Introduction

As globalization and urbanization rapidly advance in the 21st century, cities have emerged as the predominant habitat for human populations. A report by the United Nations projects a sustained increase in global urbanization, forecasting that approximately 70% of the world’s population will inhabit urban areas by 20501. The swift pace of urbanization introduces challenges including heightened population density and the concentration of critical infrastructure, which subsequently escalate the vulnerability of urban systems to seismic events. Without the implementation of robust seismic measures, densely populated regions and intricate infrastructure networks are especially vulnerable to substantial damage during seismic events, which can markedly amplify the overall impact of such disasters2. Moreover, given the dense concentration of economic activities within urban centers, localized disasters have the potential to disrupt the economic stability and development not only of individual cities but also of broader regions3. Although this transformation has catalyzed economic growth and enhanced living convenience, it has concurrently exacerbated urban vulnerability to natural disasters, particularly earthquakes. Earthquakes can result in substantial loss of life and extensive property damage, deeply affecting urban infrastructure and disrupting socio-economic activities4,5. Precise evaluation and comprehensive understanding of a city’s seismic emergency capabilities are vital for bolstering urban resilience to disasters. Enhancing urban emergency capabilities can more effectively safeguard public safety and property, foster social stability, and expedite disaster recovery, thereby establishing a robust foundation for the sustainable development of cities.

Over an extended period, scholars at both domestic and international levels have extensively investigated methods to enhance urban disaster emergency capabilities. Nevertheless, a consensus has yet to be reached on the establishment of a comprehensive system of evaluative indicators and the quantification of emergency response capabilities. In terms of selecting evaluative indicator systems, the State Capability Assessment for Readiness report by the Federal Emergency Management Agency6, highlights that the United States has established a framework for assessing the emergency management capabilities of local governments. This framework emphasizes key areas such as risk management, command, and control coordination. Furthermore, as documented in a study by Hu et al.. published in Marine Bulletin, Japan has developed a comprehensive set of indicators designed to evaluate the capabilities of regional governments in marine disaster prevention and mitigation7. In China, Xie et al.. have proposed that urban disaster mitigation capabilities can be assessed using indicators such as casualty numbers, economic losses, and post-seismic recovery times. They have developed an indicator system encompassing six key areas: hazard analysis, monitoring and prediction, seismic engineering, socio-economic disaster prevention, and recovery8. Deng et al. examined both the absolute and relative dimensions of regional seismic emergency capabilities9. Jia et al.. developed an indicator system for evaluating the seismic emergency capabilities of China’s islands, encompassing aspects such as monitoring, emergency rescue, recovery capabilities, and the impact of natural factors10. Wang et al.. introduced an innovative approach by categorizing the primary evaluation indicators from the perspective of response entities while constructing an indicator system for assessing the emergency response capabilities to major seismic disasters in China11. Han from a crisis management perspective, employed the scenario-task-capability model to quantitatively assess urban emergency capabilities12. Existing research and practices frequently concentrate on isolated aspects of emergency response capabilities, particularly immediate disaster response and short-term rescue operations. However, the overall emergency management capability of a city encompasses a much broader spectrum, necessitating a comprehensive approach that includes prevention, preparedness, response, and recovery. Definitions of emergency capability are articulated from three perspectives: crisis management13, disaster prevention and mitigation14,15, and government response capability16,17. In constructing indicator systems, crisis management is widely recognized and divided into four stages: mitigation, preparedness, response, and recovery18. In quantifying emergency rescue capabilities, Chen et al. have studied China’s urban fire stations using the Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation method to quantitatively analyze the emergency rescue levels of fire stations19. Additionally, Fang et al. used the SWOT analysis to assess the capabilities of aviation medical rescue20, while Qi developed a model using the Sparrow Search Algorithm (SSA) optimized Support Vector Machine (SVM) to evaluate the emergency rescue capabilities in coal and gas outburst incidents21. These studies indicate that quantitative methods are widely used in assessing emergency capabilities. However, given the diversity and complexity of data encountered in real-world scenarios, experts frequently find it challenging to express their preferences with precise numerical values and may often be unable to provide clear quantitative judgments. Thus, utilizing fuzzy methods to represent subjective evaluations is particularly suitable. This methodology adeptly manages uncertainty and subjectivity, thereby rendering the evaluation results more comprehensive and reliable.

Despite significant progress in disaster management research, most existing studies on seismic emergency management focus on post-disaster response, neglecting the full lifecycle management that includes pre-disaster prevention and post-disaster recovery. This narrow focus leads to limitations in emergency management and fails to provide comprehensive solutions. For instance, Tierney et al. argue that excessive focus on recovery neglects pre-emptive measures22. Cutter et al. emphasize that vulnerability and resilience must be balanced across all disaster management stages23. Turner et al. state that single-phase strategies are insufficient to address complex vulnerabilities24.In contrast, lifecycle disaster management strategies emphasize a comprehensive approach from prevention to recovery. Kennedy et al.‘s “build back better” concept advocates not just recovery but also improving infrastructure to adapt to future disasters25. Paton et al. highlight that community adaptability and resilience are crucial for long-term disaster preparedness26. Norris et al.. argue that integrating economic development, social capital, and community capacity can establish robust resilience27.

This paper introduces an evaluation indicator system for assessing seismic emergency capabilities, aiming to develop a scientific methodology for evaluating urban seismic emergency capabilities, with Changchun City serving as a case study. The overall methodology of the study is depicted in Fig. 1. This study, adopting a crisis management perspective, developed an innovative and comprehensive indicator evaluation system that encompasses the entire disaster management cycle, including mitigation, preparedness, response, and recovery. The system comprises four primary dimensions and fifteen secondary indicators, utilizing a blend of quantitative and qualitative methodologies to yield more comprehensive and accurate evaluation results. Methodologically, the study applied the coefficient of variation and Delphi methods to assign weights to each indicator and employed binary fuzzy linguistic theory to manage uncertain information. The model was developed and applied through a case study of Changchun City. The findings of the study reveal that Changchun City demonstrates outstanding performance in the areas of emergency supply reserves and emergency plan formulation. However, there is a critical need to enhance public seismic education, monitoring and early warning systems, and economic recovery capabilities. The innovations and contributions of this study are as follows: (1) Comprehensive Evaluation System: This study is pioneering in developing an evaluation indicator system from a crisis management perspective, encompassing the full spectrum of disaster mitigation, preparedness, response, and recovery. This comprehensive approach addresses the limitations and biases present in existing research. (2) Methodological Innovation: The study integrates the coefficient of variation method with the Delphi method to ensure scientific rigor and professionalism in determining the weights of evaluation indicators. Additionally, the introduction of binary fuzzy linguistic theory effectively addresses uncertain information in the evaluation process, thereby enhancing the accuracy and reliability of the results. (3) Practical Application: The case study of Changchun City validates the efficacy of the evaluation system and offers valuable experiences and methodologies for other urban areas. This research not only establishes a scientific basis for evaluating the seismic emergency capabilities of Changchun City but also provides crucial insights for other cities in managing earthquake-related disasters. It makes a substantial contribution to strengthening urban resilience in the face of natural disasters, offering both theoretical and practical advancements.

Fig. 1
figure 1

Research approach.

Full size image

Construction of a multidimensional standardized indicator system

Influencing factors

Mitigation phase

The mitigation phase, as the initial stage of emergency management, primarily seeks to reduce the likelihood of disasters or minimize their impacts28. Proactive mitigation measures, as opposed to post-disaster relief efforts, can more effectively diminish the losses and consequences of emergencies, offering long-term advantages. Mitigation measures are categorized into three aspects: (1) monitoring and early warning systems are crucial29. By conducting professional inspections, field surveys, and gathering community feedback, we can acquire critical risk information and implement effective monitoring. Risk assessments derived from this data facilitate timely warnings, thereby enabling the public to take preventive measures to minimize the impact of disasters. (2) reducing vulnerability is a core objective30. From a physical perspective, this entails adopting various measures to enhance resilience against seismic disasters. For example, installing dampers and shock absorbers, utilizing base isolation technology, and reinforcing building structure design and materials to minimize damage to buildings during earthquakes31. Additionally, constructing seismic-resistant bridges and walls, as well as other critical infrastructure, plays a vital role in strengthening disaster resilience. Culturally, it involves increasing public awareness and response capabilities through education and training, ensuring that individuals can take effective actions to safeguard lives and property during emergencies. (3) formulating and implementing relevant laws and policies is also a vital means to reduce disaster risks32. For instance, by implementing land use planning that restricts construction activities in high-risk areas and enforcing disaster-resistant building standards and regulations, new facilities can be designed to withstand the impacts of potential disasters. Building upon previous research, this paper classifies the capabilities associated with the mitigation phase into four categories: monitoring and warning capabilities, physical seismic resistance, cultural seismic resistance, and regulatory and policy capabilities, as illustrated in Fig. 2.

Preparation phase

The preparation phase constitutes the second pivotal stage of emergency management, emphasizing the organization, equipping, and training necessary to ensure the efficacy of emergency responses. (1) Development of Emergency Plans: Emergency plans are pivotal to the preparation phase, underscored by the identification and assessment of potential risks, a comprehensive analysis of possible disaster scenarios, their progression, and potential consequences. This enables precise planning of personnel allocation, material deployment, resource distribution, and coordination mechanisms. Not only does this ensure orderly emergency responses, but it also promotes the standardization and systematization of response measures. Regular simulation exercises are key to enhancing the effectiveness of these plans, revealing gaps and driving continuous optimization and timely updates of the plans33. (2) Emergency Support: Emergency support is foundational for executing planned emergency responses during a disaster. It encompasses the establishment of professional emergency rescue teams, the procurement of essential rescue materials, the allocation of emergency funds, and the provision of safe shelters. Forming a rescue team with a well-defined organizational structure and robust professional expertise is essential for effective disaster management, ensuring swift and coordinated rescue operations when disasters occur34. Drawing from the preceding analysis, this paper delineates the key capabilities integral to the preparation phase, which include plan development, plan drills, emergency support, and public education. These capabilities constitute the cornerstone of effective emergency management.

Response phase

The response phase constitutes the third pivotal stage of emergency management, focusing on addressing unavoidable disasters, swiftly mobilizing resources, and executing necessary response measures in accordance with established procedures and principles. The primary objectives of this phase are to minimize disaster response time, promptly stabilize the situation, and mitigate the impact on public life and economic activities. (1) Preliminary disposition: Thoroughly inspect the status and development trends of potential risk sources, activate emergency response mechanisms, coordinate community evacuations, and establish an emergency command center to manage the entire response process35. (2) Emergency rescue: Includes post-disaster relief actions, provision of medical care and shelters, ensuring the supply of basic necessities, securing transportation and communication, and preventing secondary disasters to protect the public and contain the worsening of the disaster situation36. (3) Disaster Chain-Derived Risk Analysis: This involves monitoring, assessing, and providing early warnings for secondary disasters potentially triggered by earthquakes and other primary events. It also includes implementing measures to mitigate further damage37. This article identifies the key capabilities of the response phase as preliminary disposition, emergency rescue, secondary disaster prevention and control, and the cooperation between the government and the public.

Recovery phase

In the recovery phase, the focus of emergency management shifts from rescue to reconstruction, with the main goal being to minimize the long-term impact of disasters, restore the order of production and daily life in affected areas, and enhance the overall safety and resilience of society38,39. (1) Social Impact Recovery: This involves implementing measures to restore the functionality and structure of affected communities, mitigate long-term impacts on individuals and communities, and endeavor to restore or enhance the socio-economic status and quality of life to pre-disaster conditions as much as possible. (2) Socio-economic Recovery: This phase involves the reconstruction of economic and social infrastructures to reinstate economic activities and employment opportunities, as well as to secure the provision of essential services and social welfare. (3) Psychological Recovery of Affected Individuals: Professional interventions and support are offered to assist disaster victims in coping with psychological trauma and emotional distress, and to restore mental health and social functioning. Based on these considerations, the recovery phase capabilities can be categorized into economic capacity, mobilization capacity, and administrative capacity.

System construction

Drawing from the analysis in “Influencing factors” and employing a task-capability dimensional analysis, this paper categorizes the urban seismic emergency capability evaluation system into three dimensions. The first dimension represents the evaluation objective (A), while the second dimension comprises primary indicators, which include Mitigation Capability (B1), Preparedness Capability (B2), Response Capability (B3), and Recovery Capability (B4). The associated secondary indicators for each primary indicator are depicted in Fig. 2. The respective secondary indicators and their descriptions are presented in Table 1.

Fig. 2
figure 2

Urban seismic emergency capability evaluation indicators.

Full size image

Data and methods

Method selection for weighting

Weight determination methods can be categorized into subjective and objective approaches. Subjective weighting depends on expert judgment to assign significance to indicators, utilizing techniques such as expert scoring, the binomial coefficient method, and the analytical hierarchy process. While this approach captures the evaluator’s intentions, it is prone to individual biases and can produce inconsistent results across different experts. Conversely, objective weighting methods, including neural networks, the Coefficient of Variation Method, and the entropy method, derive weights based on evaluation indicator data, thereby reducing subjective biases and reinforcing the mathematical rigor of the evaluation. In this study, qualitative indicators are treated separately to objectively evaluate their impact on emergency capabilities, with data sourced from expert scoring.

Building on this foundation, our study employs an innovative approach by integrating the Delphi Method and the Coefficient of Variation Method within a matrix framework for weight calculation. The Delphi Method ensures the professionalism of assessment weights by utilizing iterative expert feedback40, while the Coefficient of Variation Method objectively allocates weights based on the dispersion of indicator scores41, thereby mitigating the influence of personal biases. By combining these methods through matrix calculations, we achieve a balance between subjective expert evaluations and rigorous objective data analysis, with the flexibility to adjust their respective proportions in the overall weights42. This approach enhances the scientific rigor and objectivity of the evaluation, streamlines the calculation process, and significantly improves the transparency and reliability of assessments of urban seismic emergency capabilities.

The specific calculation steps for the coefficient of variation method are as follows:

(1) Calculate the mean and standard deviation

$$\:{\mu\:}_{i}=\frac{\sum\:_{j=1}^{n}{x}_{ij}}{n}$$
(1)

Where \(\:{\mu\:}_{i}\) is the average value of the \(\:\:{i}^{th}\) indicator, \(\:{x}_{ij}\)represents the value given by the \(\:{j}^{th}\) expert for the \(\:\:{i}^{th}\) indicator, and n is the number of experts.

$$\:{\sigma\:}_{i}=\sqrt{\frac{{\sum\:}_{j=1}^{n}{({x}_{ij}-{\mu\:}_{i})}^{2}}{n}}$$
(2)

Where \(\:{\sigma\:}_{i}\) is the measure of dispersion for the \(\:{i}^{th}\) indicator, \(\:{x}_{ij}\) represents the value given by the \(\:{j}^{th}\) expert for the \(\:\:{i}^{th}\) indicator, and n is the number of experts.

(2) Calculate the coefficient of variation.

$$\:{CV}_{i}=\frac{{\sigma\:}_{i}}{{\mu\:}_{i}}$$
(3)

Where \(\:{CV}_{i}\) represents the coefficient of variation for the \(\:\:{i}^{th}\) indicator, \(\:{\mu\:}_{i}\)is the mean value of the \(\:{i}^{th}\)indicator, and \(\:{\sigma\:}_{i}\) is the standard deviation of the \(\:\:{i}^{th}\) indicator.

(3) Calculate the weights.

$$\:{W}_{i}=\frac{{CV}_{i}}{{\sum\:}_{i=1}^{n}{CV}_{i}}$$
(4)

Where \(\:{W}_{i}\) is the weight of the\(\:\:\:{i}^{th}\)indicator, \(\:{CV}_{i}\) represents the coefficient of variation for the \(\:\:{i}^{th}\) indicator.

The specific calculation steps of the Delphi method are as follows:

$$\:{X}_{i}=\frac{\sum\:{x}_{ij}}{n}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:i=\text{1,2},3\cdots\: m$$
(5)

where: n is the number of experts, m is the total number of evaluation indicators, \(\:{X}_{i}\) is the average weight of the \(\:{j}^{th}\) indicator, \(\:{x}_{ij}\) is the score given by the \(\:{j}^{th}\) expert to the \(\:{j}^{th}\) indicator’s weight.

According to the Likert ‘five-point’ scale, the importance of each specific indicator is divided into five levels of degree. Respondents are required to make a judgment on the importance of the indicators based on their own practical experience, work insights, and professional skills.

Weight combination (matrix concept)

Due to the different indicators and the varying importance of subjective and objective weight values, the levels of importance also differ. For example, in the recovery phase, the three secondary indicators—Economic Capability (B41), Mobilization Capability (B42), and Administrative Capability (B43)—have weights of 0.078, 0.085, and 0.094, respectively, as determined by the Delphi Method, while the weights determined by the Coefficient of Variation Method are 0.080, 0.082, and 0.075, respectively. The significant differences in weights obtained by these two methods indirectly indicate that the Delphi Method and the Coefficient of Variation Method emphasize different perspectives. Therefore, we use \(\:\alpha\:\) and \(\:\beta\:\) to represent the relative importance of subjective and objective weights, respectively. Here, we will use the concept of matrices to calculate the relative importance coefficients, \(\:{\alpha\:}_{i}\) and \(\:{\beta\:}_{i}\) of subjective and objective weights. The formula is as follows:

$$\:\left\{\begin{array}{c}{\alpha\:}_{i}={v}_{i}/\left({v}_{i}+{w}_{i}\right)\\\:{\beta\:}_{i}={w}_{i}/\left({v}_{i}+{w}_{i}\right)\end{array}\right.$$
(6)

Where \(\:{v}_{i}\) represents the weight obtained by the Delphi method, and \(\:{w}_{i}\) represents the weight obtained by coefficient of variation method. After obtaining the importance coefficients \(\:{\alpha\:}_{i}\) and \(\:{\beta\:}_{i}\) for subjective and objective weights, calculate the composite weight as follows:

$$\:{Q}_{i}=\frac{{v}_{i}{\alpha\:}_{i}+{w}_{i}{\beta\:}_{i}}{\sum\:_{i=1}^{n}\left({v}_{i}{\alpha\:}_{i}+{w}_{i}{\beta\:}_{i}\right)}$$
(7)

The 2-tuple fuzzy linguistic model in emergency response capability evaluation

Triangular fuzzy numbers

Triangular fuzzy numbers are highly useful in decision analysis, risk assessment, and other fields that require dealing with uncertain information43,44. By converting expert linguistic evaluations into Triangular fuzzy numbers, vague concepts can be mathematized, allowing for analysis and processing within quantitative models. A Triangular fuzzy number is a concept in fuzzy mathematics used to represent and handle uncertainty in fuzzy environments. Triangular fuzzy numbers are particularly suited for expressing information with fuzzy characteristics, such as an expert’s uncertain evaluation of a situation. Its graphical representation takes the shape of a triangle, which is the origin of its name. A Triangular fuzzy number can be defined by an ordered triplet (\(\:l\),\(\:m\),\(\:u\)), where:\(\:l\) is the lower limit (left endpoint) of the fuzzy number,\(\:m\) is the central value or most probable value (peak) of the fuzzy number, indicating the most likely estimate of the evaluation or quantity,\(\:u\) is the upper limit (right endpoint) of the fuzzy number, representing the maximum possible estimate of the evaluation or quantity. The membership function\(\:{\:\mu\:}_{A}\left(x\right)\) of a triangular fuzzy number for different values of \(\:x\) is defined as follows:

$$\:{\mu\:}_{A}\left(x\right)=\left\{\begin{array}{ll}0&\:\text{for}\:x<l\:or\:x>u\\\:\frac{x-l}{m-l}&\:\text{for}\:l\le\:x<m\\\:1&\:\text{for}\:x=m\\\:\frac{u-x}{u-m}&\:\text{for}\:m<x\le\:u\end{array}\right.$$
(8)

The membership function \(\:{\mu\:}_{A}\left(x\right)\) of the triangular fuzzy number A is defined for \(\:x\) as follows: when\(\:\:x\:=m,\:{\mu\:}_{A}\left(x\right)=1\), indicating that \(\:x\) fully belongs to A; when\(\:\:x\:\)is within the interval \(\:\:\left[l,m\right],{\:\mu\:}_{A}\left(x\right)\) increases linearly from 0; when\(\:\:x\:\)is within the interval \(\:\left[m,u\right]\), \(\:{\mu\:}_{A}\left(x\right)\:\)decreases linearly to 0;outside of this interval, \(\:{\mu\:}_{A}\left(x\right)\:\:\) is 0, indicating that\(\:\:x\) does not belong to A.

2-Tuple fuzzy linguistic approach

2-tuple fuzzy linguistic approach, initially proposed by Herrera and Martinez (2000)45, offers an innovative approach to addressing the fuzziness in decision-making. This model utilizes a 2-tuple (\(\:{s}_{i},\alpha\:\)) to represent linguistic assessment information, where s is a term selected from a predefined set of linguistic terms \(\:S=\{{s}_{0},{s}_{1},{s}_{2},.\:.\:.\:,{s}_{g}\}\), and \(\:\alpha\:\:\)is a numerical value denoting the symbolic translation relative to \(\:{s}_{i}\), In this model, the 2-tuple not only conveys the semantic information of the evaluation, but also contains the quantitative information relative to the central term, that is, the displacement α, which represents the difference between the evaluation and the central term. For example, emergency response capability can be denoted by a set of five terms, \(\:S=\{{s}_{0}\left(VB\right),{s}_{1}\left(B\right),{s}_{2}\left(O\right),{s}_{3}\left(G\right),{s}_{4}\left(VG\right)\}\), corresponding respectively to ‘Very Bad’, ‘Bad’, ‘Ordinary’, ‘Good’, and ‘Very Good’. Each linguistic term is associated with a triangular fuzzy number, and its membership function is shown in Fig. 3; Table 2. Typically, the set of linguistic variables may contain three, five, seven terms, with five being the most common46 .

Fig. 3
figure 3

Glossary of Language Terms and Their Semantic47.

Full size image

Conversion function

The role of the conversion function is to transform traditional fuzzy evaluations, such as those represented by triangular fuzzy numbers, into a 2-tuple representation. This function addresses the issue when an evaluation does not precisely correspond to a preset linguistic label, assigning a numerical form to the subtle differences in the evaluation. Thus, even when the original linguistic labels cannot precisely describe an evaluation, the integrity of all provided information is preserved. With such transformations, decision-makers can handle experts’ evaluations more flexibly, refining the fuzzy decision-making process. The conversion function is defined as follows:

Definition 1

A finite set of linguistic terms, denoted as, where stands as a linguistic label. Define function to acquire the 2-tuple linguistic information corresponding to

$$\:\theta\::S\times\:\left[-\frac{1}{2g},\frac{1}{2g}\right]\to\:{\mathbb{L}}^{2}$$
(9)

Herein, \(\:{\mathbb{L}}^{2}\) denotes the space of 2-tuple linguistic information. For any linguistic label\(\:{s}_{i}\)within the set S, the function\(\:\:\theta\:\:\)can be specifically expressed as:

$$\:\theta\:\left({s}_{i}\right)=\left({s}_{i},0\right),\:{s}_{i}\in\:S$$
(10)

Herein, \(\:\alpha\:\)=0 signifies that the linguistic label remains true to its original connotation within the 2-tuple representation of linguistic information, ensuring the linguistic evaluation of \(\:{s}_{i}\) retains its accuracy.

Definition 2

A finite set of linguistic terms is designated as, where each signifies a specific linguistic term within the set, accompanied by an ordinal index. Within this framework, a mapping function is established to map a singular numerical ___domain onto a 2-tuple linguistic space bounded by.

$$\:\varDelta\:=[0, 1]\to\:\text{S}\times\:[-\frac{1}{{2}_{\text{g}}},\frac{1}{{2}_{\text{g}}}]$$
(11)
$$\:\varDelta\:\left(\beta\:\right)=\left({s}_{i},\alpha\:\right)\text{w}\text{i}\text{t}\text{h}\left\{\begin{array}{ll}{s}_{i}&\:i=\text{r}\text{o}\text{u}\text{n}\text{d}\left(\beta\:\times\:g\right)\\\:\alpha\:=\beta\:-\frac{i}{g}&\:\alpha\:\in\:[-\frac{1}{2g},\frac{1}{2g}]\end{array}\right.$$
(12)

In the design of the mapping function Δ, for each real number \(\:\beta\:\), we first compute \(\:\beta\:\times\:g\) and adopt the strategy of rounding to the nearest integer to determine the index \(\:i\). Subsequently, the calculation of \(\:\varDelta\:\left(\beta\:\right)\) is based on the difference \(\:\alpha\:\) between the index\(\:i\)and the real number \(\:\beta\:\), where \(\:\alpha\:=\beta\:-\frac{i}{g}\), ensuring that \(\:\alpha\:\) falls within the interval \(\:[-\frac{1}{2g},\frac{1}{2g}]\).

Definition 3

Define as a set of linguistic terms, where is a 2-tuple linguistic information with representing the transformation value from a real number to a linguistic term, specifically as follows:

$$\:{\varDelta\:}^{-1}:S\times\:[-\frac{1}{2g},\frac{1}{2g})\to\:\left[0,1\right]$$
(13)
$$\:{\varDelta\:}^{-1}\left[{s}_{i},\alpha\:\right]=\frac{i}{g}+\alpha\:=\beta\:$$
(14)

In the computation of \(\:\beta\:\times\:g\) rounded to the nearest integer to ascertain \(\:i\), where \(\:i\) corresponds to the linguistic term \(\:{s}_{i}\) ; \(\:\alpha\:\) is the difference between \(\:\beta\:\) and \(\:\frac{i}{g}\), with this deviation \(\:\alpha\:\) falling within the interval \(\:[-\frac{1}{2g},\frac{1}{2g}]\).

Definition 4

Method for comparing binary semantic variables — specifically, four rules:

  1. 1.

    If \(\:i<j\), then \(\:\left({s}_{i},{\alpha\:}_{1}\right)\)≤\(\:\left({s}_{j},{\alpha\:}_{2}\right)\) holds true.

  2. 2.

    If \(\:i=j\) and \(\:{\alpha\:}_{1}={\alpha\:}_{2}\), then the two are equal.

  3. 3.

    If \(\:i=j\) and \(\:{\alpha\:}_{1}<{\alpha\:}_{2}\), then \(\:\left({s}_{i},{\alpha\:}_{1}\right)<\left({s}_{j},{\alpha\:}_{2}\right)\) holds true.

  4. 4.

    If \(\:i=j\) and \(\:{\alpha\:}_{1}>{\alpha\:}_{2}\),then \(\:\left({s}_{i},{\alpha\:}_{1}\right)>\left({s}_{j},{\alpha\:}_{2}\right)\) holds true.

Comprehensive evaluation model

(1) Comprehensive evaluation for each standard. The comprehensive evaluation is calculated by the weighted average of binary tuple linguistic variables The formula is as follows:

$$\:{\beta\:}_{i}=\frac{\sum\:_{j=1}^{{n}_{i}}\left({\varDelta\:}^{-1}\left({s}_{ij},{\alpha\:}_{ij}\right)\times\:{w}_{ij}\right)}{\sum\:_{j=1}^{{n}_{i}}{w}_{ij}}=\left({s}_{i},{\alpha\:}_{i}\right)$$
(15)

In the formula, \(\:{\varDelta\:}^{-1}\) is the conversion function, while \(\:{s}_{i}\) and \(\:{\alpha\:}_{i}\) respectively represent the label value and deviation value of the \(\:{i}^{th}\) secondary indicator of the \(\:{j}^{th}\) primary indicator. \(\:{w}_{ij}\) is the weight of the \(\:{j}^{th}\) secondary indicator, and \(\:{\beta\:}_{i}\) is the numerical score after conversion.

(2) Calculate overall emergency response capability

$$\:\begin{array}{ll} \upbeta {= \Delta} \left(\frac{\sum\:_{i=1}^{n}\left[{\varDelta\:}^{-1}\left({s}_{k}^{i},{x}_{k}^{i}\right)\times\:{w}_{i}\right]}{\sum\:_{i=1}^{n}{w}_{i}}\right)=\varDelta\:\left(\frac{\sum\:_{i=1}^{n}\left({\beta\:}_{i}\times\:{w}_{i}\right)}{\sum\:_{i=1}^{\text{n}}{w}_{i}}\right)&\:=\left({s}^{\circ\:},{\alpha\:}^{\circ\:}\right)\end{array}$$
(16)

Where, \(\:{\beta\:}_{i}\text{=}{\varDelta\:}^{-1}\left({s}_{k}^{i},{x}_{k}^{i}\right)\), \(\:{\varDelta\:}^{-1}\) represents the conversion function, and\(\:{\:w}_{i}\) is the weight of the \(\:{i}^{th}\) primary indicator.

Model application

To assess the efficacy and robustness of the urban seismic emergency evaluation framework, an empirical investigation was undertaken in Changchun, Jilin Province. Changchun, the provincial capital and largest metropolis of Jilin, strategically situated in the heart of the Northeast Plain, functions as a pivotal economic nexus in Northeast China. The study area’s geographical positioning, as delineated in Fig. 4, underscores Changchun’s strategic significance. The city is distinguished by its advanced automotive manufacturing, electronic information, and agricultural processing sectors, meriting the designation “China’s City of Automobiles48.

This industrial configuration poses intricate challenges for emergency management amidst seismic events. For example, seismic activity could disrupt supply chains, thereby impacting automotive production lines49. The sophistication of the electronic information sector elevates the requirements for data security and the robustness of information infrastructure.

Moreover, notwithstanding the infrequency of seismic occurrences, Changchun’s high population density engenders unique emergency management challenges, particularly under severe winter conditions. As shown in Fig. 5, the population density in Changchun and its surrounding areas is among the highest in the province. The concentration of population not only complicates disaster evacuation strategies but also imposes heightened demands on the city’s infrastructure capacity50. In densely inhabited regions, the swift and orderly evacuation becomes increasingly challenging, with potential complications such as traffic congestion and the overburdening of public facilities impacting the efficiency of emergency response. Furthermore, the densely built urban environment exacerbates the risk of secondary calamities, such as fires triggered by seismic disturbances. In summary, high population density necessitates more efficient emergency management and rapid response capabilities in Changchun to handle potential emergencies.

Moreover, Changchun boasts a comprehensive transportation infrastructure, including extensive rail, road, and air networks, facilitating efficient transport of emergency supplies and evacuation of personnel. The city’s higher education resources are also robust, Prominent institutions such as Jilin University and Northeast Normal University play significant roles in emergency management research and practice. These institutions provide academic support by training professionals and conducting research related to disaster management. For example, Jilin University has established a specialized Emergency Management Research Center, which focuses on research into disaster emergency management policies, technologies, and strategies. Meanwhile, Northeast Normal University, through its Institute of Disaster Science and Emergency Management, concentrates on emergency education, public safety management, and disaster emergency response mechanisms. These academic institutions provide strong academic support and a talent pool for enhancing the city’s emergency response capabilities. They not only advance theoretical research but also offer scientific foundations and professional guidance for practical emergency management51.

The concentration of medical resources is another advantage for Changchun in responding to emergencies. The city has multiple top-tier hospitals and specialized medical institutions capable of providing timely medical rescue and long-term rehabilitation services in the event of a disaster. These institutions offer critical academic support by training professionals and conducting specialized research in disaster management.

Fig. 4
figure 4

Research area map (The figures (a), (b), and (c) were generated using ArcGIS version 10.8; https://www.esri.com/en-us/arcgis/products/arcgis-desktop/overview ): (a) Map of Changchun’s Geographic Location, (b) Geographical Location Map of Jilin Province. (c) Elevation Map of Changchun City.

Full size image
Fig. 5
figure 5

Population Density Map of Jilin Province (The figure was generated using ArcGIS version10.8; https://www.esri.com/en-us/arcgis/products/arcgis-desktop/overview ).

Full size image

Step 1: A total of 48 questionnaires were distributed to experts from universities in Changchun City, with 45 returned. Using the calculation formula in Eq. (5), the weights were calculated as displayed in Table 3. The overall ranking weight is the product of the primary and secondary indicators.

Step 2: To ensure the collected data’s scientific integrity, rationality, and representativeness, 45 individuals were selected, comprising emergency field university experts, government personnel, and research institute staff, consistent with the experts chosen via the Delphi Method described earlier. The weights determined as per Eqs. (1), (2), and (3) are shown in Table 4.

Step3: The composite weights are calculated based on matrix concepts, referring to Eqs. (6) and (7), as shown in Table 5. and Fig. 6.

Step4: Use the language item ratings shown in Table 3 to evaluate the secondary indicators relative to the primary indicators, and apply Eqs. (11) and (12) to convert them into the corresponding binary semantic groups(\(\:{s}_{ij},{\alpha\:}_{ij}\)), represented as the binary tuple for the \(\:{j}^{th}\) secondary indicator relative to the \(\:{i}^{th}\) primary indicator, the secondary indicator evaluation table and the corresponding binary tuples are shown in Table 6.

Step5: The composite score for each primary indicator and its corresponding binary tuple is calculated using Eq. (15). The processes for calculating capabilities in mitigation, preparedness, response, and recovery are as follows:

$$\:{\beta\:}^{1}=\varDelta\:\left(\frac{0.\:061\times\:1+0.\:059\times\:0.\:75+0.\:056\times\:0.\:75+0.\:057\times\:0.\:75}{0.\:061+0.\:059+0.\:056+0.\:057}\right)=\varDelta\:\left(0.\:816\right)=\left({S}_{3},0.\:066\right)$$
$$\:{\beta\:}^{2}=\varDelta\:\left(\frac{0.\:059\times\:0.\:75+0.\:058\times\:0.\:75+0.\:071\times\:1+0.\:063\times\:0.\:75}{0.\:059+0.\:058+0.\:071+0.\:063}\right)=\varDelta\:\left(0.\:821\right)=\left({S}_{3},0.\:101\right)$$
$$\:{\beta\:}^{3}=\varDelta\:\left(\frac{0.\:069\times\:0.\:75+0.\:064\times\:0.\:75+0.\:058\times\:0.\:75+0.\:074\times\:1}{0.\:069+0.\:064+0.\:058+0.\:074}\right)=\varDelta\:\left(0.\:820\right)=\left({S}_{3},0.\:07\right)$$
$$\:{\beta\:}^{4}=\varDelta\:\left(\frac{0.\:08\times\:0.\:75+0.\:083\times\:1+0.\:086\times\:0.\:75}{0.\:080+0.\:083+0.\:086}\right)=\varDelta\:\left(0.\:833\right)=\left({S}_{3},0.\:083\right)$$

Step 6: Calculate the overall seismic emergency capability using Eq. (16). After organizing, the individual primary indicators and the overall emergency response capability are as shown in Table 7.

Fig. 6
figure 6

Composite Weight Diagram (The figure was generated using Origin software (version 2024b); https://www.originlab.com/ ).

Full size image

The comparative analysis of various capabilities in Changchun City reveals, as shown in Table 7, that the city’s overall performance is slightly above average, demonstrating basic disaster emergency competence. However, longitudinal comparisons indicate that Changchun’s capabilities rank as follows across the four phases: Preparedness Capability > Recovery Capability > Response Capability > Mitigation Capability. Preparedness Capability stands out, primarily reflected in the following aspects: (1)Preparedness Capability: Changchun excels in preparedness Capability, which is evident in the development of emergency plans and the frequency of emergency drills. These measures enhance the city’s ability and efficiency in responding to emergencies.(2)Recovery Capability: Recovery Capability ranks next, primarily demonstrated by the significant GDP growth rate, indicating strong economic resilience in post-disaster recovery. Changchun’s GDP growth rate has been among the top in the nation over the past five years.(3)Response Capability: While Changchun’s response Capability is good, it is slightly lower compared to preparedness and recovery capacities. This performance is mainly reflected in the actual execution of emergency response measures and resource allocation. (4)Mitigation Capability: Mitigation Capability ranks last. Given Changchun’s ___location in Northeast China, where seismic activity is relatively low, there is substantial room for improvement in monitoring and early warning systems, as well as in the enforcement of regulations and policies. Based on these findings, targeted recommendations can be made at national, societal, and individual levels to enhance various aspects of emergency capabilities.

Discussion

This study aims to develop and validate a multidimensional evaluation framework for assessing urban seismic emergency capabilities. The framework covers critical stages from disaster mitigation to recovery, using Changchun as a case study to reveal the city’s overall performance in seismic disaster management. (1) Indicator Selection: The selection of indicators is a core component of this research. By focusing on the four critical stages of mitigation, preparedness, response, and recovery, the study comprehensively addresses the entire spectrum of seismic disaster management. Detailed indicators are established for each stage to ensure the comprehensiveness of the evaluation framework and to systematically assess all aspects of a city’s emergency response capabilities. For instance, the “Monitoring and Early Warning Capability” indicator within the mitigation stage emphasizes the importance of risk identification and information dissemination prior to an seismic event. The “Physical seismic Resistance Capability” focuses on the seismic performance of buildings and infrastructure, which are critical defenses in seismic disaster response. In selecting these indicators, we fully considered Changchun’s geographical ___location, demographic composition, and economic conditions. This localization of indicator settings ensures that the evaluation framework is not only tailored to Changchun but also serves as a customized reference for other similar cities. The framework’s scope, encompassing policy regulations, public education, practical rescue operations, and post-disaster recovery, provides comprehensive guidance for urban managers. (2) Evaluation Methodology: To determine the weights of the indicators, we employed an innovative approach by integrating the Delphi Method with the Coefficient of Variation Method. This hybrid approach incorporates expert subjective judgment while ensuring objective weight distribution through rigorous data analysis. The strength of this approach lies in its ability to balance subjectivity and objectivity, mitigating potential biases inherent in a single method and thus ensuring the scientific rigor and reliability of the evaluation outcomes. Additionally, the incorporation of binary fuzzy linguistic theory to handle uncertain information enhances the precision and adaptability of the evaluation framework, effectively addressing divergent expert opinions and data ambiguities. The application of fuzzy logic allows for more nuanced quantification and analysis of expert assessments, providing more refined decision support for urban emergency management. According to the study by Ju et al.., the use of fuzzy AHP and 2-tuple fuzzy linguistic methods effectively evaluates emergency response Capability and offers detailed quantitative analysis47. Similarly, Kaixuan Qi.‘s research demonstrates that fuzzy linguistic computing improves the evaluation of new product development performance, providing a reliable solution for complex decision-making problems52. Based on the foundations laid by these studies, this paper has innovatively developed a comprehensive, multidimensional evaluation system for assessing urban seismic emergency response capabilities through extensive literature review. (3) Combination of Localization and Universality: We thoroughly considered Changchun’s unique context, such as its geographical ___location, demographic structure, and economic conditions, to set localized indicators. This consideration ensures that the evaluation system accurately reflects the specific situation of Changchun while maintaining flexibility suitable for other cities with similar characteristics. This adaptability broadens the system’s applicability, providing tailored guidance for various cities in their seismic emergency management efforts.

Given the absence of a standardized indicator system for assessing seismic emergency response capabilities, despite Jingwen Han’s efforts to develop a system for measuring and quantifying gaps in seismic preparedness53, the diverse geographical locations and seismic risks of different cities present challenges in establishing a universal evaluation framework. This also highlights some limitations of our indicator system and evaluation methods. The study assesses Changchun’s seismic emergency response capabilities as “slightly above average” overall; however, this conclusion is primarily drawn from relative comparisons within the city, owing to the absence of a unified standard for cross-city comparison. This relative evaluation approach emphasizes internal improvements rather than benchmarking against the competitiveness of other cities.

This study provides a valuable evaluation tool for Changchun and other comparable cities in seismic emergency management. The tool enables cities to identify strengths and weaknesses in their emergency management systems, providing robust decision support for policymakers. By further refining and disseminating this system, we aim to offer more scientifically grounded and effective solutions for global disaster emergency management. Future research should consider employing broader standards and cross-city data to achieve a more universal evaluation. Additionally, quantitative analyses comparing other cities could further validate and expand the findings of this study.

Conclusion

This study developed and validated a comprehensive, multidimensional evaluation system aimed at systematically assessing urban seismic emergency capabilities. Through empirical analysis of Changchun City, we demonstrated the practical effectiveness and scientific rigor of this system. The evaluation system encompasses the four critical stages of mitigation, preparedness, response, and recovery, each characterized by detailed indicators, ensuring a comprehensive assessment of a city’s capabilities in managing seismic disasters.

In selecting the indicators, we incorporated the unique geographical ___location, demographic composition, and economic conditions of Changchun City, ensuring the system’s local adaptability and practical relevance. By innovatively integrating the Delphi Method with the Coefficient of Variation Method, we effectively combined expert subjective judgments with data-driven objective analyses, thereby enhancing the scientific validity, credibility, and operational feasibility of the evaluation results. Furthermore, the incorporation of binary fuzzy linguistic theory to manage uncertain information enables this evaluation system to offer precise and adaptable decision support, even amidst diverse expert opinions and complex data contexts.

The research findings indicate that Changchun City has a strong foundational Capability in seismic emergency management, with the city’s capabilities ranked as follows: Preparedness Capability > Recovery Capability > Response Capability > Mitigation Capability. Based on the strengths and weaknesses identified at each stage, targeted strategies can be proposed at the government, societal, and individual levels to enhance mitigation Capability, while also appropriately strengthening the other three capacities. (1) Government Level: a standardized seismic emergency plan should be developed and tailored by local authorities, with an emphasis on increasing emergency supply reserves and public disaster prevention education. Additionally, building seismic standards should be strengthened, and the seismic monitoring network expanded, particularly focusing on improving mitigation measures. (2) Societal Level: it is important to reinforce community emergency response teams and enhance the seismic resilience of public facilities to reduce seismic damage. (3) Individual Level: households should be encouraged to create clear emergency plans, and basic knowledge of seismic prevention and mitigation should be promoted through community training and online courses, including understanding safe evacuation procedures. Active participation in community disaster drills and awareness activities is also essential to boost preparedness and risk awareness. These strategies aim to comprehensively enhance Changchun City’s mitigation Capability while also strengthening other key areas of seismic emergency management.

Looking ahead, further optimization of the evaluation system should include extensive validation across additional cities and broaden its applicability to other types of natural disaster management. We anticipate that by integrating dynamic data and advanced analytical techniques, this evaluation system will have a broader and deeper impact on urban emergency management globally, providing robust theoretical support and practical guidance for enhancing cities’ disaster response capabilities.

The findings of this study are not only academically innovative and forward-looking but also provide policymakers and urban managers with scientific tools and methodologies. These contributions are crucial for enhancing the overall resilience and adaptive Capability of cities in response to complex natural disasters.

Appendix

See Tables 1, 2, 3, 4, 5, 6 and 7.

Table 1 Indicators and Their Corresponding Meanings.
Full size table
Table 2 Grading Standards for Linguistic Variables.
Full size table
Table 3 Weights Derived from the Delphi Method.
Full size table
Table 4 Weights Derived from the Coefficient of Variation Method.
Full size table
Table 5 Composite Weights.
Full size table
Table 6 Secondary Indicator Evaluation Table and Corresponding 2-Tuples.
Full size table
Table 7 Overall Emergency Capability Evaluation Table.
Full size table