of the firefighting and rescue capability of the regional cultural relic building group can be obtained, as shown in Equation (14). The evaluation level of the regional cultural relic buildings in this paper employs the same classification evaluation method as that used for the individual cultural relic building.

(14)$S_t=\sum _{i=1}^n{S}_i^{\prime }\omega {\displaystyle (}{x}_i{\displaystyle )}$

where $S_t$ is the evaluation score of the fire fighting and rescue capability of the cultural relic building group, $S_i^{\prime }$ is the compensation score of the evaluation unit $x_i$, and $\omega \left(x_i\right)$ is the variable weight of this cultural relic building.

3.2. Example Evaluation of Cultural Relic Building Complexes

3.2.1. Case Overview of Cultural Relic Building Complexes

The Yuelu Mountain scenic spot is situated in Changsha, Hunan Province. Figure 6 shows the forest fire risk warning in Hunan Province in September 2022, with the majority of warnings classified as red. Therefore, it is of paramount importance to select the Yuelu Mountain Scenic Area as the subject of this research. The Yuelu Mountain scenic spot is a nationally designated 5A-level tourist attraction characterized by a diverse range of vegetation, including subtropical evergreen deciduous forest and subtropical warm coniferous forest. The Yuelu Mountain scenic spot is home to many cultural relics, including the Yuelu Academy, Lushan Temple, Yunlu Palace, and others. These cultural artifacts integrate Confucianism, Buddhism, and Taoism culture and are of significant cultural value. The researchers gathered data from 36 research subjects through data collection and field investigation. It should be noted that Chuanshipo Lake, which is an external water source, is not included in the assessment. Furthermore, research objects, such as tombs and steles, whose main building body is made of non-combustible materials have been excluded, and 25 evaluation monomers were determined.

3.2.2. Evaluating the Results

The previous section described the method used to assess the fire and rescue capability of individual heritage buildings. This method was used to calculate the firefighting and rescue capability scores for 25 individual buildings. The firefighting and rescue capability of the regional cultural relic buildings was evaluated at 69.52 in the variable weight assessment, indicating a level of IV. The score of the fixed weight assessment was 73.91, indicating a level of III.

As illustrated in Figure 7 and Table 5, of the twenty-five assessment units within the Yuelu Mountain Scenic Area, three (12%) are classified as excellent, six (24%) as good, seven (28%) as medium, five (20%) as fair, and four (16%) as poor. The proportion of medium results is the highest, and the most probable reasons for this are the forest environment with a high vegetation cover and complex terrain. The proportion of excellent results is the lowest. To illustrate, an analysis of Yuelu Academy reveals that its rating is excellent. Firstly, Yuelu Academy is a nationally designated cultural heritage site and has a high level of fire management. Secondly, Yuelu Academy is situated at a relatively low altitude, which facilitates the rapid deployment of external rescue forces. Finally, the fire lanes and evacuation passages around Yuelu Academy are relatively well designed, which facilitates the rescue and evacuation of personnel in the event of an emergency.

The firefighting and rescue capability of the regional heritage buildings is 73.91 points, and the evaluation level is III (medium). However, due to the influence of the actual situation, the results depend on the individual cultural relic buildings with poor evaluation status. In the region, 36 per cent of heritage buildings are classified as fair or poor. This results in an increased fire risk to the regional cultural relic building groups. The fixed weighting method produces results that are too high to fully reflect the actual situation of the regional firefighting and rescue capability, while the evaluation result using the variable weighting method is 69.52 points, with the evaluation level being IV (fair). This is because, although the incentive interval scored a high “excellent” monomer variable weight, which is higher than in the qualified interval “Good” monomer, only the highest scoring monomer variable weight was more than 0.04. The variable weight of “Good” monomers in the qualifying interval is 0.0314. In the penalty interval, the lower the inherent score of the monomer, the greater the intensity of the penalty and the greater the variable weight. At the same time, most of the monomers are in the penalty interval of the compensation coefficient of 0.9, the compensation score is reduced, and the overall effect of low score and high weight further lead to the effect of the variable weighting method. The overall scores and grades obtained are lower than those of the fixed weight method. In contrast, the variable weight method yields results that are closer to the actual situation of the regional firefighting and rescue capability. The evaluation results led to the formulation of recommendations for improving the firefighting and rescue capability of the Yuelu Mountain Scenic Area (Figure 8).

4. Conclusions

This paper identifies the factors that influence the firefighting and rescue capability of cultural relic buildings in forest environments and constructs an evaluation index system based on this capability coupled with forest fires based on the analytic hierarchy process. The index weights of the system are calculated by weighted average, according to the different types of evaluators, to establish the firefighting and rescue capability evaluation model of a single cultural relic building in a forest environment.

The local penalty-incentive variable weight function was developed in conjunction with the analytic hierarchy process (AHP) and variable weight theory. This function enabled the individual scores to be compensated according to the protection level and type of cultural relic building. Ultimately, an evaluation model for firefighting and rescue capabilities in contiguous areas of cultural relics in forest environments was developed. The evaluation score for the fixed weight method is 73.91 (level III), while the evaluation score for the variable weight method is 69.52 (level IV). The variable weight method addresses the limitations of the fixed weight evaluation system, which is unable to accurately reflect the status and importance of a dynamic target. This method provides a comprehensive evaluation of the region’s precise status.

After field investigation and data processing, measures to improve the firefighting and rescue capability of the Yuelu Mountain scenic spot are proposed, which provide important technical support for improving the firefighting and rescue capability of cultural relics.

Author Contributions

Conceptualization, L.Y.; methodology, L.Y.; investigation, J.Z.; data curation, J.Z. and Q.L.; writing—original draft preparation, J.Z.; writing—review and editing, L.Y.; visualization, J.Z.; supervision, G.Z.; project administration, G.Z. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviation

Parameter	Explanation
${\omega }_{A_i}$	The weight of the intermediate layer Ai
${\omega }_{B_j}$	The weight of Bij in its intermediate layer Ai
${\omega }_{B_{ij}}$	The weight of index Bij among all indexes
${\omega }_i$	The weight of index Bij weighted by different experts
$P_i$	The score of the ith evaluation index
$S$	The evaluation score of the single cultural relic building
$\omega \left(x_i\right)$	The variable weight of the evaluation unit $x_i$
${\omega }_{x_i}^{\left(0\right)}$	The fixed weight of the evaluation unit $x_i$
$f\left(x_i\right)$	The local penalty–incentive state variable weight function
$S_i$	The score of the evaluation unit $x_i$
h	The compensation coefficient
$S_i^{\prime }$	The compensation score of the evaluation unit $x_i$
$S_t$	The evaluation score of the cultural relic building group

Footnotes

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Figures and Tables

Figure 1. Occurrence of forest fires by province in China, 2010–2019.

Figure 2. Typical fires of cultural relic buildings in forests.

Figure 3. Influencing factors of firefighting and rescue capability of cultural relic buildings.

Figure 4. Weighting coefficients and index scores.

Figure 5. Reference chart for determining variable weights: (a) penalty variable weight function [Forumla omitted. See PDF.]; (b) relationship between the value of the parameter [Forumla omitted. See PDF.] and the penalty weighting function [Forumla omitted. See PDF.]; (c) relationship between the value of the parameter [Forumla omitted. See PDF.] and the penalty weighting function [Forumla omitted. See PDF.].

Figure 6. Forest fire danger weather rating forecast map of Hunan province (September 2022).

Figure 7. Evaluation results of Yuelu Mountain scenic spot.

Figure 8. Pathways for improving firefighting and rescuing capabilities.

Table 1

Evaluation index system of the firefighting and rescue capability of cultural relic buildings.

Intermediate Layer	Serial Number	Index Layer
External firefighting and rescue forces A1	B11	Arrival time of fire service
	B12	Arrival time of fire equipment
	B13	Outdoor hydrant water supply
	B14	External fire source
Internal firefighting and rescue forces A2	B21	Supporting fire extinguishing facilities
	B22	Miniature fire station
	B23	Internal fire source
	B24	Personnel firefighting and rescue capability
Internal influencing factors A3	B31	Building structure
	B32	Combustible
	B33	Fire spacing
	B34	Fire lane
Forest influencing factors A4	B41	Forest fire barrier
	B42	Vegetation type
	B43	Climate
	B44	Dead leaves

Table 2

Expert categories and their weighting coefficients.

Group	Profession	Weight Coefficient kn
1	Firefighting and rescue personnel	k1 = 0.4
2	University scientific research personnel	k2 = 0.3
3	Building designer	k3 = 0.2
4	Building manager	k4 = 0.1

Table 3

Description of the evaluation scale.

${\mathit{a}}_{\mathit{i}\mathit{j}}$	Meaning
1	${\mathrm{A}}_i$ is as important as ${\mathrm{A}}_j$
3	${\mathrm{A}}_i$ is slightly more important than ${\mathrm{A}}_j$
5	${\mathrm{A}}_i$ is obviously more important than ${\mathrm{A}}_j$
7	${\mathrm{A}}_i$ is strongly more important than ${\mathrm{A}}_j$
9	${\mathrm{A}}_i$ is extremely more important than ${\mathrm{A}}_j$

Table 4

Classification of firefighting and rescue capability evaluation of cultural relic buildings.

Level	Score	Evaluation Results
I	(90, 100]	Excellent
II	(80, 90]	Good
III	(70, 80]	Medium
IV	(60, 70]	Fair
V	(0, 60]	Poor

Table 5

Evaluation results of firefighting and rescue capability of cultural relic building complexes.

Individual Building	${\mathit{S}}_{\mathit{i}}$	$\mathit{h}$	${\mathit{S}}_{\mathit{i}}^{\prime }$	${\mathit{\omega }}^0$	$\mathit{f}\left({\mathit{x}}_{\mathit{i}}\right)$	$\mathit{\omega }\left({\mathit{x}}_{\mathit{i}}\right)$	Evaluation Results
1	96.70	1.30	118.3443	0.0400	0.8217	0.0431	Excellent
2	92.36	1.30	113.0329	0.0400	0.6538	0.0343	Excellent
3	91.55	1.30	112.0416	0.0400	0.6337	0.0332	Excellent
4	88.65	1.10	91.8013	0.0400	0.6000	0.0314	Good
5	87.30	1.10	90.4033	0.0400	0.6000	0.0314	Good
6	87.12	1.10	90.2169	0.0400	0.6000	0.0314	Good
7	86.47	0.90	73.2631	0.0400	0.6000	0.0314	Good
8	83.22	1.30	101.8471	0.0400	0.6000	0.0314	Good
9	80.11	1.10	82.9578	0.0400	0.6000	0.0314	Good
10	77.32	1.30	94.6265	0.0400	0.6072	0.0318	Medium
11	77.58	1.10	80.3378	0.0400	0.6059	0.0318	Medium
12	75.60	1.10	78.2874	0.0400	0.6194	0.0325	Medium
13	73.89	0.90	62.6045	0.0400	0.6373	0.0334	Medium
14	73.65	0.90	62.4012	0.0400	0.6403	0.0336	Medium
15	72.98	0.90	61.8335	0.0400	0.6493	0.0340	Medium
16	72.73	1.10	75.3154	0.0400	0.6529	0.0342	Medium
17	69.23	0.90	58.6563	0.0400	0.7154	0.0375	Fair
18	67.45	0.90	57.1481	0.0400	0.7510	0.0394	Fair
19	66.89	0.90	56.6737	0.0400	0.7622	0.0399	Fair
20	65.45	0.90	55.4536	0.0400	0.7910	0.0415	Fair
21	60.67	0.90	51.4037	0.0400	0.8866	0.0465	Fair
22	55.34	0.90	46.8877	0.0400	1.0617	0.0556	Poor
23	53.21	0.90	45.0831	0.0400	1.1402	0.0598	Poor
24	47.50	1.10	49.1885	0.0400	1.3672	0.0717	Poor
25	44.78	0.90	37.9406	0.0400	1.4852	0.0778	Poor

References

1. Luo, Y.; Li, Q.; Jiang, L.; Zhou, Y. Analysis of Chinese fire statistics during the period 1997–2017. Fire Saf. J.; 2021; 125, 103400. [DOI: https://dx.doi.org/10.1016/j.firesaf.2021.103400]

2. Rupp, T.S.; Chapin, F.S.; Starfield, A.M. Response of subarctic vegetation to transient climatic change on the Seward Peninsula in north-west Alaska. Glob. Chang. Biol.; 2000; 6, pp. 541-555. [DOI: https://dx.doi.org/10.1046/j.1365-2486.2000.00337.x]

3. Wang, S.; Li, H.; Niu, S. Empirical research on climate warming risks for forest fires: A case study of grade i forest fire danger zone, Sichuan province, China. Sustainability; 2021; 13, 7773. [DOI: https://dx.doi.org/10.3390/su13147773]

4. Liu, Z.; Ballantyne, L.A.; Cooper, L.A. Biophysical feedback of global forest fires on surface temperature. Nat. Commun.; 2019; 10, 214. [DOI: https://dx.doi.org/10.1038/s41467-018-08237-z]

5. Zhou, H.; Li, B. Study on Causes for Fire Accidents in Smaller Historic Towns in Mountain Regions and Their Countermeasures. China Saf. Sci. J.; 2010; 20, pp. 76-80.

6. Jiang, Q.; Zhong, S.; Zhu, W. Research on comprehensive risk assessment of forest fire in Beijing-Tianjin-Hebei region. China Saf. Sci. J.; 2020; 30, pp. 119-125.

7. Wu, Y.; Chen, S.; Wang, D.; Zhang, Q. Fire Risk Assessment of Heritage Villages: A Case Study on Chengkan Village in China. Fire; 2023; 6, 47. [DOI: https://dx.doi.org/10.3390/fire6020047]

8. Zhang, F.; Shi, L.; Liu, S.; Zhang, C.; Liu, Z. CFD-Based Validation Study on the Fire Prevention Wisdom of Ancient Village Houses in Western Hunan. Fire; 2023; 6, 144. [DOI: https://dx.doi.org/10.3390/fire6040144]

9. Zhang, F.; Shi, L.; Liu, S.; Shi, J.; Zhang, Y. CFD-based framework for fire risk assessment of contiguous wood-frame villages in the western Hunan region. J. Build. Eng.; 2022; 54, 104607. [DOI: https://dx.doi.org/10.1016/j.jobe.2022.104607]

10. Chen, J.; Ding, L.; Ji, J.; Zhu, J. A Combined Method to Build Bayesian Network for Fire Risk Assessment of Historical Buildings. Fire Technol.; 2023; 59, pp. 3525-3563. [DOI: https://dx.doi.org/10.1007/s10694-023-01475-8]

11. Lee, C.; Sung, Y.; Lin, Y.; Hsiao, G.L.K. Evaluating the severity of building fires with the analytical hierarchy process, big data analysis, and remote sensing. Nat. Hazards; 2020; 103, pp. 1843-1856. [DOI: https://dx.doi.org/10.1007/s11069-020-04057-x]

12. Yuan, C.; He, Y.; Feng, Y.; Wang, P. Fire hazards in heritage villages: A case study on Dangjia Village in China. Int. J. Disaster Risk Reduct.; 2018; 28, pp. 748-757. [DOI: https://dx.doi.org/10.1016/j.ijdrr.2018.02.002]

13. Palazzi, N.C.; Juliá, P.B.; Ferreira, T.M.; Rosas, J.; Monsalve, M.; de la Llera, J.C. Fire Risk Assessment of Historic Urban Aggregates: An Application to the Yungay Neighborhood in Santiago, Chile. Int. J. Disaster Risk Reduct.; 2023; 86, 105899. [DOI: https://dx.doi.org/10.1016/j.ijdrr.2023.103550]

14. Hu, J.; Xie, X.; Shu, X.; Shen, S.; Ni, X.; Zhang, L. Fire Risk Assessments of Informal Settlements Based on Fire Risk Index and Bayesian Network. Int. J. Environ. Res. Public Health; 2022; 19, 15689. [DOI: https://dx.doi.org/10.3390/ijerph192315689] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/36497763]

15. Li, G.; Yuan, H.; Shan, Y.; Lin, G.; Xie, G.; Giordano, A. Architectural Cultural Heritage Conservation: Fire Risk Assessment of Ancient Vernacular Residences Based on FAHP and EWM. App. Sci.; 2023; 13, 12368. [DOI: https://dx.doi.org/10.3390/app132212368]

16. Xu, Z.; Liu, D.; Cao, H.; Fu, R. Study on fire risk assessment of historic buildings based on AHP. J. Railw. Sci. Eng.; 2015; 12, pp. 690-694.

17. Yan, Z.; Wan, J. Study on combustion performance of wood for root carving. Fire Sci. Technol.; 2019; 38, pp. 718-721.

18. Coban, H.O.; Erdin, C. Forest fire risk assessment using GIS and AHP integration in Bucak forest enterprise, Turkey. Appl. Ecol. Environ. Res.; 2020; 18, pp. 1567-1583. [DOI: https://dx.doi.org/10.15666/aeer/1801_15671583]

19. Busico, G.; Guditta, E.; Kazakis, N.; Colombani, N. A hybrid GIS and AHP approach for modelling actual and future forest fire risk under climate change accounting water resources attenuation role. Sustainability; 2019; 11, 7166. [DOI: https://dx.doi.org/10.3390/su11247166]

20. Mi, H.; Liu, W.; Wang, G.; Xiao, G. An integrated method for fire risk assessment in residential buildings. Math. Probl. Eng.; 2020; 2020, 9392467. [DOI: https://dx.doi.org/10.1155/2020/9392467]

21. Wang, Y.; Ni, X.; Wang, J.; Hu, Z.; Lu, K. A Comprehensive Investigation on the Fire Hazards and Environmental Risks in a Commercial Complex Based on Fault Tree Analysis and the Analytic Hierarchy Process. Int. J. Environ. Res. Public Health; 2020; 17, 7347. [DOI: https://dx.doi.org/10.3390/ijerph17197347] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/33050057]

22. Liu, W.; Li, Y.; Liu, D.; Xu, Z.; Zhu, S. Estimation of total effective coverage rate of regional fire service based on open network data. J. Saf. Environ.; 2024; 24, pp. 666-674.

23. Yan, J.; Zuo, Z. Research on Natural Disaster Risk Assessment Index System and Method. China Saf. Sci. J.; 2010; 20, pp. 61-65.

24. Liu, Q.; Liu, J. Regional resilience evaluation methods and influencing factors from perspective of natural disasters. China Saf. Sci. J.; 2023; 33, pp. 174-181.

25. Qi, Z.; Guo, X.; Shou, Y.; Zhang, J.; Zhang, B. Risk assessment of fire induced by overhead distribution lines across forest areas. Fire Sci. Technol.; 2023; 42, pp. 829-834.