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19 December 2025

24 Pages

Assessing Urban Flood Resilience with Unascertained Measurement Theory: A Case Study of Jiangxi Province, China

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1
Jiangxi Provincial Key Laboratory of Safe and Efficient Mining of Rare Metal Resources, Jiangxi University of Science and Technology, Ganzhou 341000, China
2
School of Safety Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
3
Yichun Lithium New Energy Industry Research Institute, Jiangxi University of Science and Technology, Yichun 336000, China
*
Author to whom correspondence should be addressed.
Sustainability2026, 18(1), 49;https://doi.org/10.3390/su18010049
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Abstract

With the acceleration of global climate change and urbanization, urban flooding disasters have become increasingly frequent, posing significant threats to urban safety and sustainable development. Enhancing Urban Flood Resilience (UFR) has become a central issue in urban risk management and spatial planning. This study aims to scientifically assess UFR by employing the core concepts of resistance, recovery, and adaptation from urban resilience theory. A set of 20 indicators for assessing UFR is selected from four aspects: infrastructure, social economy, technological monitoring, and the ecological environment. Addressing the limitations of traditional evaluation methods, which struggle to effectively handle data gaps and ambiguous boundaries, and fail to balance subjective and objective weights, this study introduces the unascertained measure theory and adopts a combined weighting method to construct a UFR evaluation model. Using 2023 statistical data from Jiangxi Province, a comprehensive evaluation of flood resilience was conducted across 11 prefecture-level cities within the province. The analysis indicates that, among level-2 indicators, infrastructure holds the highest weight at 43.7%. Regarding resilience dimensions, resistance dominates with a weight of 54.6%. Furthermore, significant spatial disparities exist in flood resilience levels across Jiangxi Province: high resilience cities are distributed in central and northern Jiangxi, moderately high resilience cities account for the largest proportion. Only one city, Pingxiang, exhibits moderate resilience.

1. Introduction

In today’s world, the interplay between urbanization and climate change effects is profoundly reshaping the global urban risk landscape. Among these, flooding—one of the most frequent, widespread, and costly natural disasters—has become a critical challenge that cannot be ignored in the sustainable development of numerous cities [1]. According to the Global Disaster Data Platform, the period from 2020 to 2024 witnessed the highest frequency of flood disasters, resulting in 32,259 deaths, affecting over 200 million people, and causing direct economic losses of USD 224.2 billion [2]. Traditional disaster management approaches, emphasizing engineering defenses and post-disaster emergency responses, have demonstrated significant effectiveness. However, their limitations are increasingly evident in the face of increasingly extreme weather events and complex, vulnerable urban systems [3]. A single rainfall event exceeding “design standards” can trigger chain reactions, paralyzing urban operational systems. For instance, on 20 July 2021, the Zhengzhou torrential rain event resulted in flooding that affected 14.786 million people across 150 counties in Henan Province, with 398 fatalities and missing persons, and direct economic losses reaching USD 16.8 billion [4].
Against this backdrop, the concept of “urban resilience” emerged, first proposed by the International Council for Local Environmental Initiatives (ICLEI) in 2002. It quickly became a core issue in global urban disaster prevention, mitigation, and sustainable development [5,6]. In 2013, the Rockefeller Foundation launched the 100 Resilient Cities initiative, aiming to help cities better address 21st-century challenges such as climate change, economic shocks, and social unrest, thereby enhancing their adaptability and recovery capacity in the face of diverse risks [7]. Current urban resilience research primarily focuses on addressing the challenges posed by global climate change and natural disasters, specifically centering on urban disaster resilience.
Flooding, as one of the primary disasters confronting cities, has become a critical risk constraining urban sustainable development. To enhance UFR, numerous scholars have conducted extensive research. Zhao [8] constructed a driving force-state-response (DSR) evaluation framework, structuring external pressures, urban system states, and response behaviors into three tiers to assess flood resilience in China’s three northeastern provinces. Ren et al. [9] employed a pressure-state-response (PSR) framework to assess flood resilience in central cities along the Yellow River basin. Similarly to DSR, the PSR framework emphasizes the causal chain between environmental pressures and system responses. Regarding indicator system development, Gu et al. [10] selected 15 indicators across five dimensions—ecological, economic, infrastructure, institutional, and social—to analyze the spatiotemporal evolution and drivers of flood resilience in Yangtze River Delta cities within East China. Cutter et al. [11] established the Disaster Resilience of Place (DROP) framework based on three dimensions—material-environmental, socio-economic, and perceptual-emotional—to systematically evaluate multidimensional characteristics of disaster resilience. Gao et al. [12] developed an UFR evaluation index system across four levels—basic resistance, disaster prevention and early warning, emergency response, and adaptive recovery—to assess resilience levels in six administrative districts of Nanjing. Regarding indicator weight determination and evaluation method selection, most scholars employ methods such as the Analytic Hierarchy Process (AHP) [13], Entropy Weight Method (EWM) [10,14,15], and CRITIC [16]. These methods calculate indicator weights through single or combined weighting approaches, followed by research utilizing techniques like the TOPSIS method [17], Fuzzy Comprehensive Evaluation (FCE) [18], and Cloud Model [13].
The aforementioned studies have laid a foundation for UFR assessment, but critical gaps remain. UFR assessment involves multiple indicators and hierarchical levels, with complex non-linear coupling relationships among evaluation factors, thereby increasing the ambiguity and uncertainty inherent in the assessment process. Existing methods either focus on one type of uncertainty or oversimplify the complexity of resilience systems, resulting in inaccurate or biased evaluation results. Table 1 summarizes the limitations of prior methods and the targeted improvements offered by this study’s approach.
Table 1. The limitations of common methods and the targeted improvements.
Therefore, this paper proposes a UFR assessment model based on Unascertained Measurement Theory, employing Interval Analytic Hierarchy Process (IAHP) and CRITIC for combined weighting. This approach rigorously handles uncertainty while quantifying the optimal balance between subjective expert knowledge and objective data variability/conflict. Unlike existing methods, it avoids arbitrary weight combinations and provides a transparent mechanism for coordinating qualitative and quantitative inputs. The Unascertained Measure Theory serves as a mathematical tool for handling uncertain information, applicable to multi-criteria, multi-level, and fuzzy complex comprehensive evaluation systems. It has been extensively applied in engineering fields such as tunnel [19], hydropower [20], and transportation [21] projects. By integrating the Resilience-Recovery-Adaptation framework with Unascertained Measure Theory, this study deepens the theoretical understanding of UFR while delivering more scientific and accurate assessments of UFR levels. This provides valuable reference for urban resilience development. The detailed research flowchart is shown in Figure 1.
Figure 1. Research flowchart for evaluating UFR.

2. Theoretical Framework

2.1. Definition of UFR

Defining UFR clearly is a prerequisite for its scientific evaluation. The etymology of resilience traces back to the Latin “resilio,” originally meaning “to bounce back to the original state” or “to return to the original form” [22]. The resilience concept was first introduced into systems ecology, subsequently evolving through phases such as engineering resilience, ecological resilience, and socio-ecological system resilience [23,24,25,26]. In 1973, Canadian ecologist Holling [27] systematically distinguished stability from resilience, introducing the concepts of “attractors” and “multistability.” He emphasized that under real-world conditions of frequent natural and human disturbances, ecosystem management should shift from pursuing equilibrium to enhancing resilience to ensure long-term ecological sustainability. This laid the intellectual foundation for the subsequent development of urban resilience theory.
Building upon Holling’s framework and the related literature [28,29,30,31], this paper defines Urban Flood Resilience (UFR) as the capacity of an urban system, when subjected to flood disasters as a disaster-bearing entity, to maintain stable operation of its core functions and effectively withstand disaster impacts. Even if some subsystems are damaged, the system can rapidly resume functioning while continuously optimizing and adjusting its internal structure during recovery, thereby enhancing its future capacity to cope with flood disasters.

2.2. Impact Dimensions of UFR

Based on urban resilience theory, this paper identifies Resistance, Recovery, and Adaptation as the three dimensions influencing UFR. Resistance refers to the capacity of urban systems to absorb or mitigate the negative impacts of flood disasters, ensuring core functions remain intact. Recovery denotes the ability of cities to swiftly restore damaged functions to desired states or near-original levels following flood events. Adaptation signifies a city’s enhancement of resilience against future flood impacts through learning, structural adjustments, or innovation.

2.3. Theoretical Contribution

This paper introduces the theory of unascertained measures as a new paradigm for addressing uncertainty in UFR assessment, distinct from existing fuzzy and probabilistic approaches. By defining resilience as an uncertain system property, its uncertainty stems from incomplete information, fuzzy boundaries, and subjective judgments rather than randomness. We expand the theoretical toolkit for quantifying resilience, addressing gaps in existing research, and provide a rigorous mathematical framework for systems exhibiting complex fuzzy relationships between assessment metrics and resilience outcomes.

2.4. Research Design

This study adopts a mixed-methods research design integrating theoretical construction, indicator system development, model establishment, and empirical validation to systematically assess UFR. The design follows a “theoretical foundation → indicator selection → weight determination → evaluation modeling → case application” logical sequence, ensuring scientific rigor, operability, and practical relevance. The core objectives of the research design are: (1) to clarify the connotation and dimensional structure of UFR based on resilience theory; (2) to construct a multi-dimensional, multi-level UFR evaluation indicator system aligned with regional characteristics; (3) to develop a comprehensive evaluation model that addresses uncertainty in the assessment process; and (4) to validate the model through a case study of Jiangxi Province and reveal spatial patterns of UFR.

3. Evaluation Indicator System Construction for UFR

3.1. Evaluation Indicators Selection

The selection of indicator system in this paper follows the principles of scientificity, availability, measurability and acceptability put forward by cutter [11]. On the basis of existing research, according to the Sustainable Cities and Communities—Indicators for Resilient Cities [32], Guide for Safety Resilient City Evaluation [33] and other specifications, and in combination with the characteristics of urban flood disasters and references, the UFR evaluation indicator system is constructed from four aspects of infrastructure, social economy, technical monitoring, ecological environment and three dimensions of resistance, recovery, and adaptation, including four secondary indicators and 20 tertiary indicators. Among these, five indicators—proportion of built-up area, permanent resident density, proportion of aging population, response time of early warning system, and daily domestic water consumption per capita—are negative indicators, while the remaining indicators are positive. The UFR indicator system is illustrated in Table 2 and Figure 2.
Table 2. Indicator system for UFR.
Figure 2. Dual classification framework of UFR indicators.
By consulting the Technical Specifications for Meteorological Disaster Risk Investigation [41], the Technical Specifications for Urban Flooding Risk Investigation [42] and other data, referring to the classification principles of relevant literature [15,34,38], combining with the characteristics of UFR in Jiangxi Province, this paper uses the natural breakpoint method to divide the UFR into five levels; namely, level I, level II, level III, level IV, and level V, corresponding to low resilience, moderately low resilience, moderate resilience, moderately high resilience, and high resilience, as shown in Table 3.
Table 3. Classification standard of indicators.

3.2. Explanation of Evaluation Indicators

Drainage pipe density (C1): Total length of drainage pipes per unit area in urban built-up areas. It directly reflects rainwater collection and discharge capacity, serving as a key indicator for flood control.
Number of hospital beds per 10,000 people (C2): Denotes the number of hospital beds available per 10,000 permanent residents. This directly reflects the healthcare system’s capacity to admit and treat casualties and respond to public health emergencies following flood disasters.
Length of flood control embankment (C3): Refers to the total length of levees constructed to defend against river or tidal flooding, directly reflecting a city’s capacity to resist external flood intrusion.
Number of emergency shelters (C4): Refers to the quantity of designated safe locations available for housing affected residents during disasters, indicating a city’s emergency relocation capacity during crises.
Proportion of built-up area (C5): Ratio of a city’s developed construction area to its total land area. A higher proportion means more impervious surfaces, weaker natural infiltration capacity, and greater flood risk.
Road area per capita (C6): The ratio of total urban road area to the resident population. A larger area indicates greater redundancy in the transportation network during disasters, facilitating evacuation and rescue operations.
Proportion of the tertiary industry (C7): The proportion of tertiary industry output in the regional gross domestic product, reflecting the city’s economic structure.
GDP per capita (C8): Measures a region’s economic development level and average resident prosperity.
Permanent resident density (C9): Refers to the number of permanent residents per unit of land area. Higher density means more people exposed to risks during disasters and greater evacuation challenges.
Gross Regional Product (C10): Measures a region’s total economic output and scale. Higher economic levels imply stronger government fiscal capacity for disaster prevention, mitigation, and post-disaster reconstruction.
Proportion of aging population (C11): The percentage of residents aged 60 and above relative to the total population. A higher proportion indicates greater societal vulnerability and significantly increases rescue challenges.
Coverage rate of meteorological and hydro-logical stations (12): The proportion of total urban area covered by various monitoring stations, measuring the spatial completeness of the disaster monitoring network.
Broadcast coverage rate (C13): The proportion of total area where radio programs can be received via wireless signals, forming the foundation for ensuring information accessibility during disasters.
Mobile phone user coverage (C14): The proportion of the total population with access to mobile phone services, impacting the scope of emergency communications during disasters.
Response time of early warning system (C15): Duration from early warning generation to issuance. Faster response provides more time for implementing emergency measures such as floodgate closure and evacuation.
Per capita park green space area (C16): The average park green space area available per permanent resident in the city.
Greening coverage (C17): The ratio of the vertical projected area of all types of green spaces to the built-up area. Green spaces effectively intercept rainwater and enhance infiltration, serving as natural “sponges” to alleviate urban flooding.
Daily domestic water consumption per capita (C18): The average daily water usage per person for daily living, serving as an indirect indicator of urban water usage characteristics and drainage pressure.
Comprehensive utilization rate of industrial solid waste (C19): The percentage of industrial solid waste that is comprehensively utilized relative to the total amount generated, reflecting the city’s level of resource recycling.
Rate of sewage disposal (C20): The proportion of treated sewage meeting standards relative to the total volume of sewage discharged. A higher treatment rate reduces secondary pollution and health risks caused by sewage overflow during disasters.

4. Construction of UFR Assessment Model Based on Unascertained Measurement Theory

This paper employs the IAHP method and CRITIC method to determine the subjective and objective weights of evaluation indicators, and introduces the unascertained measurement theory to assess the UFR. There are m cities under evaluation, forming the evaluation object space ( M = M 1 ,   M 2 ,   ⋯ ,   M m ). Each city corresponds to n evaluation indicators, with the indicator value defined as u i j . Assuming the evaluation objects are divided into t evaluation levels, this constitutes the evaluation level space, where k represents the kth level indicating UFR. Level k + 1 is defined as higher than level k. This paper categorizes UFR into five levels: low resilience (Level I), moderately low resilience (Level II), moderate resilience (Level III), moderately high resilience (Level IV), and high resilience (Level V), corresponding to D1, D2, D3, D4, and D5 respectively.

4.1. Single Indicator Unascertained Measurement

Suppose μ i j k = μ u i j ∈ D k denotes the degree to which value u i j belongs to evaluation grade Dk, satisfying the following conditions:
0 ≤ μ u i j ∈ D k ≤ 1
μ u i j ∈ E = 1
μ ( u i j ∈ ∪ k = 1 t D k ) = ∑ k = 1 t μ ( μ i j ∈ D k )
Then μ is referred to as the single indicator unascertained measurement, and the measurement matrix for the city under evaluation is expressed as:
μ i j k n × t = μ i 11 μ i 12 ⋯ μ i 1 t μ i 21 μ i 22 ⋯ μ i 2 t ⋮ ⋮ ⋮ ⋮ μ i n 1 μ i n 2 ⋯ μ i n t

4.2. IAHP-CRITIC Combination Weighting

To avoid absolute subjectivity or objectivity in the weighting process, this paper employs the Interval Analytic Hierarchy Process (IAHP) and the CRITIC method to calculate the subjective and objective weights of evaluation indicators, respectively. A distance function is then introduced to combine these two sets of weights, yielding the comprehensive weighting for the evaluation indicators.

4.2.1. IAHP Method

The IAHP method is an extension and improvement of the Analytic Hierarchy Process (AHP), serving as a subjective weighting approach. It employs interval numbers instead of exact values to compare the relative importance between pairwise factors, better aligning with the uncertainty inherent in real-world decision-making. This approach also reduces consistency requirements [20] and enhances fault tolerance. Its computational steps are as follows:
1. Construct the judgment matrix. Employ Saaty’s [43,44] 1–9 scale method to quantify the relative importance among n evaluations using interval numbers x i j = x i j − ,   x i j + . This forms the interval-based judgment matrix:
X = ( x i j − ,   x i j + ) n × n = 1 ,   1 x 12 − ,   x 12 + ⋯ x 1 n − ,   x 1 n + x 21 − ,   x 21 + 1 ,   1 ⋯ x 2 n − ,   x 2 n + ⋮ ⋮ ⋱ ⋮ x n 1 − ,   x n 1 + x n 2 − ,   x n 2 + ⋯ 1 ,   1
In the formula: 1 / 9 ≤ ( x i j − ) n × n ≤ ( x i j + ) n × n ≤ 9 , x i j − ,   x i j + = 1 / x i j + ,   1 / x i j − , x i j − ,   x i j + denotes the relative importance between indicators obtained using the binary comparison method, i ,   j = 1 ,   2 ,   ⋯ ,   n .
2. Calculation of normalized eigenvectors. Decompose the judgment matrix X into a positive judgment matrix X + ( X + = x i j + n × n ) and a negative judgment matrix X − ( X − = x i j − n × n ) , then compute the normalized eigenvectors for each judgment matrix:
w + = ∏ j = 1 n x i j + n ∑ i = 1 n ∏ j = 1 n x i j + n
w − = ∏ j = 1 n x i j − n ∑ i = 1 n ∏ j = 1 n x i j − n
3. Consistency check for judgment matrix. When k ≤ 1 and p ≥ 1 , the judgment matrix X passes the consistency check; otherwise, the interval values must be adjusted and the judgment matrix reconstructed. The formulas for calculating k and p are as follows:
k = ∑ j = 1 n 1 ∑ i = 1 n x i j + p = ∑ j = 1 n 1 ∑ i = 1 n x i j −
4. Indicator weights calculation. The IAHP weight for the indicator is:
w j ∗ = 1 2 k w j − + p w j +

4.2.2. CRITIC Method

The CRITIC method is an objective weighting approach proposed by Diakoulaki et al. [45] in 1995, which determines weights by analyzing the variability and conflict of indicators. It employs standard deviation to characterize indicator variability: greater data fluctuation (higher standard deviation) indicates richer information content, warranting higher weighting. Correlation between indicators represents conflict: lower correlation (higher conflict) signifies greater independent information contribution, justifying higher weighting. The calculation steps are as follows:
1. Dimensionless processing. To eliminate the impact of differing dimensions on evaluation results, each indicator must undergo dimensionless processing, mapping indicator data to the range [0, 1]. The CRITIC method typically employs the range method.
For positive indicators:
u i j ∗ = u i j − min u j max u j − min u j
For negative indicators:
u i j ∗ = max u j − u i j max u j − min u j
where u i j ∗ represents the dimensionless value of indicator quantity u i j , m denotes the number of cities under evaluation, and n denotes the number of evaluation indicators.
2. Calculation of indicator variability. Expressed as a standard deviation:
u ¯ j ∗ = 1 m ∑ i = 1 m t i j ∗
S j = ∑ i = 1 m u i j ∗ − u ¯ j ∗ 2 m − 1
In the formula, u ¯ j ∗ denotes the mean, S j denotes the standard deviation.
3. Indicator conflict calculation. Expressed as a correlation coefficient:
R j = ∑ j = 1 n ( 1 − r p q )
In the formula: r p q denotes the correlation coefficient between indicator p and q.
4. Information content calculation. The greater the information content, the more significant the role of the indicator within the entire evaluation system, and the greater weight it should be assigned.
C j = S j ∑ j = 1 n   1 − r p q = S j × R j
5. Calculation of indicator weights. The CRITIC weight for the indicator is:
w j o = C j ∑ j = 1 P   C j

4.2.3. Distance Function Weighting Combination

Since the IAHP method relies on experts’ subjective experience to determine weights, it exhibits strong subjectivity. In contrast, the CRITIC method objectively assigns weights by analyzing the variability and conflict among indicators. To avoid absolute subjectivity or objectivity in the evaluation process and enhance the scientific rigor of the evaluation system, distance function is employed to quantify the differences between the two weighting approaches. This constructs a combination weighting scheme that preserves expert insights while reflecting the inherent patterns within the data. The calculation process [46] is as follows:
d = 1 2 ∑ j = 1 n w j ∗ − w j o 2 1 2
d 2 = α − β 2
α + β = 1
In the formula, α and β represent the allocation coefficients for the IAHP weight and CRITIC weight, respectively.
By solving Equations (19) and (20) simultaneously, the allocation coefficients for both weights are calculated. The combination weight is a linear weighted sum of these two weights, resulting in the combination weight for the indicator:
w j = α w j ∗ + β w j o

4.3. Multi-Indicator Comprehensive Measure

Let μ i k = μ M i ∈ C k denote the degree to which a city under evaluation belongs to the kth evaluation level, then:
μ i k = ∑ j = 1 n w j μ i j k
If 0 ≤ μ i k ≤ 1 , ∑ k = 1 t μ i k = 1 , then μ i 1 ,   μ i 2 ,   ⋯ ,   μ i t is referred to as the multi-indicator comprehensive measurement evaluation vector for M i .

4.4. Confidence Recognition Criteria

To mitigate the drawback of low accuracy in maximum membership degree, a confidence-based identification criterion is introduced. If D 1 ,   D 2 ,   ⋯ ,   D t represents an ordered partition class (i.e., D 1 < D 2 < ⋯ < D t ), let λ denote the confidence level, generally defined as λ ∈ 0.5 ,   1.0 and typically set to 0.6 or 0.7. The confidence identification formula is as follows:
k 0 = min { k : ∑ l = 1 k μ i k ≥ λ , k = 1 ,   2 ,   ⋯ ,   t }
Then, k0 is considered to be the flood resilience assessment grade for the city under evaluation.

5. Case Study and Results Analysis

5.1. Overview of the Study Area

Jiangxi Province (24°29′~30°04′ N, 113°34′~118°28′ E) lies on the southern bank where the middle and lower reaches of the Yangtze River converge. Surrounded by mountains on the southeast and west, it forms a vast basin opening northward. The province boasts over 2400 rivers of varying sizes, most of which flow into Poyang Lake before emptying into the Yangtze River. Jiangxi experiences four distinct seasons under a subtropical humid monsoon climate. The primary flood season occurs between April and June, accounting for 42% to 53% of annual precipitation. Due to its unique basin topography and uneven spatiotemporal rainfall distribution, large volumes of rainwater rapidly converge into rivers and lakes. The flat terrain in the north impedes flood discharge, making the region highly susceptible to flooding. Therefore, this paper analyzes and evaluates the resilience of urban flood disasters in Jiangxi Province as a case study.
Eleven prefecture-level cities in Jiangxi were selected as research subjects. As shown in Figure 3, they are geographically divided into three regions: Northern Jiangxi, Central Jiangxi, and Southern Jiangxi. Northern Jiangxi includes Nanchang, Jingdezhen, Pingxiang, Jiujiang, Xinyu, Yingtan, Yichun, and Shangrao; Central Jiangxi includes Jian and Fuzhou; and Southern Jiangxi is primarily Ganzhou.
Figure 3. Study area.

5.2. Data Sources

The socioeconomic data in this paper primarily originate from the 2023 Jiangxi Statistical Yearbook [47] and the Statistical Bulletin on National Economic and Social Development [48]. Data on water conservancy facilities and flood disasters mainly derive from the Jiangxi Provincial Department of Water Resources website, the Jiangxi Hydrological Bulletin [49], and field investigations. Geographic information is sourced from the SRTMDEM 90 M resolution raw elevation data available on the Geospatial Data Cloud website [50]. Missing data points were supplemented using linear interpolation. Table 4 displays the original statistics, while Figure 4 illustrates the distribution of the normalized data.
Table 4. Original statistics of the indicators.
Figure 4. Normalized data distribution.

5.3. Weighting Results Analysis

The subjective weights of evaluation indicators in this paper were determined using the IAHP method. An expert survey questionnaire was designed via the Delphi method, and anonymous opinions were collected from experts in urban planning, water conservancy, emergency management, and other fields. After multiple rounds of feedback and revisions, the judgment matrix for the IAHP method was finalized, enabling the calculation of IAHP weights for the evaluation indicators. Objective weights were computed using the CRITIC method based on evaluation indicator data. The distance function was then applied to determine composite weights, with calculation methods detailed in Equations (5)–(20). Evaluation indicator weights are presented in Table 5.
Table 5. Weight values of evaluation indicators.

5.3.1. Weight of Level-2 Indicators

Figure 5 shows the distribution of subjective weights, objective weights, and composite weights for the level-2 indicators. The composite weights respect both expert experience and strategic intent while fully leveraging the objective patterns of actual data, thereby compensating for the shortcomings of any single method and making the weight allocation more scientific, reasonable, and robust. Composite weights for the four level-2 indicators: Infrastructure (B1, 0.437), Social economy (B2, 0.181), Technical monitoring (B3, 0.218), and Ecological Environment (B4, 0.162).
Figure 5. Subjective, objective and composite weights of level-2 indicators.
Infrastructure holds the highest weight at 43.7%, as it serves as the direct carrier for flood resistance and disaster absorption. Its near-half weight indicates this system is the decisive factor in UFR assessment. The composite weights of social economy, technical monitoring, and ecological environment are relatively close but still play significant roles.

5.3.2. Weight of Level-3 Indicators

Figure 6 shows the composite weights of the level-3 indicators, where drainage pipe density (0.134), Length of flood control embankment (0.119), number of emergency shelters (0.063), and coverage rate of meteorological and hydro-logical stations (0.060) carry relatively higher weight proportions. Drainage network density directly determines a city’s resilience during heavy rainfall. A high-density network rapidly removes surface water, effectively preventing urban flooding and serving as the first line of defense against common, frequent rainfall disasters. Its high weight underscores the critical importance of proactive urban drainage. Flood embankment length constitutes a key barrier against large-scale basin floods, with its scale and standards directly impacting the safety of urban core areas. Adequate and strategically distributed emergency shelters ensure swift, orderly evacuation and accommodation for affected populations, preventing casualties from secondary disasters and maintaining social stability. The coverage rate of meteorological and hydrological stations is fundamental to achieving precise forecasting and timely warnings. Its high weight underscores the critical importance of information technology and intelligent systems in modern disaster prevention and mitigation.
Figure 6. Composite weights of level-3 indicators.

5.3.3. Resilience Dimension Weights

Figure 7 illustrates the weight distribution across three resilience dimensions, with resistance weight (0.546) accounting for over half—demonstrating its dominant role in resilience and reflecting the urban system’s fundamental demand for “freedom from disaster.” It emphasizes establishing the first line of defense against external flooding and internal waterlogging through high-standard engineering measures and forward-looking spatial planning. The recovery weight (0.297) ranks second, highlighting the city’s emphasis on its ability to rapidly return to normal operations after a disaster. This dimension focuses on the city’s emergency response speed, emergency repair and rescue capabilities, resource allocation efficiency, and the self-organizing capacity of its social systems. Adaptation (0.154) holds a relatively lower weight, emphasizing learning from past disasters to dynamically adjust planning, policies, and management strategies for better preparedness against potentially intensifying climate risks. Though its weight is modest, it represents the critical shift in urban resilience—from static defense to dynamic evolution—enabling sustainable development.
Figure 7. Weight of resilience dimensions.

5.4. UFR Level Analysis

Based on the conditions of “non-negativity and boundedness,” “normality,” and “additivity” for the unidentified measure of each indicator in Equations (1)–(3) [20,51,52,53,54], linear interpolation was employed to construct the measure functions for each indicator. Due to space limitations, this paper presents only the measure functions for indicators C1 to C4, as shown in Figure 8.
Figure 8. Measure functions of indicators.
Substituting each city’s indicator data into the measurement function yields a single-indicator measurement matrix. Taking Nanchang as an example, its single indicator measurement matrix is shown in Figure 9.
Figure 9. Measurement matrix of single indicator.
Multiplying the combination weight vector of Nanchang’s level-3 indicators by its single indicator measurement matrix according to Equation (21) yields the multi-indicator composite measurement evaluation vector [0.030, 0.057, 0.237, 0.261, 0.415]. Introducing the confidence level identification criterion, with a confidence level λ = 0.6, Nanchang’s UFR grade is determined as D5 (Level V) according to Equation (22), indicating a high resilience level. Similarly, the comprehensive measurement evaluation vectors for other cities can be calculated as shown in Figure 10.
Figure 10. Comprehensive measurement evaluation vector distribution of multiple indicators.
ArcGIS 10.8 software was used to visualize the UFR grades of these cities, as depicted in Figure 11.
Figure 11. Distribution of UFR level in Jiangxi Province.
As shown in Figure 11 and Table 6, among the 11 prefecture-level cities in Jiangxi Province, four cities—Nanchang, Shangrao, Yichun, and Fuzhou—exhibit high resilience ratings. Nanchang, as the provincial capital of Jiangxi, leads the province in economic development and ranks at the forefront in urban planning, infrastructure construction, fiscal investment, and emergency management system development. This enables it to demonstrate superior performance in coping with flood disasters. Yichun, and Fuzhou. As the provincial capital, Nanchang boasts the most developed economy and leads the province in urban planning, infrastructure development, fiscal investment, and emergency management system construction, enabling its high resilience against floods. The high resilience ratings of Shangrao, Yichun, and Fuzhou stem from recent prioritized investments in water conservancy projects, ecological flood control, and disaster early warning systems. Second, the highest number of cities—six in total—exhibited moderately high resilience levels, including Jiujiang, Jingdezhen, Xinyu, Yingtan, Ji’an, and Ganzhou. Meanwhile, only Pingxiang was classified as having moderate resilience.
Table 6. UFR level of each city.
Through the above analysis, we find that Jiangxi Province exhibits significant spatial variations in flood resilience levels. Cities with high resilience are primarily concentrated in northern and central Jiangxi, where the majority of cities demonstrate moderately high resilience or higher, with only Pingxiang classified as having moderate resilience. This spatial distribution pattern is closely tied to Jiangxi’s natural geography, economic development level, infrastructure development, and disaster prevention and mitigation capabilities. The relatively higher resilience in northern and central Jiangxi stems primarily from the region’s relatively well-developed water conservancy infrastructure network, stronger regional economic support capacity, and more mature emergency management and disaster warning systems. Central cities in these areas, such as Nanchang and Shangrao, typically possess more abundant fiscal resources for flood control project construction and maintenance, more advanced monitoring and information technology for disaster assessment and early warning, and more comprehensive public service and social organization systems for disaster response and recovery. In contrast, Pingxiang stands as the sole city with moderate resilience, primarily due to its relatively underdeveloped economy, inadequate drainage system capacity, and insufficient application of disaster warning technologies.

5.5. Method Comparison

To validate the effectiveness of the model presented in this paper, a comparison was conducted between the combined model of the Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation (FCE) and the model proposed herein. The comparison results are shown in Table 7.
Table 7. Comparison of evaluation methods.
As shown in Table 7, the evaluation results of the two methods are largely consistent, indicating that the UFR assessment model constructed in this paper is feasible and reliable, offering new insights for urban resilience development. Furthermore, only Pingxiang exhibits divergent assessment outcomes, which can be attributed to the fundamental differences between the two methodologies and Pingxiang’s unique resilience characteristics. The AHP-FCE method relies on expert subjective judgment for weight allocation and evaluation, placing greater emphasis on qualitative factors or policy-driven indicators where Pingxiang City demonstrates relatively strong performance, such as socioeconomic and ecological environment indicators. This tendency may lead to higher overall scores within an expert-dominated framework. In contrast, the method proposed in this study balances expert intent by integrating quantitative data analysis. It places greater emphasis on objective, outcome-oriented patterns or statistically derived regularities within the dataset, thereby providing a scientific basis for resilience assessment.

6. Recommendations and Measures to Enhance UFR

6.1. Strengthen Infrastructure Development

Among the level-2 indicators, the combined weight of infrastructure (0.437) holds the largest share, accounting for nearly half. Infrastructure serves as the physical backbone for cities to withstand flood impacts and should be the core focus of construction investments. Among these, drainage pipe density (C1) is the most critical factor. Upgrading the drainage network system is paramount for enhancing UFR. Comprehensive surveys and systematic renovations of drainage networks should be conducted in urban areas prone to frequent flooding. Establishing a Geographic Information System (GIS) for drainage networks and an online monitoring network will enable dynamic management and preventive maintenance, ensuring optimal operational conditions. Simultaneously, among the three resilience dimensions, resistance holds the dominant position. This underscores that during urban flood management, safeguarding the core functionality of systems against catastrophic failure remains the primary objective. Strengthening urban infrastructure development is a vital means of flood resistance.

6.2. Enhance the Intelligent Development of the Technical Monitoring System

Utilize digital twin technology to construct urban flood simulation systems for dynamic disaster progression forecasting. Integrate multi-source data from meteorology, hydrology, and IoT to enable disaster early warning, information sharing, and coordinated response, establishing a unified early warning and emergency platform. Continuously enhance communication infrastructure, particularly in remote areas and underground spaces, ensuring uninterrupted connectivity between core networks and end-point sensors during extreme weather events.

6.3. Advancing the Development of Sponge Cities

Transforming urban parks, green spaces, wetlands, and other open areas into sponge-like structures with stormwater retention capabilities—such as designing sunken green spaces below surrounding ground levels that serve as temporary water storage during rainfall. This approach not only enhances the ecological benefits of increased green coverage but also endows the green space system with hydrological regulation functions, significantly boosting the city’s systemic resilience and buffering capacity against extreme rainfall events.

7. Discussion

Nanchang, Yichun, Fuzhou, and Shangrao all demonstrate high levels of urban resilience, indicating these cities possess strong advantages in infrastructure development, socioeconomic progress, monitoring technology application, and ecological environmental governance. Analysis of standardized data reveals that Nanchang boasts the highest per capita GDP among these cities. This economic strength ensures robust investment capacity in areas such as livelihood security, public service upgrades, and emergency system improvements, laying a solid economic foundation for enhancing urban resilience. Yichun, Fuzhou, and Shangrao boast some of the densest drainage networks among Jiangxi’s cities. This comprehensive municipal infrastructure layout significantly enhances their capacity to withstand disasters like heavy rainfall and urban flooding, further solidifying the hardware foundation for high-resilience development. Additionally, while the six cities with moderately high resilience levels each possess distinct advantages in healthcare, urban development, and ecological environments, they also exhibit notable shortcomings. For instance, Yingtan has a relatively low drainage network density, Xinyu lacks sufficient emergency shelters, and Ganzhou has a comparatively lower per capita GDP. These factors constrain their advancement toward high resilience levels. Pingxiang’s lag in infrastructure development, socioeconomic progress, and monitoring technology application has hindered its ability to achieve higher resilience standards.
The findings of this study offer insights for urban planning and disaster risk reduction policies. The high weight assigned to infrastructure indicates that cities should continue investing in drainage networks, embankments, and shelter construction. The relatively lower weight for the adaptation dimension suggests cities need to shift from static defenses toward dynamic learning and systemic adaptation—such as updating building codes, promoting sponge city initiatives, and incorporating climate forecasts into land-use planning.

8. Conclusions

To address the uncertainty and complexity inherent in UFR assessment, this study establishes a comprehensive UFR evaluation model based on the unascertained measurement theory. The model integrates subjective weights derived from the distance function-based IAHP and objective weights obtained via the CRITIC method, effectively reconciling the subjectivity of expert judgment and the objectivity of data characteristics. Taking Jiangxi Province as an empirical case, systematic analysis was conducted, and the key findings and research significance are summarized as follows:
(1)
This study constructs a UFR assessment framework encompassing four primary aspects (infrastructure, social economy, technical monitoring, and ecological environment) and three core resilience dimensions (resistance, recovery, and adaptation), forming a multi-level indicator system that comprehensively reflects the holistic performance of UFR. Based on this framework, the unascertained measurement model is established, which effectively quantifies the ambiguous and uncertain relationships between evaluation indicators and resilience levels, providing a scientific and operable tool for UFR assessment.
(2)
The composite weighting approach adopted in this study achieves a balanced integration of subjective and objective weights, ensuring the rationality and reliability of indicator weight assignment. Among the level-2 indicators, infrastructure ranks first in terms of influence, serving as the fundamental and core support for urban flood prevention and control. At the level-3 indicator level, drainage pipe density, length of flood control embankments, number of emergency shelters, and broadcast coverage rate occupy the highest weight proportions, indicating that these factors are the key breakthrough points for improving UFR in Jiangxi Province. In terms of resilience attributes, resistance plays a dominant role, emphasizing that enhancing cities’ ability to resist flood disasters is the primary task of UFR improvement.
(3)
The empirical results reveal significant spatial heterogeneity in UFR levels across Jiangxi Province. High resilience cities are concentrated in the northern and central regions of the province, and most cities in the province have achieved moderately high or high resilience levels, with only one city at the moderate resilience level. This spatial pattern is closely related to the regional differences in economic development, infrastructure construction, and ecological environment quality, providing targeted spatial guidance for the formulation of regional flood management policies.
(4)
Theoretically, this study enriches the application of unascertained measurement theory in the field of disaster resilience assessment, breaks through the limitations of single weighting methods in traditional assessment models, and provides a new methodological perspective for solving uncertain problems in UFR evaluation. Practically, the constructed evaluation model and the identified key influencing factors can provide decision-making support for the government of Jiangxi Province and relevant departments to formulate targeted UFR improvement strategies, optimize the allocation of flood control resources, and promote the balanced development of regional flood resilience. Additionally, the research framework and methods can be extended to other regions with similar natural and social economic conditions, contributing to the improvement of national urban flood disaster prevention and mitigation capabilities and the construction of resilient cities.
This study presents a scientific and applicable assessment model for UFR based on unascertained measurement theory. However, the model has several limitations that merit further discussion. First, it did not account for spatial interactions between cities, which may influence regional flood dynamics and resilience outcomes. Future research could incorporate spatial autocorrelation analysis or network models to capture these interdependencies. Second, the model is static and does not reflect temporal changes in resilience. Longitudinal studies using panel data or dynamic modeling could reveal how UFR evolves under climate change and urban growth. Third, the model is constrained by data availability and indicator selection to some extent. On the one hand, certain critical indicators (e.g., real-time urban flood monitoring data, community-level resilience survey data) were not fully included due to limited data accessibility, which may have reduced the comprehensiveness of the assessment. On the other hand, the selected indicators were mainly framed around macro-level dimensions (e.g., infrastructure, socio-economy) and lacked more granular metrics related to micro-level resilience factors such as residents’ emergency response capacity and community self-governance ability. These constraints may have led to a slight underestimation or overestimation of UFR for individual cities with distinctive micro-level characteristics.

Author Contributions

S.L.: investigation, data curation, writing—original draft preparation, and visualization. L.F.: writing—review and editing. J.X.: formal analysis and data curation. Y.K.: conceptualization, methodology, formal analysis, writing—review and editing, funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Key Basic Research Project of Yichun Science and Technology Special Fund (No. 2023ZDJCYJ05).

Institutional Review Board Statement

Ethical review and approval were waived for this study due to Guidelines for Academic Norms in Philosophical and Social Sciences Research in Institutions of Higher Education (Issued by the Social Science Committee of the Ministry of Education), routine social science studies like ours—such as questionnaire surveys conducted with professional experts (who are not vulnerable groups) and focusing on professional content without involving sensitive information—mandatory approval from an ethics committee or IRB is not required, provided that basic ethical principles (e.g., informed consent) are followed.

Data Availability Statement

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

Acknowledgments

We thank the reviewers for commenting on this paper.

Conflicts of Interest

We declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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