1 Introduction

Since the beginning of the twenty-first century, all kinds of public emergencies frequently occurring have brought great challenges to the global public economy. This kind of public emergency often has a serious impact on the economic operation system. In 2020, sudden outbreak of COVID-19 causes great impact on the economic development of all countries and even the whole world. It has quickly brought serious disruption to the economy and society on an unprecedented scale. Policymakers must assess the scale of economic damage so that they can formulate effective policies to mitigate the economic collapse caused by the pandemic.

Economic resilience refers to the ability of an economy to resist, recover, readjust and create a new growth path after being hit by external shocks [1]. It is an indicator that reflects the ability of the regional economy to withstand shocks (resistance, recovery, adjustment and transformation), which can effectively evaluate the resilience of the regional economy [2]. It has become a popular concept, which offers a new perspective on analyzing difference of regional response under recession shock. In the context of major public emergencies, a timely dynamic evaluation of regional economic resilience can provide an objective basis for economic regulation and control behavior, which is conducive to carrying out macroeconomic adjustments by government economic departments, stabilizing economic order, and efficiently achieving economic development goals.

In terms of evaluation methods, considering the lack of data directly related to major public emergencies, the statistical cycles and calibers of different regions are different, and the data varies greatly in different regions and different periods, so it presents the characteristics of poor information. The conventional and static evaluation method of economic resilience will be limited. For example, core variables method (such as GDP, employment rate, trade volume and other key macroeconomic indicators), special coefficient characterization method (such as economic adaptability, sensitivity coefficient, etc.), entropy weight method (EWM), EWM-TOPSIS method [3], K-means Clustering analysis [4], etc. Therefore, we improve the minimum distance-maximum entropy combination weighting method, comprehensively use grey incidence projection model, fuzzy matter element model, combination weighting model, and dynamic evaluation model, then propose an improved dynamic evaluation model of grey incidence projection- fuzzy matter element. Finally, the model is applied to the dynamic evaluation of regional economic resilience under major public emergencies.

It should be noted that the improved evaluation model can not only be applied to the dynamic evaluation of economic resilience under public emergencies, but also can be widely applied to other research contexts, such as the evaluation of the transformation capability of emergency scientific research results under emergencies, the disaster and calamity evaluation, the evaluation of the risk of emergencies, the screening of optimal solutions for emergencies, the evaluation of the comprehensive performance of complex equipment, etc. The improved model is not only a theoretical model, but also an empirical analysis tool that can be applied and optimized.

For example, the improved model in this paper can be applied to realize the evaluation of the transformation capability of emergency scientific research results under emergencies. Since the data related to the transformation of emergency scientific research results are insufficient, and the data vary greatly and fluctuate significantly, the commonly used evaluation methods such as the entropy weight method (EWM) are no longer applicable, and the improved evaluation model of this paper can be applied. By constructing an evaluation index system for the transformation capability of emergency scientific research results under emergencies, collecting and sorting out relevant data, and applying the improved model in this paper, it is able to obtain the evaluation results of the transformation capability of emergency scientific research results under emergencies. Another example is that the improved model in this paper can be applied to achieve disaster and calamity evaluation. Similarly, due to the lack of relevant data and abnormal data characteristics in the disaster context, the improved evaluation model in this paper can be applied to complete the disaster and calamity evaluation in time to provide reference for the formulation and implementation of subsequent disaster emergency management measures. By constructing a disaster and calamity evaluation index system, collecting and sorting out relevant data, and applying the improved model of this paper, the disaster and calamity evaluation results can be obtained. Moreover, the model in this paper can also be applied to evaluate the comprehensive performance of complex equipment. Complex equipment mostly presents characteristics such as complexity, uncertainty and multi-levelness. The traditional equipment performance evaluation mainly relies on the monofactor analysis method and Delphi method to realize the weight assignment. By forming a pool of experts, the important technical indicators are selected individually item by item and repeatedly tested and compared several times to draw conclusions. The workload is large, inefficient and influenced by human factors. In the actual performance analysis and evaluation, it is extremely difficult to conduct comprehensive evaluation because of its complex structure, involving many indicators and difficult to quantify concretely with numbers. The grey system theory and fuzzy mathematics are the two most active uncertainty system theories at present. The improved evaluation model in this paper combines the advantages of both and can be applied to realize the comprehensive performance evaluation of complex equipment.

To sum up, according to the existing evaluation model, an improved dynamic evaluation model of grey incidence projection-fuzzy matter element is proposed. This paper constructs an evaluation indicator system of area economic resilience under major public emergencies. The improved dynamic evaluation model of grey incidence projection- fuzzy matter element is used to evaluate economic resilience of Hubei province (with its neighboring areas) in context of COVID-19. At the same time, the relative validity of the model is tested based on the empirical evaluation results. The general idea of this paper is as follows: Improve the model (which can be used in different contexts) → Construct the evaluation index system (this paper constructs an evaluation index system for regional economic resilience under public emergencies. Other evaluation index systems can be constructed for different contexts and different evaluation objects) → Empirical case study (this paper takes the COVID-19 epidemic as an example, and selects relevant data in the context of the COVID-19 epidemic to evaluate economic resilience of Hubei province (with its neighboring areas) in context of COVID-19).

In order to achieve the research objectives above, this article is structured as follows: Sect. 2 reviews literature from three aspects: economic resilience, grey incidence projection model and fuzzy matter-element theory. Section 3 describes three basic models, which provide basic method support to improve dynamic evaluation model in this paper. Section 4 illustrates the main process of improvement of minimum distance-maximum entropy combination weighting method. It proposes the calculation steps of the improved dynamic evaluation model of grey incidence projection-fuzzy matter element and the relative validity test steps of the evaluation model. Section 5 selects multiple economic indicators to construct the comprehensive evaluation indexes system of area economic resilience under major public emergencies. Section 6 applies the improved dynamic evaluation model of grey incidence projection- fuzzy matter element to empirically evaluate economic resilience of Hubei province (with its neighboring areas) in context of COVID-19, and tests the relative validity of evaluation model. Section 7 concludes the important findings of this study. Finally, Sect. 8 presents the limitations and possible research directions in the future.

The innovations of this article are reflected in the following aspects. (1) The innovation of evaluation method. Considering the lack of data directly related to major public emergencies, the statistical cycles and calibers of different regions are different, and the data varies greatly in different regions and different periods, so it presents the characteristics of poor information. The conventional and static evaluation method of economic resilience will be limited. Therefore, an improved dynamic evaluation model of grey incidence projection- fuzzy matter element is proposed to evaluate economic resilience under major public healthy emergencies. (2) The innovation of evaluation index system. The major public emergencies have huge impact on economic development and bring complex consequences. It is necessary to combine the characteristics of economic development in the context of public emergencies, and comprehensively select economic resilience evaluation indicators from the five aspects of market, industry, investment, foreign trade, and finance to construct a comprehensive evaluation index system of regional economic resilience under the background of major public emergencies. (3) This paper uses progress data (monthly) to realize the timely evaluation of economic resilience. Different from most existing literates that use annual data, the use of monthly progress data for analysis is more conducive to obtaining the immediate characteristics of regional economic resilience under the impact of emergencies, and provides a reliable basis for efficient, accurate and timely decision-making. (4) It realizes the dynamic evaluation of regional economic resilience under major public healthy emergencies. Different from the static evaluation of area economic resilience in the existing literates, the dynamic evaluation results can more objectively reflect the change trend and evolution law of regional economic resilience under public emergencies.

2 Literature review

2.1 Economic resilience

The economic resilience reflects the ability of the regional economy to cope with shocks from external events. It mainly consists of four aspects, namely, resistance (the degree of sensitivity and response of the regional economy to external shocks), restorability (the speed and degree of recovery of the regional economy from external shocks), adaptability (the ability of the regional economy to readjust the structure of industries, technology, labor force, etc. in the face of external shocks) and the ability to create economic growth paths (the ability of the regional economy to open new and stable growth paths after a shock). Most of the existing related studies of economic resilience focus on five aspects, including connotation definition, regional evaluation measurement, regional spatial differences, influencing factors, and the influence mechanism of individual factors on economic resilience.

Among them, most of the economic resilience evaluation methods are core variables method (such as GDP, employment rate, trade volume and other key macroeconomic indicators), special coefficient characterization method (such as economic adaptability, sensitivity coefficient, etc.), entropy weight method (EWM), EWM-TOPSIS method, etc. For example, T.B. Yang et al. measured the economic resilience of urban agglomerations with the regional economic resistance index measured by GDP [5]. Mao et al. measured urban economic resilience by the performance difference of the sensitivity of core economic indicators at the city level [6]. Huang et al. constructed the index system of economic resilience into resistance and recovery ability, adaptation and adjustment ability, innovation and transformation ability, and used the entropy weight method to calculate the economic resilience of eight urban agglomerations in China [7]. Fan et al. defined economic resilience from three dimensions: resistance and resilience, adaptation and adjustment, innovation and transformation, and finally calculated the economic resilience index by using the entropy weight TOPSIS method [8]. These methods are usually based on a large amount of data, accurate data, and refined data. However, under public emergencies, there are often insufficient relevant data, abnormal data characteristics, and limited data timeliness. The above methods are then not applicable to the evaluation of economic resilience under emergency event shocks. Therefore, it is necessary to construct a new evaluation model to effectively solve the problems of insufficient data, abnormal data characteristics, limited data timeliness, and excessive data fluctuations, so as to achieve the scientific evaluation of economic resilience under emergencies and improve the reliability of evaluation results.

2.2 Grey incidence projection model

The grey system theory is a new method to analyze the problem of less data and poor information uncertainty. The theory is based on the “less data” and “poor information” uncertainty system with “partial information is consistent and partial information is unknown”. It mainly extracts valuable information from the “partial” known information, realizes the correct description and effective monitoring of system's operational behavior and evolutionary laws [9].

After more than 30 years of development, the grey system theory has established a structural system of emerging disciplines. Its main contents include the basic theory of grey system such as grey number operation and grey algebra system, grey equation; sequence operator and grey information mining method; a series of grey incidence analysis models; multiple grey clustering evaluation models for classification problems; grey prediction models and grey prediction methods, etc.

Among them, grey incidence projection model is a new method to discuss multi-objective decision-making from the perspective of vector projection. Its principle is to determine the fit degree (deviation degree) between the evaluation sample and the ideal value according to the size of the evaluation sample’s projection value on the ideal sample, as the standard to evaluate the quality of the sample. This method has advantages in multi-objective grey evaluation and decision-making. The existing literature mainly focuses on model improvement, model application and model combination. For example, Zang et al. use the centralized trend measurement and discrete trend measurement in descriptive statistics and introduce the expression advantage of the probabilistic multi-valued neutrosophic numbers to construct the distance formula of probabilistic multi-valued neutrosophic statistical distance, on this basis, the paper combines compromise idea and bidirectional projection technology to propose the grey compromise bidirectional projection decision-making method based on the probabilistic multivalued neutrosophic statistical distance [10]. Fan et al. make a dynamic comprehensive evaluation of technological innovation capability of high-tech industries based on TOPSIS-grey incidence projection method [11]. Nan et al. construct an evaluation index system of management model selection for energy storage on grid side according to the industry development stage and the characteristics of the project. On this basis, three theories of TOPSIS method, grey incidence analysis method and vector projection method are applied to establish the project management mode selection model of energy storage on grid side based on TOPSIS grey incidence projection method [12].

2.3 Fuzzy matter-element model

The fuzzy matter-element model is mainly used to solve the problem of multiple incompatible, fuzzy and uncertain factors [13]. It has been widely applied in comprehensive evaluation. The existing literature mainly focuses on model improvement and model application. For example, based on the connotation of marine economic resilience, Wang’s study constructed the evaluation index system from the aspects of resistance, recovery capability, reorganization capability and innovation capability, used the fuzzy matter element evaluation model to calculate the marine economic resilience of 11 provinces in China [14]. Liang et al. combined with the grey system theory, improved Euclid approach degree which describes the similar degree between the sample to be evaluated and standard sample in the fuzzy matter-element analysis method, and used the projection value of the sample to be evaluated on the standard sample to make a comprehensive evaluation [15]. In the study of Xu et al. a tourism ecological safety evaluation index system is constructed based on the DPSIR model, and the dynamic evaluation of tourism ecological safety in 31 provinces (municipalities and districts) of China (excluding Hong Kong, Macao and Taiwan) is carried out using the fuzzy matter-element model [13].

In conclusion, this paper improves the evaluation model (universal and applicable to different contexts) based on the grey system theory and fuzzy matter element theory, and constructs the economic resilience evaluation index system to realize the scientific evaluation of regional economic resilience under emergencies. On the one hand, it is conducive to enriching the research results of grey system theory, fuzzy matter element model, economic resilience and other related fields. On the other hand, it is conducive to providing reference basis for economic macro adjustment, better realizing the management and planning of economic resilience.

3 Basic theoretical model

3.1 Combination weighting method

There are four typical models of subjective and objective combination weighting method, including addition synthesis method, multiplication synthesis method, level difference maximization method and objective modification subjective method. Among them, the most commonly used methods are additive synthesis method and multiplication synthesis method.

3.2 Fuzzy matter element analysis

As the basic element of describing things, “fuzzy matter element” is a ternary ordered group, which is mainly composed of three elements: “thing”, “feature” and “fuzzy value”. Let \(R\) represent “fuzzy matter element”, \(M\) represent “thing”, \(C\) represent “feature”, and \(x\) represent “fuzzy value” corresponding to feature \(C\), then, the fuzzy matter element could be presented as follows:

$$R = \left[ {\begin{array}{*{20}c} {} & M \\ C & x \\ \end{array} } \right]$$

If a thing \(^{\prime}M^{\prime}\) has \(k\) features (\(^{\prime}C_{1} ,C_{2} , \ldots ,C_{n} ^{\prime}\)), whose corresponding fuzzy values are \(^{\prime}x_{1} ,x_{2} , \ldots x_{n} ^{\prime}\), the \(u_{{i_{0} j_{0} }}^{(k)}\)-dimension fuzzy-matter element \(^{\prime}R_{n} ^{\prime}\) is formed. If there are \(r_{ij}^{(k)} = \frac{{u_{ij}^{(k)} - u_{{i_{0} j_{0} }}^{(k)} }}{{\mathop {\max }\limits_{i} \mathop {\max }\limits_{j} \left\{ {u_{ij}^{(k)} } \right\} - u_{{i_{0} j_{0} }}^{(k)} }}\) things (\(^{\prime}M_{1} ,M_{2} , \ldots ,M_{m} ^{\prime}\)) in total and each thing has the same \(n\) features (\(^{\prime}C_{1} ,C_{2} , \ldots ,C_{n} ^{\prime}\)), then the \(n\)-dimension composite fuzzy-matter element \(^{\prime}R_{mn} ^{\prime}\) of \(m\) things is formed.

The fuzzy matter element model is a simple and effective method for judging fuzzy things, whose result is determined, and can effectively solve the incompatibility among individual indicators. The main steps are as follows [16]: (1) Construct a fuzzy matter element \(R_{mn}\). (2) Standardize the fuzzy value, and obtain the fuzzy matter element \(\mathop {R_{mn} }\limits^{\sim }\) with the optimal subordinate degree. (3) Construct the standard fuzzy matter element \(R_{0n}\). (4) Calculate the Euclid approach degree of \(\mathop {R_{mn} }\limits^{\sim }\) and \(R_{0n}\) for comprehensive evaluation.

3.3 Grey incidence projection method

Grey incidence projection is a new method, which mainly discusses multi-objective decision-making from the perspective of vector projection [17]. This method has advantages in solving multi-objective grey evaluation and decision-making. The steps are as follows: (1) Establish the sample matrix and initial it. (2) Construct the grey incidence judgment matrix. (3) Determine the weight of grey incidence projection. (4) Calculate the grey incidence projection value.

4 The improved dynamic evaluation model of grey incidence projection- fuzzy matter element

Evaluation behavior generally involves “thing” (i.e., evaluation object), “feature” (i.e., evaluation index) and quantity value (i.e., index data). It is believed that evaluation analysis is based on “matter element”. Under the background of major public emergencies, the statistical calibers of the evaluation objects are inconsistent, the short-term progress data is less, at the same time, the accuracy of data is adversely affected by the shock of the emergency. The value of the matter element is “fuzzy” and shows characteristic of “poor information”, so that the evaluation system belongs to “fuzzy matter element”. Therefore, the model of grey incidence projection- fuzzy matter element is used to evaluate regional economic resilience under major public emergencies, which is in line with the evaluation characteristics and requirements. At the same time, in the evaluation process, the value of fuzzy matter element is changing dynamically, so there are many fuzzy matter elements in the evaluation cycle. Each fuzzy matter element corresponds to a certain evaluation stage and a group of static evaluation results \(S_{j}\), and multiple fuzzy matter elements in different stages correspond to a set of dynamic evaluation results \(L_{j}\) (as shown in Fig. 1).

Fig. 1
figure 1

The static and dynamic evaluation logic of fuzzy matter element

Full size image

Based on an analysis of the existing model limitation [15], considering the interaction of evaluation indicators, dynamic fluctuation of index value and subjective–objective comprehensive evaluation, this paper improves the minimum distance-maximum entropy combination weighting method, and finally puts forward an improved dynamic evaluation model of grey incidence projection- fuzzy matter element. It should be noted that the improved evaluation model can not only be applied to the dynamic evaluation of economic resilience under public emergencies, but also can be widely applied to other research contexts. The improved model is a universal evaluation model that can be used in different situations. The difference only lies in the fact that different evaluation index systems need to be constructed in different contexts.

4.1 The improvement of minimum distance- maximum entropy combination weighting method

The original data of indexes need to be dimensionless. The target standardization method is selected to process the data of index dimensionless to eliminate the influence of the original indicator unit and its order of magnitude (due to factors such as regional size), and the formula is as follows:

$$x_{ij}^{*} = \left\{ {\begin{array}{*{20}c} {\frac{{x_{ij} }}{{x_{0j} }},\quad x_{ij} {\text{ is the positive index}}} \\ {\frac{{x_{0j} }}{{x_{ij} }},\quad x_{ij} {\text{ is the inverse index}}} \\ {\frac{1}{{1 + \left| {x_{ij} - x_{0j} } \right|}},\quad x_{ij} {\text{ is the moderate index}}} \\ \end{array} } \right.$$
(1)

Among them, \(x_{ij}\) is the original index data, \(x_{0j}\) is the ideal value of indicator, \(x_{ij}^{*}\) is index data after dimensionless processing, \(i\) represents the ordinal number of evaluation indexes(\(i = 1,2, \ldots ,n\)),\(j\) means the ordinal number of evaluation objects (\(j = 1,2, \ldots ,m\)).

4.1.1 Analytic network process method (ANP)

ANP has been found to be one of the most effective decision-making evaluation techniques, which is an evaluation method with complex structure, and there are feedback and dependence within the structure level [18]. Since it allows multiple indicators that are quantifiable or difficult to quantify to coexist, ANP reflects and describes the decision-making problem more realistically.

4.1.2 Coefficient of variation weighting method

It is an objective and diversity-based weighting method, which completes the index weighting according to the index difference and is widely used in risk assessment and decision-making [19, 20]. The basic principle is as follows: in the evaluation index system, the indexes with greater difference in value, that is, the indexes that are more difficult to achieve, can better reflect the differences of the evaluation objects.

4.1.3 Indicator difficulty ratio weighting method

The indicator difficulty ratio weighting method is based on the improvement difficulty of the evaluation index, and uses the deviation degree between the maximum and the average of the index data to express the improvement difficulty. Generally speaking, it is relatively difficult to improve the key indicators. The index with greater improvement difficulty has greater distinction degree of the evaluation object. When this index has greater weight, the distinction degree of the comprehensive evaluation result can be improved.

4.1.4 Improved minimum distance-maximum entropy combination weighting method

Based on the relevant literature [21], the weights \(w_{i}^{q} \left( {q = 1,2,3} \right)\) are obtained separately by using ANP, coefficient of variation weighting method, and indicator difficulty ratio weighting method, then, the improved combination weights are as follows:

$$w_{i} = \sum\limits_{q = 1}^{3} {\lambda_{q} w_{i}^{q} }$$
(2)

where, \(\lambda_{q}\) is the combination coefficient \(\left( {\sum\limits_{q = 1}^{3} {\lambda_{q} = 1} } \right)\) and \(w_{i}^{q}\) is the weight of the \(i{\text{ - th}}\) evaluation index obtained by the \(q{\text{ - th}}\) weighting method. Considering the “distance” and “entropy” comprehensively, determine the combination coefficient \(\lambda_{q}\):

  1. (1)

    The generalized distance between the weighted value(for each evaluation object) and the ideal point is the minimum,

    $$\min \sum\limits_{j = 1}^{m} {d_{i} = \sum\limits_{j = 1}^{m} {\sum\limits_{i = 1}^{n} {\sum\limits_{q = 1}^{3} {\lambda_{q} w_{i}^{q} \left( {1 - x_{ij}^{*} } \right)} } } }$$
    (3)
  2. (2)

    In order to avoid individual single weighting method being removed because of its little contribution to the combination weighting result, the principle of maximum entropy is introduced. Based on the principle of maximum consistency of the weighting results, the objective function is constructed,

    $$\max H = - \sum\limits_{q = 1}^{3} {\lambda_{q} \ln \lambda_{q} }$$
    (4)

The programming model is constructed based on the above two aspects:

$$\begin{gathered} \min \left[ {\mu \sum\limits_{j = 1}^{m} {\sum\limits_{i = 1}^{n} {\sum\limits_{q = 1}^{3} {\lambda_{q} w_{i}^{q} \left( {1 - x_{ij}^{*} } \right) + \left( {1 - \mu } \right)\sum\limits_{q = 1}^{3} {\lambda_{q} \ln \lambda_{q} } } } } } \right] \hfill \\ s.t.\left\{ \begin{gathered} \sum\limits_{q = 1}^{3} {\lambda_{q} = 1} \hfill \\ \lambda_{q} \ge 0 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$
(5)

where, the parameter \(\mu\)(\(0 < \mu < 1\)) represents the balance coefficient between the two objectives (minimum distance and maximum entropy), which is usually taken as \(\mu = 0.5\), and \(x_{ij}^{*}\) is the value after dimensionless processing of the index data of each evaluation object.

By solving this model, the optimal solution \(\lambda_{q}\) of combination coefficient can be obtained. Substituting the solved \(\lambda_{q}\) into the formula (2), so as to obtain the minimum distance-maximum entropy combination weight of each evaluation index.

4.2 Static evaluation model of grey incidence projection-fuzzy matter element

Based on grey incidence projection model and fuzzy matter element analysis model, combined with the improved minimum distance-maximum entropy combination weighting method, an improved static evaluation model of grey incidence projection- fuzzy matter element is proposed. The main analysis steps are as follows:

  1. (1)

    Construct the fuzzy matter element \(R_{mn}\),

    $$R_{mn} = \left[ {\begin{array}{*{20}c} {} & {M_{1} } & \cdots & {M_{j} } & \cdots & {M_{m} } \\ {C_{1} } & {x_{11} } & \cdots & {x_{j1} } & \cdots & {x_{m1} } \\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {C_{i} } & {x_{1i} } & \cdots & {x_{ji} } & \cdots & {x_{mi} } \\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {C_{n} } & {x_{1n} } & \cdots & {x_{ji} } & \cdots & {x_{mn} } \\ \end{array} } \right]$$
    (6)

There are \(m\) evaluation objects (\(^{\prime}M_{1} ,M_{2} , \ldots ,M_{m} ^{\prime}\)) and \(n\) features (i.e. evaluation indexes, \(C_{1} ,C_{2} , \cdots ,C_{n}\)), forming the \(n\)-dimension composite fuzzy-matter element \(R_{mn}\) of \(m\) evaluation objects.

  1. (B)

    Standardize the fuzzy value \(x_{ji}\), and construct the fuzzy matter element \(\mathop R\limits^{\sim }_{mn}\) with optimal subordinate degree,

    $$\mathop R\limits^{\sim }_{mn} = \left[ {\begin{array}{*{20}c} {} & {M_{1} } & \cdots & {M_{j} } & \cdots & {M_{m} } \\ {C_{1} } & {\mu_{11} } & \cdots & {\mu_{j1} } & \cdots & {\mu_{m1} } \\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {C_{i} } & {\mu_{1i} } & \cdots & {\mu_{ji} } & \cdots & {\mu_{mi} } \\ \vdots & \vdots & \cdots & \vdots & \cdots & \vdots \\ {C_{n} } & {\mu_{1n} } & \cdots & {\mu_{ji} } & \cdots & {\mu_{mn} } \\ \end{array} } \right]$$
    (7)

where, \(\mu_{ji}\) means the standardization result of fuzzy value \((j = 1,2, \ldots m;i = 1,2, \ldots ,n)\).

  1. (C)

    Construct the standard fuzzy matter element \(R_{0n}\). Let \(\mu_{0i} = \max \left\{ {\mu_{1i} ,\mu_{2i} , \cdots ,\mu_{mi} } \right\}\)\(\left( {i = 1,2, \cdots ,n} \right)\), that means, the maximum value of standardized value of the \(i - {\text{th}}\) index of all evaluation objects. On this basis, the standard n-dimension fuzzy matter element could be obtained as \(R_{0n}\):

    $$R_{0n} = \left[ {\begin{array}{*{20}c} {} & {M_{0} } \\ {C_{1} } & {\mu_{{{0}1}} } \\ {C_{2} } & {\mu_{{{02}}} } \\ \vdots & \vdots \\ {C_{n} } & {\mu_{{{0}n}} } \\ \end{array} } \right]$$
    (8)

    where ξ means the distinguishing coefficient. It is usually taken as ξ = 0.5.

  2. (D)

    Construct the grey incidence judgment matrix \(R^{*}\). The degree of grey incidence \(r_{ij}\) between \(\mathop R\limits^{\sim }_{mn}\) and \(R_{0n}\) is calculated, and the grey incidence judgment matrix \(R^{*} = (r_{ij} )_{n \times m}\) is constructed.

    $$r_{ij} = \frac{{\mathop {\min }\limits_{n} \mathop {\min }\limits_{m} \left| {\mu_{0i} - \mu_{ji} } \right| + \xi \mathop {\max }\limits_{n} \mathop {\max }\limits_{m} \left| {\mu_{0i} - \mu_{ji} } \right|}}{{\left| {\mu_{0i} - \mu_{ji} } \right| + \xi \mathop {\max }\limits_{n} \mathop {\max }\limits_{m} \left| {\mu_{0i} - \mu_{ji} } \right|}},i = 1,2, \ldots ,n;j = 1,2, \ldots ,m$$
    (9)

    where ξ means the distinguishing coefficient. It is usually taken as ξ = 0.5.

  1. (E)

    Determine the weight \(\overline{w}_{i}\) of grey incidence projection. The combination weight \(W = (w_{1} ,w_{1} , \cdots ,w_{n} )^{T}\) is obtained by the improved minimum distance- maximum entropy combination weighting method. Then, the improved grey incidence projection weight is \(\overline{W} = (\overline{w}_{1} ,\overline{w}_{2} , \cdots ,\overline{w}_{n} )\),

    $$\overline{w}_{i} = \frac{{w_{i}^{2} }}{{\sqrt {\sum\limits_{i = 1}^{n} {w_{i}^{2} } } }}(i = 1,2,...,n)$$
    (10)

The angle \(\theta_{j}\) between \(M_{0}\)(the standard fuzzy matter element ideal sample) and \(M_{j}\)(the fuzzy matter element individual sample) is called grey incidence projection angle. The cosine value of this angle is as follows:

$$\cos \theta_{j} = \frac{{M_{j} \cdot M_{0} }}{{\left| {M_{j} } \right| \cdot \left| {M_{0} } \right|}} = \frac{{\sum\limits_{i = 1}^{n} {w_{i} r_{ij} w_{i} } }}{{\sqrt {\sum\limits_{i = 1}^{n} {(w_{i} r_{ij} )^{2} } } \cdot \sqrt {\sum\limits_{i = 1}^{n} {w_{i}^{2} } } }} \, (i = 1,2, \ldots ,n;j = 1,2, \ldots ,m)$$
(11)
  1. (F)

    Calculate the grey incidence projection value \(S_{j}\). Considering the modulus and angle cosine value comprehensively, the projection value of \(M_{j}\)(fuzzy matter element individual sample) on \(M_{0}\)(standard fuzzy matter element ideal sample) is obtained as follows:

    $$S_{j} = d_{j} \cdot \cos \theta_{j} = \sum\limits_{i = 1}^{n} {w_{i} r_{ij} w_{i} /\sqrt {\sum\limits_{i = 1}^{n} {w_{i}^{2} } } = } \sum\limits_{i = 1}^{n} {r_{ij} \overline{w}_{i} } \, (i = 1,2, \ldots ,n;j = 1,2, \ldots ,m)$$
    (12)

The larger the grey incidence projection value, the closer the evaluation sample is to the ideal sample. According to the projection value, the static comprehensive evaluation can be carried out.

4.3 Dynamic evaluation model of grey incidence projection-fuzzy matter element

The key problem of dynamic comprehensive evaluation is to determine the weight of time series. The time series weighted average operator is used for twice weighting, so as to highlight the influence of time on the basis of static evaluation, and then the dynamic comprehensive evaluation of each evaluation object in the time interval \(\left[ {1,h} \right]\) is carried out. The steps are as follows:

  1. (1)

    Obtain the static evaluation value \(S_{j} \left( t \right)\) of the \(j{\text{ - th}}\) evaluated object at time \(t\) from the static evaluation.

  2. (2)

    Determine the weight of time series. Let the weighting vector of time series be \(w_{t} :w_{t} = \left( {w_{1} ,w_{2} , \cdots ,w_{h} } \right)^{T}\), and \(w_{t}\) can be obtained by solving the following nonlinear programming problems:

    $$\begin{gathered} \max \left( { - \sum\limits_{t = 1}^{h} {w_{t} \ln w_{t} } } \right) \hfill \\ s.t.\left\{ \begin{gathered} \sum\limits_{t = 1}^{h} {\frac{h - t}{{h - 1}}w_{t} = \theta } \hfill \\ \sum\limits_{t = 1}^{h} {w_{t} = 1} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$
    (13)

where, the parameter \(\theta\) indicates the importance of time, and the specific values are shown in Table 1.

Table 1 The importance of time
Full size table
  1. (C)

    Using time series weighted average operator, the static evaluation value \(S_{j} \left( t \right)\) is twice weighted, and the dynamic evaluation value of grey incidence projection- fuzzy matter element is obtained as follows:

    $$L_{j} = A\left( {\left\langle {1,S_{j} \left( 1 \right)} \right\rangle ,\left\langle {2,S_{j} \left( 2 \right)} \right\rangle , \cdots ,\left\langle {h,S_{j} \left( h \right)} \right\rangle } \right) = \sum\limits_{t = 1}^{h} {S_{j} \left( t \right)} \cdot w_{t}$$
    (14)

In summary, the calculation steps of the improved dynamic evaluation model of grey incidence projection-fuzzy matter element are as follows (as shown in Fig. 2): (1) Set the fuzzy matter element \(R_{mn}\); (2) Standardize the fuzzy value \(x_{ji}\), and set the fuzzy matter element \(\mathop R\limits^{\sim }_{mn}\) with optimal subordinate degree;(3)Construct the standard fuzzy matter element \(R_{0n}\);(4) Construct the grey incidence judgment matrix \(R^{*}\); (5) Obtain the combination weight \(w_{i}\) by the improved minimum distance- maximum entropy combination weighting method;(6) Determine the weight \(\overline{w}_{i}\) of grey incidence projection;(7) Calculate the grey incidence projection value \(S_{j} \left( t \right)\), which is the static evaluation value of the evaluated object \(M_{j}\) at time \(^{\prime}t^{\prime}\);(8) Determine the weight of time series \(w_{t}\);(9) Obtain the dynamic evaluation value \(L_{j}\) of grey incidence projection- fuzzy matter element.

Fig. 2
figure 2

The calculation steps of the improved dynamic evaluation model of grey incidence projection-fuzzy matter element

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4.4 The relative validity test of the evaluation model

Based on the evaluation value and ranking results obtained by the above model, the relative validity measurement method of the model [21] is used to test the relative effectiveness of the improved dynamic evaluation model of grey incidence projection- fuzzy matter element. The steps are as follows:

  1. (1)

    The Spearman coefficient of rank correlation is used to calculate the coefficient of rank correlation of evaluation results obtained by different evaluation models:

    $$K_{uv} = 1 - \frac{{6\sum\limits_{i = 1}^{n} {f_{i}^{2} } }}{{n(n^{2} - 1)}},u = 1,2, \ldots ,o;v = 1,2, \ldots ,o;v \ne u$$
    (15)

where, \(u\) is the ordinal number of evaluation model, \(K_{uv}\) is the rank correlation coefficient of the ranking results of the \(u{\text{ - th}}\) and \(v{\text{ - th}}\) evaluation model, and \(f_{i}\) is the ranking gap of the \(i{\text{ - th}}\) evaluation object based on the ranking results of the \(u{\text{ - th}}\) and \(v{\text{ - th}}\) evaluation model. Let \(J_{iu}\)(\(J_{iv}\)) represent the ranking of the \(i{\text{ - th}}\) evaluation object in the ranking results of the \(u{\text{ - th}}\)(\(v{\text{ - th}}\)) evaluation model, then \(f_{i} = J_{iu} - J_{iv}\). The average coefficient of rank correlation between the ranking results of the \(u{\text{ - th}}\) evaluation model and the ranking results of other evaluation models can be further calculated, namely the similarity degree of the evaluation results obtained by the evaluation model (the higher the similarity degree, the more effective the evaluation model is compared with other evaluation models):

$$K_{u} = \frac{1}{o - 1}\sum\limits_{u = 1,u \ne v}^{o} {K_{uv} ,u = 1,2, \ldots ,o;v = 1,2, \ldots ,o;v \ne u}$$
(16)
  1. (B)

    Calculate the dispersion of the comprehensive evaluation model:

    $$P_{u} = \frac{1}{o - 1}\sum\limits_{u = 1,u \ne v}^{o} {\sum\limits_{i}^{n} {\left| {J_{iu} - J_{iv} } \right|} } ,u = 1,2, \ldots ,o;v = 1,2, \ldots ,o;v \ne u$$
    (17)

The higher the dispersion of the evaluation model, the greater the difference between the ranking results of this evaluation model and other evaluation models, and the lower the relative validity of the evaluation model.

  1. (C)

    Proceed dimensionless processing on the similarity degree and dispersion of each evaluation model obtained above (this paper adopts extremum processing method, similarity degree \(K_{u}\) is a positive index, and dispersion \(P_{u}\) is an inverse index), and add the dimensionless processing results together to get the relative validity score of the evaluation model.

5 The evaluation index system of regional economic resilience under major public emergencies

At present, there is no unified consensus on the definition of the connotation of economic resilience. Most research scholars believe that the so-called economic resilience refers to the ability of an economy to effectively respond to external disturbances, resist external shocks, and achieve sustainable economic development by adjusting its economic structure and growth mode. There are mainly two ways to measure economic resilience, including comprehensive index method and core variable method [22]. The comprehensive index method is to measure economic resilience by building a comprehensive index system [23]. The core variable method is to select or construct a single variable that can directly reflect the strength of economic resilience to measure [24]. The core variable method does not reflect the different dimensions of “resilience”, and the core variable cannot be decomposed, so there is a lack of comprehensiveness.

As the consequences of major public emergencies are serious and complex, which have a lot of impacts on regional economic development, it is more suitable to select the comprehensive index method to evaluate economic resilience under major public health emergencies. At the same time, in the context of major public health emergencies, the statistical caliber and cycle of monthly progress data in various regions are different. Some districts only publish quarterly data, not monthly progress data. Therefore, according to the principle of index system construction- “systematic, typical, dynamic, scientific, operable, and comprehensive”, through the rigorous index system construction process, the primary index set and the optimized index set are gradually obtained. Then, combining the availability of progress data (monthly), the index set is revised and improved after discussing with experts and teams. Finally, the comprehensive evaluation index system of regional economic resilience under major public emergencies is constructed, as shown in Table 2. Due to the limited space, the more specific construction process, selection basis and connotation explanation of the index system can be obtained by contacting the author.

Table 2 The comprehensive evaluation index of regional economic resilience in context of major public emergencies
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6 Empirical analysis

6.1 6.1 Research object and data source

Since the outbreak of COVID-19, China has conducted scientific prevention and control, actively treated COVID-19 patients, effectively fought the epidemic and formed a scientific anti-epidemic model, thus provides valuable experience for the global fight against COVID-19. The sudden outbreak of COVID-19 not only poses a serious threat to the health and safety of Chinese people, but also influences the national economic development significantly, resulting in huge losses. Under the above background, this paper separately evaluates the economic resilience of Hubei province (with its adjacent areas) by using the improved dynamic evaluation model of grey incidence projection- fuzzy matter element. Hubei is the “epicenter” of this epidemic in China. Its economy has suffered the most severe damage and also causes great economic fluctuations in neighboring areas. The restoration and revitalization in this region are facing great challenges. Therefore, it’s typical to analyze the economic resilience of Hubei province (with its adjacent areas).

In summary, based on above comprehensive evaluation index system of regional economic resilience under major public emergencies, we use the improved dynamic evaluation model of grey incidence projection- fuzzy matter element, and choose Hubei province (with its adjacent areas) to be the research objects. The relevant data of each province from February 2020 (large-scale outbreak of the epidemic in China) to May 2020 (the epidemic in China is basically under control, and the epidemic prevention, control and treatment work of the epidemic has shown the normalization trend) is collected and sorted out.

In order to accurately evaluate the regional economic resilience under the background of the COVID-19, the progress data (monthly) in this paper coming from the official websites of the national and local statistical bureaus are used to ensure reliability, authenticity and timeliness of data. In addition, Matlab2017 software is used in this paper for data operation analysis.

6.2 Results and discussion

6.2.1 Static evaluation

Hubei province and its adjacent areas include 6 provinces: Anhui, Jiangxi, Henan, Hubei, Hunan and Shaanxi. Combined with the evaluation index system of regional economic resilience under major public healthy emergencies (as shown in the Table 2), the fuzzy matter element \(R_{6,7}\)Footnote 1 is constructed:

$$R_{6,7} = \left[ {\begin{array}{*{20}c} {} & {M_{1} } & {M_{2} } & {M_{3} } & {M_{4} } & {M_{5} } & {M_{6} } \\ {C_{1} } & {100.8} & {101.100} & {100.900} & {102.300} & {100.900} & {101.200} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {C_{6} } & {207.898} & {116.100} & {472.560} & {126.800} & {145.045} & {290.730} \\ {C_{7} } & {0.901} & {0.527} & {0.368} & {0.108} & {0.425} & {0.318} \\ \end{array} } \right]$$
(18)

where, \(M_{1} \sim M_{6}\) represent Anhui, Jiangxi, Henan, Hubei, Hunan and Shaanxi respectively, and \(C_{1} \sim C_{7}\) represent the evaluation indexes (Table 2).

The fuzzy value of fuzzy matter element is standardized to construct \(\mathop R\limits^{\sim }_{6,7}\) with optimal subordinate degree:

$$\mathop R\limits^{\sim }_{6,7} = \left[ {\begin{array}{*{20}c} {} & {M_{1} } & {M_{2} } & {M_{3} } & {M_{4} } & {M_{5} } & {M_{6} } \\ {C_{1} } & {1.000} & {0.769} & {0.909} & {0.400} & {0.909} & {0.714} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {C_{6} } & {0.440} & {0.246} & {1.000} & {0.268} & {0.307} & {0.615} \\ {C_{7} } & {1.000} & {0.585} & {0.409} & {0.120} & {0.472} & {0.353} \\ \end{array} } \right]$$
(19)

According to the construction principle of standard fuzzy matter element, the standard fuzzy matter element \(R_{0,7}\) is set. As formula (9), the degree of grey incidence between fuzzy matter element \(\mathop R\limits^{\sim }_{6,7}\) with optimal subordinate degree and standard fuzzy matter element \(R_{0,7}\) is calculated. As shown in Table 3.

Table 3 The degree of grey incidence between \(\mathop R\limits^{\sim }_{6,7}\) and \(R_{0,7}\)
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According to the improved minimum distance- maximum entropy combination weighting method, the combination weights \(w_{i} (i = 1,2, \ldots ,7)\) of indexes \(C_{1} \sim C_{7}\) can be calculated (Table 4).

Table 4 The combination weights \(w_{i}\) (for Hubei province and its adjacent areas)
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On the basis of formula (10), the weights \(\overline{w}_{i} (i = 1,2, \ldots ,7)\) of grey incidence projection can be determined, which is shown in Table 5.

Table 5 The weights \(\overline{w}_{i}\) of grey incidence projection (for Hubei province and its adjacent areas)
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According to formula (12), the grey incidence projection value \(S_{j} \left( t \right) \, (j = 1,2, \ldots ,6;t = 2,3, \ldots ,6)\) can be calculated, which is the static evaluation result (as shown in Table 6). In order to analyze the static evaluation results more intuitively, so as to find the rules and differences, Fig. 3 is drawn according to Table 6.

Table 6 Static evaluation result of economic resilience in Hubei province and its adjacent areas
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Fig. 3
figure 3

Static evaluation result of economic resilience in Hubei province and its adjacent areas

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In accordance with Table 6 and Fig. 3, in the static evaluation result of economic resilience in Hubei province and its adjacent areas under the background of COVID-19, the ranking of economic resilience average value (from February to May) is as follows: Hunan (0.320), Jiangxi (0.283), Shaanxi (0.246), Anhui(0.232), Henan (0.211), Hubei (0.166). Where, the economic resilience of Hunan is generally strong with an inverted U-shaped trend; the economic resilience of Jiangxi is second only to Hunan and continues to rise; the economic resilience of Shaanxi and Anhui show the U-shaped change trend; Henan's economic resilience is weaker; Hubei is severely hit by the COVID-19 epidemic and its economic resilience is weakest, but it continues to rise.

6.2.2 Dynamic evaluation

According to the dynamic evaluation step (2), the time series weight \(w_{t} {\text{ (t}} = {2,3,} \ldots {,6)}\) is determined (as shown in Table 7). To highlight the importance of recent data, let \(\theta = 0.4\).

Table 7 The time sequence weight \(w_{t}\)
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Based on formula (14), the dynamic evaluation value of grey incidence projection-fuzzy matter element \(L_{j} \, (j = 1,2, \ldots ,6)\)(as shown in Table 8) is calculated, which is the dynamic evaluation result of economic resilience of Hubei and its adjacent areas under the COVID-19 epidemic. At the same time, the dynamic evaluation value of each first level index can be obtained. In order to analyze intuitively, Fig. 4 is drawn.

Table 8 Dynamic evaluation result of economic resilience of Hubei and its adjacent areas
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Fig. 4
figure 4

Dynamic evaluation of first-level index( for Hubei and its adjacent areas)

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Table 8 shows that in the dynamic evaluation of the economic resilience of Hubei and its adjacent areas, Hunan has the strongest economic resilience, which exceeds the average; Hubei is on the lowest level; the economic resilience of Jiangxi and Shaanxi are lower than that of Hunan, but above the average; and the economic resilience of Anhui and Henan are lower than the average. According to Fig. 4, as the “epicenter” of this epidemic in China, Hubei has been severely impacted by the epidemic and its economic resilience in various aspects are low. Anhui has strong market resilience and fiscal resilience, but weak invest resilience; Jiangxi has strong invest resilience, but weak market resilience, industrial resilience and foreign trade resilience; Henan has strong foreign trade resilience but weak industrial resilience; Hunan shows strong industrial resilience and investment resilience; industrial resilience of Shaanxi is stronger while other aspects of economic resilience need to be improved.

6.3 Results of model relative validity test

Referring to the existing relevant literature [21], the relative validity analysis method is used to compare the models. The detailed description of each model is shown in Table 9. Among these models, the original static evaluation model of grey incidence projection-fuzzy matter element (Model1) uses the entropy weight method to calculate the index weight \(w_{i}\), further obtains the grey incidence projection weight of each index, and finally realizes the static evaluation. In the process of model expansion, many literature commonly use ANP to calculate the index weight (Model2), and gradually realize the static evaluation of grey incidence projection-fuzzy matter element. Since the relative validity analysis method is more suitable for the comparison of multiple models, the coefficient of variation weighting method and indicator difficulty ratio weighting method involved in this paper are used to construct the corresponding evaluation models of grey incidence projection-fuzzy matter element, namely Model3 and Model4, so as to enrich the comparison set of models to improve the reliability of model comparison conclusion. Finally, the improved evaluation model of grey incidence projection-fuzzy matter element proposed in this paper is marked as Model5, and compared with the above four models. At the same time, the dynamic evaluation results of each model are incorporated into the comparison data set to achieve a comprehensive comparison of the static and dynamic evaluation effects of various model. Due to limited space, specific characteristics and differences of each evaluation model can be obtained by contacting the author. According to the relative validity analysis method provided in Sect. 4.4, model comparison is made among Model 1 ~ Model 5 The comparison analysis results of various models are shown in Table 10.

Table 9 Description of each comparison model
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Table 10 The relative validity test result of the evaluation model
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Specifically: (1) At the level of similarity, among the five comparative models, the Model5 has a relatively high degree of similarity on the whole and ranks high. Among the comparison of static evaluation results, the similarity of Model5 from February to April ranks the first (May ranks the second). In the comparison of dynamic evaluation results, the similarity of Model5 is 0.621, ranking the third. As a positive indicator, the higher the degree of similarity is, the more effective this evaluation model is compared to other evaluation models. Therefore, Model5 is more effective than other evaluation models. (2) At the level of dispersion, among the five comparison models, the dispersion of Model5 is the lowest (including the ranking of static evaluation results from February to May, and the ranking of dynamic evaluation results). Between February and May, the dispersion of Model5 ranks first in all static evaluations. In the comparison of dynamic evaluation results, Model5 ranks first with a dispersion of 4.0. As a negative index, the higher the dispersion of the evaluation model, the larger the difference between the evaluation model and the ranking results of other evaluation models, and the lower the relative validity of the evaluation model. Therefore, Model5 is more effective than other evaluation models. (3) The relative validity score of the model can be obtained by combining the similarity degree and dispersion degree. It can be seen from the relative validity score that the Model5 has the highest value of relative validity score (including the ranking of static evaluation results from February to May, and the ranking of dynamic evaluation results). In comparison of static evaluation results, the relative validity score of Model5 ranks first from February to May. In comparison of dynamic evaluation results, the relative validity score of Model5 is 1.958, ranking first. Therefore, Model5 is more effective than other evaluation models. In summary, the improved dynamic evaluation model of grey incidence projection-fuzzy matter element proposed in this paper shows the best relatively validity, which means it is a more effective evaluation method.

7 Conclusions

In accordance with fuzzy matter element analysis model and grey incidence projection model, the improved dynamic evaluation model of grey incidence projection- fuzzy matter element is proposed by improving the minimum distance- maximum entropy combination weighting method. Through the rigorous index system construction process, the evaluation indexes are selected from the market, industry, investment, foreign trade and finance, and then the comprehensive evaluation index system of regional economic resilience under major public emergencies is constructed. Taking Hubei province (with its neighboring areas) as examples, based on the comprehensive evaluation index system of regional economic resilience under major public emergencies, the dynamic evaluation of regional economic resilience in context of COVID-19 is carried out by using the improved dynamic evaluation model of grey incidence projection- fuzzy matter element. According to the above analysis, the following conclusions are drawn:

(1) In the static evaluation result of economic resilience in Hubei province and its adjacent areas under the background of COVID-19, the ranking of economic resilience average value is as follows: Hunan, Jiangxi, Shaanxi, Anhui, Henan, Hubei. In the dynamic evaluation, Hunan has the strongest economic resilience, which exceeds the average while that of Hubei is on the lowest level. The results of dynamic evaluation of first level indexes show that Hubei, as the “epicenter” of this epidemic in China, has been severely impacted by the epidemic and its economic resilience in various aspects are low; Anhui has strong market resilience and fiscal resilience, but weak invest resilience; Jiangxi has strong invest resilience, but weak market resilience, industrial resilience and foreign trade resilience; Henan has strong foreign trade resilience but weak industrial resilience; Hunan shows strong industrial resilience and investment resilience; industrial resilience of Shaanxi is stronger while other aspects of economic resilience need to be improved. At the same time, there is small difference on market resilience among different provinces. (2) In the relative validity test of the evaluation model, the improved dynamic evaluation model of grey incidence projection- fuzzy matter element proposed in this paper has the highest comprehensive score and best relative validity, and is a more effective evaluation method, which verifies the feasibility and rationality of the evaluation model.

8 Limitations and future research directions

It should be pointed out there are still limitations in this paper. In the context of the COVID-19 epidemic, the statistical caliber and focus of the national economic development progress data are inconsistent, and the availability of evaluation index data is limited, so that there is no empirical evaluation of the nationwide economic resilience in this paper. In follow-up studies, data related to evaluation indicators should be further collected and screened to try to achieve a nationwide empirical evaluation of economic resilience in the context of the epidemic. At the same time, the evaluation system can be further optimized and adjusted to analyze the law of regional economic resilience in the context of the trend of normalized epidemic prevention and control. In addition, Hubei Province can be taken as the main research object, and the improved model of this paper can be used to dynamically evaluate the economic resilience of various regions in Hubei Province and analyze its temporal and spatial evolution laws in depth.