Resilience Assessment of Forest Fires Based on a Game-Theoretic Combination Weighting Method

Abstract

The increasing frequency and severity of forest fires, driven by climate change and intensified human activities, pose substantial threats to ecological security and sustainable development. However, most assessments remain centered on occurrence risk, lack a resilience-oriented perspective and comprehensive indicator systems, and therefore offer limited guidance for building system resilience. This study developed a forest fire resilience (FFR) assessment framework with 25 indicators in three levels and six domains across four resilience dimensions. Balancing expert judgment and data, we obtained indicator weights by integrating the Analytic Hierarchy Process (AHP) and the Criteria Importance Through Intercriteria Correlation (CRITIC) via a game-theoretic scheme. The analysis revealed that, among the level-2 indicators, climate factors, infrastructure, and vegetation characteristics exert the greatest influence on FFR. At the level-3 indicator scale, monthly minimum relative humidity, fine fuel load per unit area, and the deployment of smart monitoring systems were critical. Among the four resilience dimensions, absorption capacity plays the predominant role in shaping disaster response. Building on these findings, the study proposes targeted strategies to enhance FFR and applies the assessment framework to twelve administrative divisions of Baise City, China, highlighting marked spatial variability in resilience levels. The results offer valuable theoretical insights and practical guidance for strengthening FFR.

1. Introduction

Forests are a critical part of terrestrial ecosystems and play a key role in regulating Earth’s climate. They support biodiversity, influence global climate patterns, conserve water, and contribute to carbon sequestration and emission reduction [1,2]. However, the frequency and intensity of forest fires have increased significantly in recent years [3,4,5]. For example, on 30 March 2019, a wildfire in Muli County, Sichuan Province, China, rapidly escalated due to sudden wind shifts. The fire resulted in 31 firefighter fatalities and destroyed over 43.90 hectares of forest. In 2021, wildfires in California released about 161 million tons of CO₂, nearly 40% of the state’s fossil-fuel emissions in 2020. Furthermore, the 2019–2020 Australian bushfire season burned 8.19 million hectares of intact forest, accounting for 81% of the total area affected [6,7]. These events highlight the severe threats forest fires pose to ecological security and sustainable development, emphasizing the urgent need to improve fire prevention and enhance FFR.

Forest fire risk is quantitatively assessed using a range of approaches; statistical methods, machine learning (ML), and multi-criteria decision analysis (MCDA) are particularly prominent, each with distinct strengths and limitations [8]. Statistical approaches have been instrumental in identifying and characterizing key drivers of fire behavior. For example, Daşdemir [9] used multivariate statistical analysis in Turkey and found that wind speed, wind direction, canopy cover, tree age, elevation, and slope significantly influence forest fires. Similarly, Parisien [10] analyzed 5533 large forest fires (≥200 ha) in Canada using multivariate methods and revealed pronounced spatial heterogeneity in fire patterns, highlighting regional variation in driver importance.

ML techniques have also been widely adopted. Catry [11] applied logistic regression to predict fire-occurrence probability in Portugal, producing risk maps to guide management. Ma [12] employed a random-forest model to examine drivers across regions of China, identifying region-specific risk factors and high-risk areas to support tailored strategies. Eskandari [13] employed Support Vector Machines to assess fire susceptibility, finding distance to villages, mean annual precipitation, and elevation were significant factors. Kantarcioglu [14] demonstrated the effectiveness of Artificial Neural Networks in regional fire susceptibility assessment in Turkey. Gao [15] compared multiple ML models, and found that the Multi-Layer Perceptron model performed best, with climate and topography being critical influencing factors. While statistical methods and ML have significantly advanced forest fire risk assessment, they often emphasize historical or natural environmental data, potentially overlooking anthropogenic factors such as equipment, management practices, and social influences. This can limit the comprehensiveness of assessments needed for effective fire risk management.

MCDA offers a comprehensive approach to address these limitations, particularly when considering the complexity of multiple factors. Researchers have integrated Geographic Information Systems and AHP to weight fire risk factors and generate risk maps, providing a scientific basis for fire management and prevention [16,17,18]. However, AHP can introduce uncertainties through expert evaluations, leading to variations in assessment results. To mitigate this, Uçar [19] employed the Fuzzy Analytic Hierarchy Process to handle these uncertainties. Nevertheless, the Fuzzy Analytic Hierarchy Process primarily addresses fuzziness in expert judgments, neglecting objective information within the data. Therefore, a model that integrates both expert judgment and objective data is needed for a more comprehensive and accurate determination of indicator weights. Furthermore, while extensive research has focused on quantitative forest fire risk assessment, most studies still concentrate on evaluating the risk factors of fire occurrence. Research assessing FFR, especially a holistic assessment covering pre-fire, during-fire, and post-fire stages, remains scarce. Therefore, it is necessary to shift the research focus from simple risk assessment to a more comprehensive resilience assessment to improve the overall anti-interference ability of forest ecosystems.

FFR is influenced by a range of factors. Hartung [20] found climatic variables have a stronger influence on FFR than topography or human activities. Koontz [21] showed forests with greater structural diversity exhibit higher resilience to wildfires. Hayes [22] emphasized that FFR depends on complex interactions among forest structure, climate conditions, fire-management policies, silvicultural practices, and human activities. To date, however, there is no comprehensive set of evaluation metrics for FFR, nor systematic analysis of how these factors collectively affect overall resilience.

This study aims to improve FFR assessment by developing a three-level hierarchical indicator framework. Subjective weights were derived using AHP, while objective weights were calculated based on CRITIC method. These weights were then optimally integrated using a game-theoretic approach to produce combined weights that accurately identify key FFR determinants. The proposed framework was applied to evaluate the FFR of twelve administrative divisions in Baise, China. The detailed research workflow is illustrated in Figure 1.

2. Theoretical Framework of FFR

2.1. Concept of FFR

The concept of resilience has been studied for over fifty years. In 1973, Canadian ecologist Holling [23] introduced resilience into ecology, defining it as a system’s capacity to maintain its fundamental structure and function when disturbed. Holling emphasized that, in unpredictable environments, maintaining resilience is more important than achieving static stability. The concept evolved through stages including engineering resilience, ecological resilience, and adaptive resilience [24,25]. It has since been applied across various fields such as psychology, engineering, urban studies, and economics [26,27,28,29].

Building on Holling’s work and considering the specific context of forest-fire management, this study defines FFR as a forest’s ability to maintain its core structural integrity and normal functions when disturbed by fire-related factors, or to preserve system dynamism and restore itself after disturbance.

2.2. Capacity Characterization of FFR

According to resilience theory, forest resilience to fire is reflected in four key capacities: absorption, resistance, recovery, and adaptation [30]. Absorption capacity is the ability to eliminate latent hazards and prevent fire occurrence. Resistance capacity refers to reducing fire impact intensity and minimizing damage. Recovery capacity is the ability to quickly restore post-fire conditions and sustain essential ecosystem functions. Adaptation capacity involves enhancing internal structures and processes post-disturbance to better withstand future fires. Strengthening these capacities mitigates fire damage and enhances overall FFR.

2.3. Triggering Mechanism of FFR

This study integrates fire genesis mechanisms with resilience theory and forest fire characteristics to propose an emergent mechanism of FFR, illustrated in Figure 2. The FFR triggering mechanism operates through a cascading sequence: external disturbances manifesting as unsafe conditions within hazard-conducive environments induce abrupt system transitions beyond critical safety thresholds, thereby igniting wildfires; the resultant impact severity is governed by synergistic interactions between intrinsic resilience capacities (absorption, resistance, recovery, adaptation) and strategic management interventions; consequently, post-disaster adaptive learning drives progressive resilience optimization through a self-reinforcing cycle. This framework establishes a pivotal theoretical foundation for governing FFR.

3. Evaluation Index System of FFR

3.1. Selection of Evaluation Indicators

The selection of evaluation indicators follows principles of systematicity, scientific rigor, hierarchy, operability, and quantifiability [31,32]. It is grounded in regulatory frameworks such as the Forest Fire Prevention Regulations, National Forest Fire Prevention Plan (2016–2025), and National Forest Fire Emergency Response Plan. A thorough review of domestic and international literature on forest fire prevention and control informed the process [33,34,35,36,37,38,39,40,41,42,43,44]. Additionally, a six-month field survey and multi-dimensional interviews were conducted in key forest regions to capture practical challenges in fire prevention, suppression, and post-fire recovery.

To ensure the independence of evaluation indicators and minimize redundancy, we strengthen the correlations between indicators at different hierarchical levels while minimizing correlations within the same level. Additionally, we conduct adequacy assessments, redundancy analyses, and feasibility checks to identify necessity. Indicators are selected not only based on their contribution to fire resilience but also on their ability to effectively cover all aspects of forest fires. Both subjective and objective indicators are carefully considered.

Based on these foundations, a comprehensive evaluation index system was developed to operationalize FFR. As shown in

Table 1. Evaluation indicator system for FFR.

Level-1 Indicator (A)	Level-2 Indicators (B)	Level-3 Indicators (C)	Resilience Capability Dimension
FFR(A)	Vegetation Factor (B1)	Fine fuel load per unit area (C1)	Absorption capability
		Dominant species (group) flammability (C2)	Absorption capability
		Vegetation cover (C3)	Resistance capability
	Topography Factor (B2)	Slope (C4)	Resistance capability
		Slope aspect (C5)	Absorption capability
		Elevation (C6)	Absorption capability
	Climate Factor (B3)	Monthly mean temperature (C7)	Resistance capability
		Monthly mean wind speed (C8)	Resistance capability
		Monthly minimum relative humidity (C9)	Absorption capability
		Monthly mean precipitation (C10)	Absorption capability
	Infrastructure Factor (B4)	Smart monitoring systems (C11)	Absorption capability
		Fire suppression equipment (C12)	Recovery capability
		Firebreaks (C13)	Resistance capability
		Medical facilities (C14)	Recovery capability
		Water-supply support facilities (C15)	Recovery capability
	ManagementFactor (B5)	Routine fire-prevention inspections (C16)	Absorption capability
		Firefighting and emergency response capacity (C17)	Recovery capability
		Government investment in disaster risk reduction (C18)	Adaptation capability
		Fire regulation reform and improvement (C19)	Adaptation capability
		Firefighting force development (C20)	Resistance capability
		Emergency plan optimization and improvement (C21)	Adaptation capability
	Social Factor (B6)	Individual fire safety competence (C22)	Adaptation capability
		Public education and awareness campaigns (C23)	Adaptation capability
		Traditional cultural practices (C24)	Absorption capability
		Fire use in livelihood and production activities (C25)	Absorption capability

, six primary dimensions are defined at level 2: Vegetation (B1), Topography (B2), Climate (B3), Infrastructure (B4), Management (B5), and Social Factors (B6). These are further subdivided into 25 level-3 sub-indicators, numbered accordingly in Table 1. Considering the four core resilience capacities—absorption, resistance, recovery, and adaptation—these indicators were systematically grouped into corresponding categories (Figure 3), forming a hierarchical framework for capacity assessment. In applying this framework to the forest fire context, indicators were classified according to their dominant stage of influence. Those shaping the pre-ignition phase, such as by reducing ignition probability or altering fuel moisture, were assigned to absorption. Indicators that primarily affected fire spread and intensity after ignition were assigned to resistance. Factors that shortened the post-fire disruption period and supported the restoration of essential functions were classified as recovery, while those linked to long-term institutional adjustment, learning, and adaptation were assigned to adaptation. Although certain variables exert effects across multiple stages, we assigned them to the stage where their influence is most pronounced.

This evaluation index system emphasizes that FFR differs from urban applications, as resilience in forest systems is inseparable from environmental risk precursors, making the framework effectively a risk–resilience assessment.

3.2. Description of Evaluation Indicators

Fine Fuel Load per Unit Area (C1): The dry weight of fine surface fuels per unit area. Higher fuel loads increase fire spread rates and combustion intensity by enhancing fuel continuity and energy release, reducing forest resilience.

Dominant Species (Group) Flammability (C2): Characterizes combustion properties of dominant tree species, influenced by their chemical and physical traits. Flammability levels are categorized as high, moderate, or low.

Vegetation Cover (C3): Percentage of ground covered by vertical projection of vegetation. It affects fuel availability, microclimate, and fire pathways, influencing fire occurrence and spread.

Slope (C4): Land inclination degree, expressed as elevation change over horizontal distance. Slope accelerates fire spread via physical mechanisms and complicates suppression efforts, increasing impact severity.

Slope Aspect (C5): Compass orientation of slope surfaces. Sun-exposed slopes (e.g., southern in the Northern Hemisphere) receive more solar radiation, reducing moisture and raising fire risk compared to shaded slopes.

Elevation (C6): Vertical distance above sea level. Elevation influences climate, vegetation, fuels, and human activity, thereby affecting fire behavior and occurrence.

Monthly Mean Temperature (C7): Average daily temperature over a month. It regulates fuel moisture, vegetation health, weather conditions, and human activities, impacting fire probability and intensity.

Monthly Mean Wind Speed (C8): Average near-surface wind speed monthly. Wind increases fire spread and intensity by enhancing oxygen supply and heat transfer.

Monthly Minimum Relative Humidity (C9): Lowest relative humidity in a month. Low humidity dries fuels, increasing their flammability and fire risk.

Monthly Mean Precipitation (C10): Average precipitation over multiple years in a month. Less rainfall leads to drier soils and vegetation, elevating fire risk.

Smart Monitoring Systems (C11): Integrated platforms using sensors, remote sensing, and data analytics for real-time environment monitoring and early warnings. These systems detect anomalies quickly, enabling prompt fire response and reducing spread.

Fire Suppression Equipment (C12): Tools and facilities such as pumps, extinguishers, and aerial firefighting aircraft critical for effective fire control.

Firebreaks (C13): Vegetation-free strips or physical barriers that interrupt fuel continuity and slow fire spread, aiding suppression efforts.

Medical Facilities (C14): Infrastructure for emergency care and treatment, crucial for reducing casualties during fire events.

Water-Supply Support Facilities (C15): Mobile installations providing rapid water delivery to fires, forming barriers and supporting ecological restoration.

Routine Fire-Prevention Inspections (C16): Regular government-led hazard identification and mitigation measures critical for early fire risk reduction.

Firefighting and Emergency Response Capacity (C17): Ability of agencies and personnel to rapidly organize and respond to fires, reducing losses.

Government Investment in Disaster Risk Reduction (C18): Public funding for infrastructure, technology, and training vital for effective fire prevention and response.

Fire Regulation Reform and Improvement (C19): Ongoing enhancement of fire-related legal and institutional frameworks to improve disaster governance.

Firefighting Force Development (C20): Strengthening fire control through recruitment, training, and equipment to ensure efficient suppression and rescue.

Emergency Plan Optimization and Improvement (C21): Continuous refinement of emergency response plans to address weaknesses and improve coordination and effectiveness.

Individual Fire Safety Competence (C22): Public knowledge and skills for prevention, initial suppression, and self-protection, critical for community resilience.

Public Education and Awareness Campaigns (C23): Initiatives to foster responsible behavior and reduce human-caused fires through informed communities.

Traditional Cultural Practices (C24): Rituals involving open flames that may elevate fire risk if improperly managed.

Fire Use in Livelihood and Production Activities (C25): Human activities such as agricultural burning and industrial fires that can trigger wildfires if mismanaged.

4. Methods

This study employs a hybrid weighting approach that integrates AHP, CRITIC and game-theoretic optimization to determine comprehensive weights for FFR evaluation indicators. First, a hierarchical AHP model is developed to derive subjective weights based on expert judgment matrices. Next, the CRITIC method calculates objective weights by assessing each indicator’s comparative strength—quantified by standard deviation—and inter-indicator conflict—measured by correlation. This approach effectively mitigates biases associated with purely subjective methods. Finally, game-theoretic optimization combines subjective and objective weights to produce a final weight vector, balancing expert knowledge with data-driven evidence. This integration retains the advantages of both AHP and CRITIC, while improving the rationality and robustness of weight allocation. The approach provides a scientifically rigorous, flexible, and systematic strategy for weighting FFR indicators [45,46].

4.1. AHP Method

4.1.1. Construction of the Judgment Matrix

The judgment matrix was constructed based on the 1–9 scale, which facilitates the pairwise comparison of the relative importance of the evaluation criteria. The criteria for assigning values within this scale are detailed in

Table 2. Scale and interpretations.

Scales	Interpretations
1	Factor 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

. This study used the Delphi method to anonymously collect opinions from 20 experts from forestry, fire protection, and government agencies. After multiple rounds of feedback, consensus was reached to form the final judgment matrix $A={\left(a_{ij}\right)}_{n\times n}$.

4.1.2. Consistency Test

The Consistency Ratio (CR), calculated using Equation (1), was used to assess the consistency of the pairwise comparison results. The CR value greater than 0.1 indicates unacceptable inconsistency, and the corresponding judgment matrix was considered unreliable and excluded from the analysis. In this study, all judgment matrices satisfy the condition of CR < 0.1, thereby meeting the required standards for consistency and reliability.

$$CR={\displaystyle \frac{CI}{RI}}$$

(1)

where RI represents the Random Index, which is the average consistency index derived from numerous randomly generated reciprocal matrices. The value of RI depends on the matrix order and is provided in

Table 3. Ratio index scale.

n	1	2	3	4	5	6	7	8	9
RI	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45

. CI denotes the Consistency Index, quantifying the deviation from perfect consistency within the matrix, and is calculated using Equation (2).

$$CI={\displaystyle \frac{{\lambda }_{max}}{n-1}}$$

(2)

where ${\lambda }_{max}$ is the largest eigenvalue of judgment matrix, and n is the order of judgment matrix.

4.1.3. Weight Calculation

Based on judgment matrix, this study employs the “square root method” to determine the weights of the indicators, as expressed in Equation (3).

$${w_i}^{\prime }={\displaystyle \frac{\overline{w_i}}{{\displaystyle \sum _{i=1}^n\overline{w_i}}}}\hspace{1em}\hspace{1em}(i=1\hspace{0.33em},\hspace{0.33em}2\hspace{0.33em},\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},\hspace{0.33em}\hspace{0.33em}n)$$

(3)

where ${w^i}_{\prime }$ represents the weight derived through the AHP method, $\overline{w_i}={\left({\displaystyle \prod _{j=1}^n{a}_{ij}}\right)}^{{\displaystyle \frac{1}{n}}}$.

4.2. CRITIC Method

The CRITIC method is a representative objective weighting approach that captures both data dispersion and inter-factor conflict by using standard deviation and correlation coefficients. A higher standard deviation reflects greater variability in the data, leading to a higher weight, while a higher correlation indicates stronger conflict or redundancy between factors, resulting in a lower weight [47,48].

4.2.1. Indicator Standardization

To eliminate the influence of different units and scales among indicators, the original data $x_{uv}$ must be standardized. The standardized values are mapped into the range [0, 1], facilitating subsequent comparisons. According to the nature of the indicators, the standardization formulas are shown in Equations (4) and (5):

For positive indicators:

$$z_{uv}={\displaystyle \frac{x_{uv}-\text{min}\left(x_v\right)}{\text{max}\left(x_v\right)-\text{min}\left(x_v\right)}}$$

(4)

For negative indicators:

$$z_{uv}={\displaystyle \frac{\text{max}\left(x_v\right)-x_{uv}}{\text{max}\left(x_v\right)-\text{min}\left(x_v\right)}}$$

(5)

where $z_{uv}$ is the normalized value of indicator v $\left(v=\hspace{0.33em}\hspace{0.33em}1,\hspace{0.33em}\hspace{0.33em}2,\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},\hspace{0.33em}n\right)$ for evaluation object u $\left(u=\hspace{0.33em}\hspace{0.33em}1,\hspace{0.33em}\hspace{0.33em}2,\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},\hspace{0.33em}m\right)$$;$ m denotes the number of evaluation objects, and n denotes the number of evaluation indicators.

4.2.2. Weight Calculation

First, the standard deviation $S_v$ of each indicator v is calculated using Equation (6), which measures the degree of variability in the data.

$$S_v=\sqrt{{{\displaystyle \frac{{\displaystyle \sum _{u=1}^m\left(z_{uv}-\overline{z_v}\right)}}{m-1}}}^2}$$

(6)

where $\overline{z_v}$ represents the mean value of indicator v after standardization, $\overline{z_v}={\displaystyle \frac{1}{m}}{\displaystyle \sum _{u=1}^m{z}_{uv}}$.

Next, the correlation coefficient $r_{vw}$ is computed using Equation (7), representing the linear relationship between indicator v and indicators w.

$$r_{vw}={\displaystyle \frac{{\displaystyle \sum _{u=1}^m\left(z_{uv}-\overline{z_v}\right)\left(z_{uw}-\overline{z_w}\right)}}{\sqrt{{\displaystyle \sum _{u=1}^m{\left(z_{uv}-\overline{z_v}\right)}^2\times {\displaystyle \sum _{u=1}^m{\left(z_{uw}-\overline{z_w}\right)}^2}}}}}$$

(7)

The conflict between indicators is expressed by the correlation coefficient $r_{vw}$, where a lower correlation indicates greater conflict and higher indicator independence. The overall conflict degree $R_v$ for indicator v is computed using Equation (8).

$$R_v={\displaystyle \sum _{w=1,w\ne v}^n\left(1-r_{vw}\right)}$$

(8)

The information amount $C_v$, representing the contribution of indicator v to the evaluation system, is computed using Equation (9). A higher $C_v$ implies greater significance and thus a higher weight.

$$C_v=S_v\times R_v$$

(9)

Finally, the objective weight ${w_v}^{″}$ of each indicator is obtained by normalizing the information amount, as shown in Equation (10):

$${w_v}^{″}={\displaystyle \frac{C_v}{{\displaystyle \sum _{v=1}^n{C}_v}}}$$

(10)

4.3. Game-Theoretic Combination Weighting Method

Game theory offers a robust methodological framework for analyzing strategic interactions among decision-makers. By identifying optimal strategies in scenarios characterized by conflicting or convergent interests, it enables the rigorous integration of subjective weights derived from AHP and objective weights obtained through CRITIC, ultimately yielding a scientifically defensible determination of allocation coefficients [49,50].

4.3.1. Weight Integration Modeling

According to the previous sections, the subjective weight vector derived from the AHP method is denoted as $W_1=\left({w_1}^{\prime },\hspace{0.33em}{w_2}^{\prime },\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},{w_v}^{\prime }\right)$, while the objective weight vector obtained through the CRITIC method is denoted as $W_2=\left({w_1}^{″},\hspace{0.33em}{w_2}^{″},\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},{w_v}^{″}\right)$ To achieve a balanced evaluation, the comprehensive weight vector W is constructed by linearly combining these two vectors using game theory, as shown in Equation (11).

$$W={\alpha }_1{W_1}^T+{\alpha }_2{W_2}^T$$

(11)

where ${\alpha }_1$ and ${\alpha }_2$ are the linear combination coefficients corresponding to the subjective and objective weights, respectively. These coefficients are obtained as the initial optimal values from the game-theoretic coefficient optimization process (Section 4.3.2), which may take positive or negative values and are not normalized; they reflect the relative tendency to favor the subjective or objective weight vector. ${W_1}^T$ and ${W_2}^T$ represent the transposed forms of the subjective and objective weight vectors.

4.3.2. Coefficient Optimization

According to game theory, to obtain the optimal combined weight, the key is to minimize the deviation between the combined weight vector and each individual weight vector, as shown in Equation (12):

$${\text{min}}_{{\alpha }_1,{\alpha }_2}\left({‖W-{W_1}^T‖}^2+{‖W-{W_2}^T‖}^2\right)$$

(12)

By applying the properties of matrix differentiation and performing a first-order derivative, we arrive at the optimal linear system, as shown in Equation (13).

$$\left[\begin{array}{cc}{W}_1{W_1}^T& W_1{W_2}^T\\ W_2{W_1}^T& W_2{W_2}^T\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\end{array}\right]=\left[\begin{array}{c}{W}_1{W_1}^T\\ W_2{W_2}^T\end{array}\right]$$

(13)

4.3.3. Composite Weight Output

The linear combination coefficients are normalized according to Equation (14), producing the final coefficients ${\alpha }_1^{\ast }$ and ${\alpha }_2^{\ast }$, which sum to 1. Specifically, ${\alpha }_1^{\ast }$ denotes the relative contribution of the subjective weights derived from AHP, where a larger value indicates a stronger dominance of expert judgment in the composite weight; ${\alpha }_2^{\ast }$ denotes the relative contribution of the objective weights obtained from CRITIC, where a larger value signifies a greater influence of data-driven information.

$${\alpha }_k^{\ast }={\displaystyle \frac{\left|{\alpha }_k\right|}{\left|{\alpha }_1\right|+\left|{\alpha }_2\right|}}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(k=\hspace{0.33em}\hspace{0.33em}1,\hspace{0.33em}\hspace{0.33em}2\right)$$

(14)

The game-theoretic composite weight $W^{\ast }$ is then determined by Equation (15). The obtained combination weights will be applied in the subsequent resilience evaluation model to ensure a balance between subjective and objective information.

$$W^{\ast }={\alpha }_1^{\ast }{W_1}^T+{\alpha }_2^{\ast }{W_2}^T$$

(15)

4.4. Multi-Region Resilience Evaluation Method

For the evaluation of FFR across multiple regions, as shown in Equation (16):

$$R_d=C_d{W}^{\ast }\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left(d=\hspace{0.33em}\hspace{0.33em}1,\hspace{0.33em}\hspace{0.33em}2,\hspace{0.33em}\hspace{0.33em}\dots \hspace{0.33em}\hspace{0.33em},\hspace{0.33em}\hspace{0.33em}t\right)$$

(16)

where $R_d$ is the comprehensive FFR score of the region d, $C_d$ is a row vector of the indicator scores for that region (each indicator has a full score of 100 points), the scores are assigned by experts. t denotes the number of evaluation regions.

5. Results and Analysis

5.1. Weighting Results

To ensure the validity and reliability of the FFR assessment, we applied a hybrid weighting method that integrates the AHP method, the CRITIC method, and a game-theoretic combination approach. Indicator data were obtained through two distinct methods. Quantifiable indicators, such as vegetation cover, monthly mean temperature, and government investment in disaster risk reduction, were collected from remote sensing sources, meteorological records, and official statistics. Non-quantifiable indicators, such as individual fire safety competence and traditional cultural practices, were assessed using a 5-point scale by 20 experts from the fields of forestry, fire protection, and government agencies. The final scores for these non-quantifiable indicators were calculated from the average of the expert ratings. The final weights for all indicators were then determined according to Equations (1)–(15). The resulting indicator weights are presented in

Table 4. Weight values of evaluation indicators for FFR.

Level-1 Indicator (A)	Level-2 Indicators (B)	Level-3 Indicators (C)	AHP Subjective Weights	CRITIC Objective Weights	Game-Theoretic Combination Weights
FFR(A)	Vegetation Factor (B1)	C1	0.1351	0.0690	0.1067
		C2	0.0409	0.0223	0.0329
		C3	0.0744	0.0393	0.0593
	Topography Factor (B2)	C4	0.0256	0.0336	0.0290
		C5	0.0256	0.0331	0.0288
		C6	0.0128	0.0174	0.0148
	Climate Factor (B3)	C7	0.0751	0.0282	0.0549
		C8	0.0278	0.0102	0.0202
		C9	0.2045	0.0754	0.1490
		C10	0.0751	0.0276	0.0547
	Infrastructure Factor (B4)	C11	0.0649	0.1272	0.0917
		C12	0.0228	0.0561	0.0371
		C13	0.0228	0.0115	0.0179
		C14	0.0094	0.0044	0.0072
		C15	0.0397	0.1201	0.0743
	ManagementFactor (B5)	C16	0.0368	0.1123	0.0693
		C17	0.0137	0.0066	0.0106
		C18	0.0137	0.0073	0.0109
		C19	0.0232	0.0111	0.0180
		C20	0.0081	0.0037	0.0062
		C21	0.0052	0.0026	0.0041
	Social Factor (B6)	C22	0.0068	0.0698	0.0340
		C23	0.0041	0.0019	0.0032
		C24	0.0119	0.0053	0.0091
		C25	0.0200	0.1040	0.0561

.

The combined weights reflect both the intrinsic characteristics of the targets and expert judgments, thereby enhancing the evaluation’s applicability, precision, and robustness. Figure 4 compares subjective, objective, and combined weights.

5.2. Weights of Level-2 Indicators

Figure 5 presents the weights for level-2 indicators based on the game-theoretic combination: Vegetation Factors (B1) at 0.1989, Topography Factors (B2) at 0.0726, Climate Factors (B3) at 0.2788, Infrastructure Factors (B4) at 0.2282, Management Factors (B5) at 0.1191, and Social Factors (B6) at 0.1024.

Climate Factors hold the largest share at 27.88%, emphasizing their critical influence on fire ignition and spread within FFR. Infrastructure and Vegetation together contribute 42.71%, underscoring the importance of strong fire-prevention infrastructure and active vegetation management. Although Topography, Management, and Social Factors carry lower weights, their effects remain significant and should be considered contextually.

5.3. Weights of Level-3 Indicators

Table 2 and Figure 6 detail the weights of level-3 indicators. Nine indicators stand out as most influential, collectively representing 71.6% of the total weight. These include monthly minimum relative humidity (C9, 0.149), fine fuel load per unit area (C1, 0.1067), smart monitoring systems (C11, 0.0917), water-supply support facilities (C15, 0.0743), routine fire-prevention inspections (C16, 0.0693), vegetation cover (C3, 0.0593), fire use in livelihood and production (C25, 0.0561), monthly mean temperature (C7, 0.0549), and monthly mean precipitation (C10, 0.0547).

Monthly minimum relative humidity (C9) emerges as the principal risk factor, highlighting the critical role of extreme dryness. Climate-related indicators C9, C7, and C10 together account for 0.2586, reinforcing the foundational impact of climate. The smart monitoring system (C11) ranks among top infrastructure indicators, reflecting the increasing role of digital technologies in fire management. Notably, fire use in livelihood and production activities (C25) carries greater weight than natural terrain factors such as slope (C4) and slope aspect (C5), stressing the need to manage human behavior to enhance resilience.

5.4. Analysis of Resilience Capacities

Figure 7 shows the distribution of weights among the four resilience capacities. Absorption capacity dominates at 61.31%, followed by resistance at 18.75%, recovery at 12.92%, and adaptation at 7.02%.

Absorption capacity emerges as the core driver of FFR. It reflects the system’s ability to lower ignition risk through hazard elimination, risk reduction, and the enhancement of monitoring and early warning mechanisms. As the first line of defense, absorption capacity provides the foundation for the overall resilience framework. Resistance and recovery together contribute more than 30% of the total weight, underscoring the importance of limiting fire spread once ignition occurs and ensuring rapid post-fire restoration. Although adaptation accounts for the smallest share, it plays an indispensable role in post-disaster structural adjustments, management improvements, and long-term preparedness. Continuous reinforcement of adaptation capacity is therefore essential to maintaining sustained resilience.

The results further demonstrate that the predominance of absorption capacity reflects the decisive role of early climatic and fuel conditions in determining both the ignition and spread of forest fires. This finding highlights the importance of pre-ignition risk precursors in shaping FFR. Under such circumstances, resilience and risk must be evaluated jointly within an integrated assessment framework. In designing this framework, we emphasized the dominant stage of influence, which led to the classification of indicators such as precipitation and fine fuel load under absorption, even though they also affect resistance processes. We acknowledge that this classification represents a simplification of complex realities. Future studies should explore weighted or dynamic classification methods to more accurately capture cross-phase effects and to distinguish between the differing mechanisms of natural and human-induced ignition events.

6. Strategies for Enhancing FFR

6.1. Strengthen Climate Monitoring

Climate factors represent the most influential level-2 indicators, with a combined weight of 0.2788. Among them, monthly minimum relative humidity (C9) is particularly critical, holding a weight of 0.1490. Although direct control over climate is impossible, adaptive management based on real-time climate data is vital. Establishing comprehensive meteorological monitoring networks that continuously track temperature, relative humidity, wind speed, and precipitation can provide actionable insights for local governments and forest managers. For instance, fire-risk models updated with real-time climate data can guide dynamic allocation of firefighting resources, inform temporary access restrictions in high-risk areas, and adjust prescribed burn schedules. Policymakers can integrate these data streams into early warning protocols, enabling preemptive measures such as targeted evacuations or temporary closure of vulnerable forest areas. By translating climate data into operational decisions, authorities can proactively reduce fire hazards and enhance FFR.

6.2. Improve Forest Fuel Management and Absorption Capabilities

Fine fuel load per unit area (C1) is the highest weighted level-3 indicator (0.1067), and absorption capacity dominates resilience dimensions (0.613). Therefore, effective fuel management is central to strengthening FFR. Decision-makers can implement strategic fuel-reduction measures—including controlled burning, mechanical thinning, and selective harvesting—to reduce fire intensity and limit spread. Establishing fuel breaks and firebreaks (C13) along critical corridors allows compartmentalization of forests, limiting large-scale fire propagation. Policy implications include prioritizing high-risk zones for fuel reduction and incentivizing forest owners to adopt fire-resistant vegetation. Moreover, promoting fire-resistant species and optimizing vegetation cover (C3) balances ecosystem health with risk mitigation. Regular assessment of combustible vegetation can be operationalized through forest management plans and performance monitoring frameworks, providing clear targets for both local authorities and forest managers to enhance the forest’s absorptive resilience.

6.3. Enhance Forest Fire Monitoring and Early Warning Systems

Infrastructure factors are highly influential, with intelligent monitoring systems (C11) among the top level-3 indicators (weight 0.0917). Deploying modern technology-based monitoring networks is essential for early detection and rapid response. Installing comprehensive intelligent monitoring systems—integrating infrared thermal cameras, smoke detectors, and weather stations—combined with satellite remote sensing, allows real-time surveillance of vegetation status, weather changes, and potential ignition sources. Decision-makers can operationalize these insights by triggering automated alerts, guiding the deployment of firefighting teams, and activating contingency protocols. For emergency planners, such systems provide data-driven evidence to optimize resource allocation, plan evacuation routes, and prioritize fire suppression in high-risk areas, directly translating technical monitoring into actionable emergency responses.

6.4. Enhance Emergency Response and Recovery Capabilities

Management factors carry a weight of 0.1191 and are critical for effective fire control. Key level-3 indicators include fire suppression equipment (C12), firefighting force development (C20), and emergency plan optimization (C21). Enhancing professional firefighting capacity requires regular training, modern equipment, and inter-agency coordination drills, with strategic placement of suppression and rescue resources to minimize response times. Policymakers can leverage the proposed FFR framework to identify gaps in emergency infrastructure, prioritize investment in high-risk regions, and develop multi-stakeholder recovery plans. Post-fire recovery should implement rapid ecosystem restoration, soil erosion control, and community support initiatives. Embedding FFR assessment into emergency planning allows local governments to evaluate the effectiveness of interventions, refine fire suppression strategies, and engage communities in risk-reduction programs. Additionally, integrating simulation-based exercises and public education campaigns ensures continuous learning and adaptive management, reinforcing the forest’s resilience to future disturbances.

7. Case Study

7.1. Study Area

Baise City, situated in the western Guangxi Zhuang Autonomous Region of China (22°51′–25°07′ N, 104°28′–107°54′ E), spans approximately 320 km east–west and 230 km north–south. Baise, with an area of 36,252 km², has an approximate population of 3.465 million. The terrain is predominantly mountainous and hilly, with elevations ranging from 98 m to 2062 m. This creates a diverse landscape featuring karst peaks, river valley basins, and plateau highlands. Administratively, Baise City is divided into twelve divisions: Youjiang District, Tianyang District, Tiandong County, Pingguo City, Debao County, Jingxi City, Napo County, Lingyun County, Leyu County, Tianlin County, Longlin Autonomous County, and Xilin County (Figure 8).

Forests constitute a significant portion of Baise City’s land cover, extending over 2.7467 million hectares and accounting for 75.4% of its total area. The dominant forest types include South Asian tropical evergreen broadleaf forests, pine forests, Cunninghamia lanceolata forests, and karst mountainous shrub forests. Notably, pine forests comprise approximately 30% of the forested area. Chinese red pine stands are particularly susceptible to fire due to the high resin content in their needles and the accumulation of dry litter on the forest floor, posing a significant fire risk. Karst shrub forests are also vulnerable due to low precipitation during the dry season. This study evaluated the FFR of all twelve administrative divisions within Baise City.

We applied the game-theoretically integrated weights for the 25 evaluation indicators (Table 4). Each indicator was then quantified using a detailed five-tier classification system. This system provides a graduated scale, where a grade of one signifies that the assessed object is in a very bad state, indicating critical deficiencies or vulnerabilities. A grade of two represents a bad state, suggesting significant issues that require attention. A grade of three indicates a moderate state, implying that the object is functioning adequately but with room for improvement. A grade of four signifies a good state, reflecting positive conditions and effective management. Finally, a grade of five represents a very good state, indicating optimal performance and resilience. Comprehensive FFR scores for each division were subsequently calculated by inputting standardized scores and weights into Equation (16).

7.2. Regional Result Analysis

Figure 9 presents the comprehensive FFR scores for Baise’s twelve divisions. Pingguo County ranks highest at 65.765, followed by Youjiang District (62.926), Jingxi County (62.405), Tiandong County (58.908), Tianyang District (58.097), Debao County (57.849), Lingyun County (56.888), Napo County (56.656), Xilin County (56.449), Leye County (53.910), Tianlin County (52.687), and Longlin Autonomous County (49.932).

7.2.1. Sensitivity and Robustness Analysis

To further examine the robustness of the proposed framework, we performed additional sensitivity analyses, including weight perturbation and indicator selection sensitivity tests. The test results are presented in

Table 5. Leave-one-domain-out sensitivity results.

Omitted Domain	Spearman ρ	Kendall τ	Δrank
B1	0.867	0.758	4
B2	0.993	0.97	1
B3	0.993	0.97	1
B4	0.986	0.939	1
B5	0.993	0.97	1
B6	0.986	0.939	1

.

(1)

Weight Perturbation Tests

We applied one-at-a-time perturbations of ±10% to each third-level indicator weight, followed by re-normalization of the weight vector and recomputation of regional FFR scores and rankings. Results: the rankings were invariant to all perturbations: the maximum rank change for every indicator was Δrank = 0, the rank correlations with the baseline were Spearman’s ρ = 1.000 and Kendall’s τ = 1.000, and the Top-3 set was 100% identical to the baseline. Given this complete invariance, we omit the tornado chart and report these statistics as direct evidence of robustness.

(2)

Indicator Selection Sensitivity

We implemented a leave-one-domain-out test by setting to zero all indicators within one domain at a time and re-normalizing the remaining weights. The results show that rankings are generally stable across domains. Omitting Domain B1 had the largest effect (ρ = 0.867, τ = 0.758, max Δrank = 4), while omitting the other domains yielded near-baseline rankings (ρ ≥ 0.986, τ ≥ 0.939, max Δrank ≤ 1), with the Top-ranked regions preserved.

Taken together, the analyses confirm that the proposed framework is robust to moderate weight changes and largely insensitive to the exclusion of any single indicator domain (except for a moderate effect when B1 is omitted). These findings enhance confidence in the reliability and practical applicability of the assessment for policy and management.

7.2.2. Regional Resilience Analysis

The assessment of FFR revealed a spatial heterogeneity across Baise City, with distinct performance tiers observed among its constituent regions. Pingguo, Youjiang, and Jingxi demonstrated the highest resilience (scores > 62), attributable to a combination of economic, infrastructural, and management advantages. Specifically, Pingguo’s robust economic base facilitates substantial investment in fire-prevention infrastructure and proactive fire management strategies. The implementation of a grid-based fire source control system within the interface between agricultural land and forests further mitigates anthropogenic fire risks, thereby establishing a strong foundation for resilience. Youjiang, as the administrative center, benefits from advanced fire-fighting technology and a coordinated multi-agency emergency response framework. This system effectively compensates for the topographic challenges posed by the mountainous terrain prevalent in western Guangxi. Moreover, the relatively flat terrain of the Youjiang River basin aids in efficient fire detection and suppression operations. Despite its location in a karst region, Jingxi exhibits high resilience through strategic groundwater resource management, the construction of firebreaks, and collaborative cross-border fire-prevention initiatives, particularly crucial during dry seasons.

In contrast, Tiandong, Tianyang, Debao, Lingyun, Napo, and Xilin exhibited moderate levels of FFR. These regions possess inherent natural advantages that are, however, counterbalanced by infrastructural and managerial limitations. For instance, Tiandong and Tianyang, situated within the Youjiang River valley, benefit from the fragmented agricultural landscape of the alluvial plains, which reduces the potential for large-scale fire propagation. However, challenges in controlling agricultural fires, coupled with outdated fire-fighting equipment and a lack of advanced monitoring capabilities, impede the translation of these natural advantages into enhanced resilience. Debao and Lingyun experience slower fire spread rates due to their higher altitudes and relatively humid climates. Nevertheless, the complex karst topography, characterized by peak clusters and canyons, complicates fire suppression efforts. Furthermore, Debao’s extensive border necessitates a broad and diffuse fire source monitoring effort, straining available forest ranger resources and limiting overall resilience. Although Napo benefits from substantial monsoon rainfall and elevated humidity that reduce the flammability of surface fuels, insufficient coverage of fire-monitoring systems and the widespread shortage and aging of suppression equipment in mountain villages constrain preparedness and response, resulting in low FFR. Xilin’s resilience is compromised by the complex terrain of its mountainous regions, which complicates forest-fire suppression. Additionally, inadequate forest road density impedes the timely deployment of fire-fighting resources. These areas require targeted investments in modernizing fire-fighting equipment and enhancing fire-prevention capabilities in remote communities.

Leye, Tianlin, and Longlin exhibited the lowest FFR scores, with Longlin displaying particularly pronounced vulnerability. Leye faces unique challenges due to the enclosed topography of its karst sinkhole clusters, which severely restricts fire suppression operations. The high accumulation of litter (20 t/hm²) in its subtropical evergreen broad-leaved forests, combined with limited fire-fighting equipment coverage, exacerbates fire risk. In Tianlin, located in a mountainous area bordering multiple provinces, the fuel load in mixed monsoon evergreen broad-leaved and coniferous forests exceeds critical thresholds (30 t/hm²), and a substantial portion (40%) of the forest area lacks fire-fighting infrastructure, relying primarily on manual tools. This confluence of high ecological vulnerability and inadequate resources creates a negative feedback loop. Longlin, situated in a transition zone between dry-hot valleys and plateaus, experiences prolonged periods of high fire risk throughout the year. This is compounded by significant underinvestment in fire-prevention infrastructure due to economic constraints, and comparatively weak management practices. These regions exemplify low resilience due to the synergistic effects of adverse natural conditions and insufficient investment in fire management.

In conclusion, the spatial variation in FFR across Baise City is determined by the interplay of natural environmental factors and anthropogenic interventions. High-resilience areas effectively mitigate environmental limitations through strategic investments. Medium-resilience areas are constrained by a combination of inherent natural advantages and infrastructural deficits. Low-resilience areas exhibit pronounced vulnerability due to the convergence of unfavorable natural conditions and inadequate fire suppression capabilities. By integrating the FFR framework into regional planning, policymakers and forest managers can translate technical assessment into actionable strategies, including the adoption of proven practices from high-resilience areas, modernization of equipment in medium-resilience zones, and infrastructure and ecological interventions in low-resilience regions. This tiered, evidence-based approach provides a systematic pathway for enhancing Baise City’s overall FFR.

7.2.3. Evaluation Method Comparison

To evaluate the effectiveness and advantages of the proposed method, we conducted a comparison with the widely adopted Fuzzy AHP method [51]. The comparison revealed notable differences in weight distribution and overall resilience assessments between the two methods.

Table 6. Comparison of evaluation methods: FFR scores and ranking changes.

Region	Ping guo	You jiang	Jing xi	Tian dong	Tian yang	De bao	Ling yun	Napo	Xilin	Leye	Tian lin	Long lin
Proposed Method	65.765	62.926	62.405	58.908	58.097	57.849	56.888	56.656	56.449	53.910	52.687	49.932
Fuzzy AHP Method	63.254	62.182	62.056	59.325	58.978	57.035	57.529	56.814	56.241	52.312	52.712	50.259
Ranking Change	0	0	0	0	0	−1	1	0	0	0	0	0

presents a side-by-side comparison of the resilience scores and ranking changes across the 12 regions evaluated using both methods.

The ranking shifts observed in Debao and Lingyun, along with the variations in resilience scores across several regions, underscore the differences in how the two methods allocate weights and conduct comprehensive assessments. The Fuzzy AHP method primarily relies on subjective expert judgments, which may fail to account for the objective data inherent in the indicators, potentially leading to biases in the ranking. In contrast, our method integrates both expert judgment and objective data, utilizing the CRITIC method to assign weights. This combined approach ensures a more balanced and accurate assessment of regional resilience by reducing the influence of subjective biases, thereby producing more stable and reliable results.

Although some individual regions experienced slight fluctuations in their rankings, the overall ranking order remained unchanged, and the resilience classification (high, medium, low) across regions was consistent. This indicates that, while enhancing evaluation accuracy, the proposed method maintains the stability of the results. The method effectively balances expert judgment with objective, data-driven evidence, ensuring robust and consistent resilience assessments.

8. Conclusions

This study developed a comprehensive framework to assess FFR. A multi-level indicator system was constructed, and a game-theoretic combination weighting method was applied. Key influencing factors were identified, and targeted strategies proposed. The main conclusions are as follows:

(1)

Theoretical foundations of FFR were established by examining four resilience capacities: absorption, resistance, recovery, and adaptation. A triggering mechanism model was developed to illustrate dynamic interactions among internal and external factors influencing resilience outcomes.

(2)

A three-tier evaluation index system was designed, comprising 25 level-3 indicators across six dimensions: vegetation, topography, climate, infrastructure, management, and social factors. These indicators were further classified by the four resilience capacities, creating a dual framework for structural and functional assessment of FFR.

(3)

Using a game-theoretic integration of AHP and CRITIC methods, comprehensive weights were derived. Climate, infrastructure, and vegetation emerged as the most influential level-2 indicators. Among level-3 indicators, monthly minimum relative humidity, fine fuel load per unit area, and smart monitoring systems were identified as critical. Absorption capacity dominated among the resilience functions, highlighting the vital role of proactive risk mitigation.

(4)

A case study in Baise City revealed spatial variation in FFR across twelve administrative divisions. Resilience outcomes depended on the interplay between natural conditions and human interventions. Furthermore, sensitivity and robustness analysis demonstrated the framework’s reliability and practical robustness. The comparison of evaluation methods further demonstrated the superior performance of the proposed approach, highlighting its ability to provide a balanced and accurate assessment of FFR.

This work delivers a robust spatial assessment framework but does not yet incorporate temporal dynamics (seasonal, interannual, long-term). In future iterations, we will integrate downscaled Coupled Model Intercomparison Project Phase 6 projections with historical observations via long short-term memory and Transformer models for time-series forecasts; dynamically update fuels and exposure using remote-sensing–based ML with scenario-based cellular automata and agent-based models; and incorporate interannual variability through climate indices such as the El Niño—Southern Oscillation. Moreover, current mainstream models often systematically underestimate future risks, particularly in projecting atmospheric moisture reduction trends. This suggests that the actual risk and severity of forest fires may be higher than the results presented in this study, making our findings somewhat conservative.