System Factors Shaping Digital Economy Sustainability in Developing Nations

Abstract

The gradual recovery of the economy has positioned the digital economy as a vital force driving global economic growth. However, the sustainability of this emerging economic sector is being tested by unexpected systemic shocks. There is a scarcity of research on the factors influencing the sustainable development of the digital economy. Therefore, developing a framework to assess the sustainability of the digital economy is significant. Building on previous research, this study established an evaluation system that extracts key indicators across four dimensions: society, the economy, the environment, and technology. Data were then collected through questionnaires and in-depth interviews with experts. Subsequently, this study employed the fuzzy Decision-Making Trial and Evaluation Laboratory–Analytical Network Process (fuzzy DANP) method to determine the weight of each indicator and used the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method to evaluate the sustainability of the digital economy in three cities. Sensitivity analysis was conducted to validate this comprehensive evaluation method. The results indicate that society and the economy are the two most crucial dimensions, while the regional economic development level, enterprise innovation culture, and digital divide are the top three indicators affecting the sustainable development of the digital economy industry. This work suggests that the digital economy industry should enhance regional economic levels, strengthen technological and innovative corporate cultures, and narrow the digital divide to achieve the goal of sustainable development in the digital economy sector.

1. Introduction

Digital technologies—such as big data, artificial intelligence, the Internet of Things, cloud computing, and block chain—are regarded as key production indicators for the digital economy industry [1]. Against the backdrop of sluggish global economic recovery, the digital economy has become an important force driving global economic development. Due to the impact of the digital economy on agriculture, commerce, education, health, transportation, and many other economic sectors, the digital economy is considered one of the important foundations for growth, development, and prosperity in various countries, as it helps to create employment opportunities, entrepreneurship, and innovation [2]. Traditional manufacturing has saved energy through digital transformation, alleviating the crisis caused by global energy scarcity [3]. Governments at all levels have regarded the development of the digital economy as a new engine of economic development, but this has made the competition in the digital economy industry more intense [4,5]. However, the sustainable development of the digital economy industry still faces many problems and challenges. Privacy infringement, platform monopoly, data leakage, false information, and other issues are emerging one after another and becoming increasingly important issues that threaten personal rights, industry development, and national security [6]. The development of the digital economy also faces difficulties and challenges related to infrastructure, key technologies, professional talent, governance and regulation, and other aspects that seriously constrain high-quality development of the digital economy [7]. Only by analyzing the current indicators affecting the sustainable development of the digital economy industry, creating a favorable development environment, and actively seeking sustainable development of the digital economy can we grasp opportunities to enhance national competitiveness in the development of the digital economy.

Recently, there has been an increasing amount of research on the influencing indicators of the development of the digital economy, and scholars have proposed solutions from different research perspectives to promote the development of the digital economy industry. Ran et al. (2023) stated that efficient utilization of human resources has opened new avenues for the development of the digital economy [8]. Wu (2023) proposed that the application of big data cloud platforms can increase the development share of digital media and digital transactions and can optimize the structure of the digital economy [9]. Battisti et al. (2022) argued that the digital economy is increasingly influenced by emerging digital technologies and that digital transformation is the best way to avoid short-term economic collapse and respond flexibly to the COVID-19 pandemic [10]. Beautification of the natural environment is also an important reason for countries to implement digital economy strategies [11,12]. However, there is little research analyzing the key indicators affecting the sustainable development of the digital economy industry from a multidimensional perspective, especially in developing countries. To fill this research gap, this study extracted the key indicators that affect the digital economy industry and deeply analyzed the causal relationships between these indicators, thus providing suggestions for the development of the digital economy.

The indicators that affect the sustainable development of the digital economy industry involve multiple aspects such as the economy, society, the environment, technology, and so on. Hence, based on the concept of sustainable development, this paper establishes a framework for assessing the sustainable development of the digital economy. It thoroughly examines the interrelationships and significance levels of diverse indicators, aiming to assess the developmental status of the digital economy in a country or region. To achieve this research goal, this study used a hybrid multiple-criteria decision-making (MCDM) model, which combined rough fuzzy technology with a decision-making trial- and evaluation laboratory-based analytic network process method (called the rough fuzzy DANP) to mine the influential relationships between indicators and their weights. Fuzzy technology can reduce the subjectivity of expert decision making and is therefore commonly used in uncertain environments [13]. The combination of rough set theory and the DANP can be used to integrate the judgments of multiple experts [14]. Therefore, this study applied the fuzzy DANP model to thoroughly examine the interrelationships of indicators affecting the sustainable development of the digital economy industry and to identify the key indicators while integrating expert opinions and reducing the subjectivity of their judgments. This is one of the research contributions of this paper. Finally, this study applied an ideal reference method (the TOPSIS) to evaluate the sustainability of three cities in China as a case study. The contributions of this study can be summarized as follows:

(i) Establishment of a comprehensive evaluation framework for sustainable development in the digital economy.

This study constructed a structured and multidimensional evaluation system that integrates social, economic, environmental, and technological indicators. This framework provides a systematic basis for assessing the sustainability of the digital economy, filling a critical gap in the existing literature.

(ii) Development of a fuzzy DANP model to mitigate uncertainty and subjectivity in expert judgments.

To enhance the reliability of expert-based assessments, this research introduced a hybrid model combining fuzzy set theory with the Decision-Making Trial and Evaluation Laboratory–Analytic Network Process (DANP). This approach effectively reduces the ambiguity and bias inherent in qualitative expert evaluations.

(iii) Clarification of causal relationships among indicators and identification of key dimensions and critical factors.

Through causal analysis and network modeling, this study elucidated the interdependencies among various indicators. It identified key dimensions—particularly society and the economy—and highlighted critical factors, such as regional economic development, enterprise innovation culture, and the digital divide, that significantly influence sustainable development in the digital economy.

(iv) Empirical validation of the model’s practicality and applicability through case study analysis.

The proposed model was applied to three Chinese cities using the TOPSIS method to evaluate their digital economy sustainability. The results demonstrate the model’s practical utility and robustness, confirming its potential for broader application in policy making and strategic planning.

The remainder of this study is presented as follows: Section 2 introduces the literature about indicators that influence the sustainable development of the digital economy industry; Section 3 presents the steps of the fuzzy DANP, as well as the TOPSIS theory, laying the foundation for the processing in the following text; the data analysis process is implemented in Section 4; Section 5 discusses the processes of case analysis and sensitivity analysis; and Section 6 presents the conclusions.

2. Literature Review

Sustainability is a multidimensional concept that encompasses multiple aspects such as society, the economy, the environment, and technology. In recent years, the United Nations Sustainable Development Goals (UN SDGs) and the triple bottom line theory have become important frameworks for sustainability research. The UN SDGs are 17 specific goals aimed at addressing various global challenges, including poverty, inequality, climate change, and environmental protection [14]. The triple bottom line theory emphasizes the economic, social, and environmental responsibilities of enterprises and indicates that the sustainable development of enterprises needs to achieve a balance between these three dimensions [15].

Tapscott (1996) first proposed the concept of the “digital economy,” which they believed is a new economic form, an important manifestation of the knowledge economy, and a new trend in economic development [16]. They explained and described the connotation of the digital economy but did not use effective methods to specifically classify and measure the digital economy. In 2016, the G20 Summit, which was held in Hangzhou in China, defined the meaning of the digital economy: the digital economy represents a novel economic paradigm centered on data resources, utilizing modern information networks as its primary infrastructure. It relies on the integration and application of information and communication technology, along with the digital transformation of all factors. This serves as a crucial driving force to advance a more cohesive, equitable, and efficient system. The digital economy is the main economic form after agriculture and industry and has become a key force in restructuring global factor resources, reshaping the global economic structure, and changing global competition patterns [17]. Williams (2021) argued that the digital economy refers to the portion of economic output based on digital services or goods, mainly or entirely from digital initiatives [18]. The digital economy is closely linked to the UN SDGs and the triple bottom line theory. The digital economy drives sustainable development by supporting goals such as industry innovation, sustainable cities, and climate action through technological advancements and infrastructure development [19]. The triple bottom line theory, emphasizing economic, social, and environmental sustainability, aligns with the digital economy’s potential to foster inclusive growth, reduce inequality, and promote environmental responsibility. By bridging the digital divide and ensuring data privacy, the digital economy can enhance social well-being and contribute to the overall sustainability agenda.

Given the positive role of the digital economy in transforming and upgrading various industries, it is important to identify key indicators that affect the sustainable and healthy development of the digital economy industry. Exploration of the development path of the digital economy should not only consider scientific development strategies but should also have a sustained innovation orientation and the ability to ensure long-term, sustained, and stable development. This study constructed an evaluation system for indicators that affect the sustainable development of the digital economy industry based on four dimensions: society indicators, economy indicators, environment indicators, and technology indicators.

2.1. Society

With the development of digital technology, the digital divide has become a global concern [20]. Bruno et al. (2023) believed that the distribution of digital technology development levels was severely imbalanced, leading to a gap between developed and underdeveloped countries and regions [21]. He et al. (2022) proposed that older people face the awkward situation of a “digital divide” in the context of lagging digital consumption concepts and a poor digital knowledge foundation [22]. This not only restricts their ability to participate in the digital economy but also hinders the sharing and development ability of the entire society. The digital divide is directly related to quality education and reducing inequality related to the UN SDGs. The existence of the digital divide hinders equal access to educational opportunities and exacerbates social inequality. It can be seen that it is necessary to curb the expansion of the digital divide and its negative impact in order to reduce its impact on the sustainable development of the digital economy industry. Peng et al. (2023) proposed that enterprise innovation culture is an inevitable choice for achieving sustainable development in the digital economy industry [23]. Technological and organizational innovation are also important driving forces for the sustainable development of social, economic, and environmental aspects of the digital economy industry [24]. The digital economy industry needs to vigorously cultivate digital talent to alleviate the structural contradiction between talent supply and employment demand in the digital economy [25]. Human resource management issues in the digital economy industry have attracted scholars’ attention. High-level human resource management is conducive to opening new avenues for the development of the digital economy industry [8,11].

Based on the above analysis, three indicators were placed in the society dimension in this study: the digital divide, enterprise innovation culture, and human resource management.

2.2. Economy

Undoubtedly, the level of local economic development is closely related to the quality of the development of the digital economy industry. The government needs to provide policy support and sustained funding in areas such as ICT (information and communication technology) to ensure the momentum required for the development of the digital economy [6]. Due to the different levels of economic development in different regions, there will be significant gaps in investment in digital economy infrastructure, resulting in significant gaps in the levels of digital economy infrastructure construction in different regions [22]. Most of the enterprises involved in digital economy business are small and medium-sized enterprises, and the difficulty and high cost of financing are global challenges. Jones et al. (2021) showed that large investments of time and money are required in the digital economy industry to enable enterprises to adjust their operations, production lines, supply chains, and work environments [26].

Therefore, the regional economic development level, capital investment, and government financial and tax policies were included in the economy dimension.

2.3. Environment

Chen et al. (2023) pointed out that there are imbalanced and imperfect issues in the development of the digital economy in China [6]. They stated that the most important indicator affecting the sustainable development of the digital economy is the level of digital infrastructure improvement. Convenient and intelligent infrastructure is conducive to sustainable development of the digital economy [27]. Application of innovative business models such as the platform economy, sharing economy, circular economy, and short video economy guarantees sustainable development of the digital economy industry [28]. The continuous and iterative business model in the digital economy industry promotes healthy competition, thereby objectively promoting its healthy development [29]. Sustainable development of the digital economy requires a good business environment to encourage technological innovation and business model innovation, to effectively guide and regulate enterprise behavior, and to consciously form a reasonable market competition order. In the development process of the digital economy, new formats and models are constantly emerging, and the uncertainty of the interactions between business entities is strong [30]. New characteristics, trends, situations, and problems are constantly emerging. This highlights the importance of optimizing the digital business environment. The quality of the business environment directly determines the speed, quality, and level of the development of the digital economy. The government utilizes digital technology to promote cross-departmental, cross-hierarchical, and cross-regional government data fusion and strengthens the collection of key social data related to areas such as communication, healthcare, scientific research, transportation, logistics, and manufacturing, creating a centralized aggregation of public data and a comprehensive intelligent analysis platform [31,32].

Therefore, digital infrastructure, the innovation level of business models, the business environment, and the government digital management level were placed in the environment dimension in this study.

2.4. Technology

Digital technology is a tool and a means for promoting the sustainable development of the digital economy industry. Digital technology includes technologies used for storing, processing, and transmitting information, such as cloud computing, big data analysis, artificial intelligence, the Internet of Things, blockchain, and other emerging technologies [33]. The viewpoint that digital technology plays a crucial role in the development of the digital economy and the acceleration of the digital transformation of the economy and society suggests fully leveraging the amplification, superposition, and multiplication effects of digital technology on economic development [34]. With more and more personal information being collected and used, people’s privacy is facing unprecedented threats. Therefore, the significance of data privacy protection has become particularly important in the current society. Data privacy protection not only protects individuals’ privacy and information but also concerns the interests of the entire society. Data privacy is closely linked to the UN’s definition of sustainable development, which emphasizes promoting peaceful societies, ensuring access to justice, and building accountable institutions. Specifically, it highlights the importance of protecting fundamental freedoms, including the right to privacy and access to information. In the digital economy, safeguarding personal data is essential for maintaining public trust, strengthening institutional accountability, and supporting inclusive governance. Therefore, the importance of ensuring data privacy cannot be ignored [35]. The use of technological means to achieve data desensitization and the development of privacy protection laws and regulations are essential measures [36]. We considered placing the technological innovation capability, core technology construction, the enterprise digital technology level, and data privacy protection in the dimension of technology.

Table 1. Factors affecting the sustainable development of the digital economy.

Dimensions	Indicators	Explanation
Society	Digital divide (S1)	Gap in digital technology usage among different groups.
	Enterprise innovation culture (S2)	Willingness and ability of enterprises to drive digital transformation.
	Human resource management (S3)	Efficiency of digital talent cultivation and utilization.
Economy	Regional economic development level (E1)	Regional economic output and residents’ consumption level.
	Capital investment (E2)	Scale of capital invested in digital industries.
	Government financial and tax policies (E3)	Government support for digital economy through fiscal and tax policies.
Environment	Digital infrastructure (EN1)	Hardware and network foundation supporting digital economy development.
	Innovation level of business models (EN2)	New business models driven by digital technologies.
	Business environment (EN3)	Market and institutional environment for digital industry development.
	Government digital management level (EN4)	Government use of digital tools to improve governance and services.
Technology	Technological innovation capability (T1)	Supporting role of emerging digital technologies in industries.
	Core technology construction (T2)	Application level of key technologies like 5G, AI, and big data.
	Enterprise digital transformation capability (T3)	Overall capability of enterprises to promote digital transformation.
	Data privacy protection (T4)	Security management and desensitization of sensitive data.

summarizes the proposed dimensions and indicators affecting the sustainable development of the digital economy.

3. Research Method

This study did not involve human or animal experimentation; therefore, ethical committee approval was not sought. As this study did not involve human trials or animal experiments, there were no issues concerning human rights or animal rights. This study utilized data from expert questionnaires. During the data collection process, we ensured that no personal identifying information was recorded to protect individual privacy. Consequently, this study did not pose any risks to personal privacy.

A diagram of the overall framework of the construction and verification of the evaluation model in this paper is shown in Figure 1. The fuzzy DANP method was used to analyze each evaluation indicator and determine the weight of each evaluation indicator and the relationships between them. Then the TOPSIS method was used to analyze case cities to further demonstrate the practicability and promotion value of the model.

3.1. Fuzzy Set Theory

The inherent uncertainty in the decision-making process makes it difficult for decision makers to accurately determine the interactions of various indicators, and they often rely on their professional knowledge and experience to evaluate these interactions using qualitative descriptions such as “good” or “bad” [37,38]. To reduce the influence of such subjective judgments, fuzzy theory methods are proposed to translate these fuzzy evaluations into concrete values. In this paper, we use the triangular fuzzy number method to convert the expert evaluations into quantifiable data for further analysis and evaluation.

Let the triangular fuzzy number (Z) be (L, M, U), where L and U are the lower and upper limits of the fuzzy values, respectively, and M is the most probable value. The affiliation function of the triangular fuzzy number is shown below:

$${\sigma }_z(x)=\left\{\begin{array}{c}(x-L)/(M-L),L\le x\le M\\ (U-x)/(U-M),M\le x\le U\\ 0,other\end{array}\right.$$

(1)

where L, M, and U are real numbers. When L = M = U, the triangular fuzzy number (Z) is an ordinary positive real number. For any two triangular fuzzy numbers (Z₁(L₁, M₁, U₁) and Z₂(L₂, M₂, U₂)), the following operator is satisfied:

$$\left\{\begin{array}{c}{Z}_1+Z_2=(L_1+L_2,M_1+M_2,U_1+U_2)\\ Z_1-Z_2=(L_1-L_2,M_1-M_2,U_1-U_2)\\ \lambda Z_1=(\lambda L_1,\lambda M_1,\lambda U_1) \end{array}\right.$$

(2)

The center-of-gravity method has the advantage that it is simpler and more effective and does not need to consider the preference of the decision maker [36]. Therefore, in this study, we chose the center-of-gravity method to solve the ambiguity. The specific Equation of the center-of-gravity method is as follows:

$$\beta ={\displaystyle \frac{(U-L)+(M-L)}{3}}+L$$

(3)

3.2. Fuzzy DANP

The DANP combines a DEMATEL and the ANP to calculate influence weights [39]. The method derived from the existing literature for combining a DEMATEL and the ANP involves using a DEMATEL to establish the network structure and internal associations, followed by employing the ANP to analyze external associations and calculate weights. This integrated approach, known as the DEMATEL-ANP method, not only plays a role in mapping the network diagram but also comprehensively assesses weights, thoroughly addressing the analysis of associations and the determination of weights.

The DANP is simpler than the ANP and makes pair-to-pair comparison questionnaires more practical. Therefore, combined with previous studies, this study adopted the fuzzy DANP to deal with and analyze the influencing factors of the sustainable development of the digital economy industry. The specific process was as follows:

Step 1: Verifying the consistency of the expert questionnaire opinions.

Experts were invited to evaluate the direct impact strengths between the digital economy sustainability indicators in this paper on a five-level scale from 0 to 4. Then, the consensus was verified using Equation (4) [40]. If the ratio value was less than 0.05, the experts’ opinions were deemed to be consistent. In this equation, k is the number of experts, n is the number of criteria, and a_ij is the impact strength of criterion i for criterion j.

$$ratio={\displaystyle \frac{1}{n(n-1)}}{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^n\left(\left|a_{ij}^k-e_{ij}^{k-1}\right|/a_{ij}^k\right)}}$$

(4)

Step 2: Using the pair-to-pair comparison method.

Then, these scores were converted into triangular fuzzy numbers [13]. The transformation relationship is shown in

Table 2. Conversion relationship between linguistic variables and fuzzy numbers.

Linguistic Variable	Influence Degree Value	Corresponding Triangular Fuzzy Numbers
Extremely high impact	4	(0.7, 0.9, 1.0)
High impact	3	(0.5, 0.7, 0.9)
Medium impact	2	(0.3, 0.5, 0.7)
Low impact	1	(0.1, 0.3, 0.5)
No impact	0	(0, 0.1, 0.3)

.

Step 3: Construct the fuzzy direct relation average matrix ($\tilde{Z}$).

By interviewing k experts and comparing n criteria, k fuzzy direct-relation matrices were obtained. Then the average matrix of sustainable development of the digital economy ($\tilde{Z}$) was calculated. Equation (5) is as follows:

$$\tilde{Z}={\displaystyle \frac{1}{k}}{\displaystyle \sum _{k=1}^k{Z}_{ij}^k}$$

(5)

Step 4: Calculate the fuzzy initial influence relationship matrix ($\tilde{P}$).

The fuzzy initial influence relation matrix was the result of normalizing the fuzzy direct relation average matrix.

$$\tilde{P}=s\ast \tilde{Z}$$

(6)

$$s=\min \left[1/\underset{i}{\max }{\displaystyle \sum _{j=1}^n[{\tilde{z}}_{ij}]},1/\underset{j}{\max }{\displaystyle \sum _{i=1}^n[{\tilde{z}}_{ij}]}\right]$$

(7)

Step 5: Generate the fuzzy total influence matrix.

The fuzzy total influence relation matrix was calculated according to matrix $\tilde{P}$, as shown in Equation (8), where I is the identity matrix:

$$\tilde{T}=\underset{k\to \infty }{\lim }(\tilde{P}+{\tilde{P}}^2+\cdots {\tilde{P}}^k)=\tilde{P}\otimes {(I-\tilde{P})}^{-1}$$

(8)

Step 6: Calculate the influence degree, center degree, and cause degree of the fuzzy total influence relationship matrix, and set them as R, D, R + D, and R − D in sequence.

Equation (3) was used to defuzzify, where R is the sum of rows i of the fuzzy total influence relation matrix and D is the sum of column j (see Equations (9) and (10)).

$$R={(R)}_{n\times 1}=\left|{\displaystyle \sum _{j=1}^n{\overline{t}}_{ij}}\right|$$

(9)

$$D={(D)}_{1\times n}={(D)}_{n\times 1}^{\prime }={\left|{\displaystyle \sum _{i=1}^n{\overline{t}}_{ij}}\right|}^{\prime }$$

(10)

Step 7: Draw a network diagram.

R + D was the horizontal axis, R − D was the vertical axis, and an R − D value greater than 0 was drawn above the horizontal axis to indicate that the element had a great influence on other factors and was called a cause factor. If it was less than 0, it was below the axis, indicating that it was greatly affected by other factors and was called the result factor.

Step 8: Construct the fuzzy unweighted super matrix.

The fuzzy matrix of the total-impact relationships for the dimensions and indicators was represented in terms of ${\tilde{T}}_B$ and ${\tilde{T}}_A$, as shown in Equation (11):

$${\tilde{T}}_A=\begin{array}{c} \\ \\ B_1\\ \\ ⋮\\ \\ \\ B_i\\ \\ ⋮\\ \\ \\ B_n\\ \end{array}\begin{array}{c}{a}_{11}\\ a_{12}\\ ⋮\\ a_{1m_1}\\ ⋮\\ a_{i1}\\ a_{i2}\\ ⋮\\ a_{i{m}_2}\\ ⋮\\ a_{n1}\\ a_{n2}\\ ⋮\\ a_{n{m}_n}\end{array}\stackrel{\begin{array}{cccccccccccccccc} & B_1& & & & & B_j& & & & & & & B_n& & \\ a_{11}& \dots & a_{1m_1}& & & a_{j1}& \dots & a_{j{m}_j}& & & & & a_{n1}& \dots & a_{n{m}_n}& \end{array}}{\left[\begin{array}{cccccccccccccc}{\tilde{T}}_A^{11}& & & \dots & & & {\tilde{T}}_A^{1j}& & & & \dots & & & {\tilde{T}}_A^{1n}\\ & & & & & & & & & & & & & \\ & & & & & & & & & & & & & \\ ⋮& & & & & & ⋮& & & & & & & ⋮\\ & & & & & & & & & & & & & \\ & & & & & & & & & & & & & \\ & & & & & & & & & & & & & \\ {\tilde{T}}_A^{i1}& & & & & & {\tilde{T}}_A^{ij}& & & & \dots & & & {\tilde{T}}_A^{in}\\ & & & & & & & & & & & & & \\ & & & & & & & & & & & & & \\ ⋮& & & & & & ⋮& & & & & & & ⋮\\ & & & & & & & & & & & & & \\ & & & & & & & & & & & & & \\ {\tilde{T}}_A^{n1}& & & \dots & & & {\tilde{T}}_A^{nj}& & & & \dots & & & {\tilde{T}}_A^{nn}\end{array}\right]}$$

(11)

${\tilde{T}}_A$ was standardized according to the following methods to obtain the standardized fuzzy total influence relationship matrix (${\tilde{T}}_A^{\eta }$), as seen in Equation (12), where the sum of the elements in row i in ${\tilde{T}}_A^{11}$ is represented by ${\tilde{s}}_i^{11}$.

$${\tilde{T}}_A^{11}=\begin{array}{c}{a}_{11}\\ ⋮\\ a_{1i}\\ \\ a_{1m_1}\end{array}\stackrel{\begin{array}{ccccc}{a}_{11}& \dots & a_{1j}& \dots & a_{1m1}\end{array}}{\left[\begin{array}{ccccc}{\tilde{t}}_{11}^{11}& \dots & {\tilde{t}}_{1j}^{11}& \dots & {\tilde{t}}_{1m_1}^{11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{i1}^{11}& \dots & {\tilde{t}}_{ij}^{11}& \dots & {\tilde{t}}_{i{m}_1}^{11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{m_{1}1}^{11}& \dots & {\tilde{t}}_{m_{1}j}^{11}& & {\tilde{t}}_{m_1{m}_1}^{11}\end{array}\right]}\begin{array}{c}\to \\ \\ \to \\ \\ \to \end{array}\begin{array}{c}{\tilde{s}}_1^{11}={\displaystyle \sum _{j=1}^{m_1}{\tilde{t}}_{1j}^{11}}\\ {\tilde{s}}_i^{11}={\displaystyle \sum _{j=1}^{m_1}{\tilde{t}}_{ij}^{11}}\\ {\tilde{s}}_m^{11}={\displaystyle \sum _{j=1}^{m_1}{\tilde{t}}_{m_{1}j}^{11}}\end{array}$$

(12)

(i) Each element of row i of the matrix was divided by the sum of row i. Then, the normalized fuzzy total influence relation submatrix (${\tilde{T}}_A^{\eta 11}$) was obtained, as seen in Equation (13):

$${\tilde{T}}_A^{\eta 11}=\left[\begin{array}{ccccc}{\tilde{t}}_{11}^{11}/{\tilde{s}}_1^{11}& \dots & {\tilde{t}}_{1j}^{11}/{\tilde{s}}_1^{11}& \dots & {\tilde{t}}_{1m_1}^{11}/{\tilde{s}}_1^{11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{i1}^{11}/{\tilde{s}}_i^{11}& \dots & {\tilde{t}}_{ij}^{11}/{\tilde{s}}_i^{11}& \dots & {\tilde{t}}_{i{m}_1}^{11}/{\tilde{s}}_i^{11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{m_{1}1}^{11}/{\tilde{s}}_{m_1}^{11}& \dots & {\tilde{t}}_{m_{1}j}^{11}/{\tilde{s}}_{m_1}^{11}& & {\tilde{t}}_{m_1{m}_1}^{11}/{\tilde{s}}_{m_1}^{11}\end{array}\right]=\left[\begin{array}{ccccc}{\tilde{t}}_{11}^{\eta 11}& \dots & {\tilde{t}}_{1j}^{\eta 11}& \dots & {\tilde{t}}_{1m_1}^{\eta 11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{i1}^{\eta 11}& \dots & {\tilde{t}}_{ij}^{\eta 11}& \dots & {\tilde{t}}_{i{m}_1}^{\eta 11}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_{m_{1}1}^{\eta 11}& & {\tilde{t}}_{m_{1}j}^{\eta 11}& & {\tilde{t}}_{m_1{m}_1}^{\eta 11}\end{array}\right]$$

(13)

(ii) Each standardized submatrix was transposed individually and then positioned at the corresponding location in the matrix to construct a fuzzy unweighted super matrix ($\tilde{W}$). See Equation (14):

$$\tilde{W}={\left({\tilde{T}}_A^{\eta }\right)}^{\prime }=\begin{array}{c} \\ \\ B_1\\ \\ ⋮\\ \\ \\ B_i\\ \\ ⋮\\ \\ \\ B_n\\ \end{array}\begin{array}{c}{a}_{11}\\ a_{12}\\ ⋮\\ a_{1m_1}\\ ⋮\\ a_{i1}\\ a_{i2}\\ ⋮\\ a_{i{m}_2}\\ ⋮\\ a_{n1}\\ a_{n2}\\ ⋮\\ a_{n{m}_n}\end{array}\stackrel{\begin{array}{ccccccccccccc} & B_1& & & & & B_j& & & & & B_n& \\ a_{11}& \dots & a_{1m_1}& & & a_{j1}& \dots & a_{j{m}_j}& & & a_{n1}& \dots & a_{n{m}_n}\end{array}}{\left[\begin{array}{ccccccccccccc}{\tilde{W}}_{11}& & & \dots & & & {\tilde{W}}_{1j}& & & \dots & & & {\tilde{W}}_{1n}\\ & & & & & & & & & & & & \\ & & & & & & & & & & & & \\ ⋮& & & & & & ⋮& & & & & & ⋮\\ & & & & & & & & & & & & \\ & & & & & & & & & & & & \\ {\tilde{W}}_{i1}& & & & & & {\tilde{W}}_{ij}& & & \dots & & & {\tilde{W}}_{in}\\ & & & & & & & & & & & & \\ & & & & & & & & & & & & \\ ⋮& & & & & & ⋮& & & & & & ⋮\\ & & & & & & & & & & & & \\ & & & & & & & & & & & & \\ {\tilde{W}}_{n1}& & & \dots & & & {\tilde{W}}_{nj}& & & \dots & & & {\tilde{W}}_{nn}\end{array}\right]}$$

(14)

Step 9: Build a fuzzy weighted super matrix.

(i) The fuzzy total influence matrix (${\tilde{T}}_B$) for the dimensions was normalized using a method analogous to that used for ${\tilde{T}}_A$, resulting in matrix ${\tilde{T}}_B$; see Equation (15):

$${\tilde{T}}_B^{\eta }=\left[\begin{array}{ccccc}{\tilde{t}}_B^{11}/s_1^{~}& \dots & {\tilde{t}}_B^{1j}/s_1^{~}& \dots & {\tilde{t}}_B^{1m}/s_1^{~}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_B^{i1}/s_i^{~}& \dots & {\tilde{t}}_B^{ij}/s_i^{~}& \dots & {\tilde{t}}_B^{im}/s_i^{~}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_B^{n1}/s_m^{~}& \dots & {\tilde{t}}_B^{mj}/s_m^{~}& \dots & {\tilde{t}}_B^{mm}/s_m^{~}\end{array}\right]=\left[\begin{array}{ccccc}{\tilde{t}}_B^{\eta 11}& \dots & {\tilde{t}}_B^{\eta 1j}& \dots & {\tilde{t}}_B^{\eta 1m}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_B^{\eta i1}& \dots & {\tilde{t}}_B^{\eta ij}& \dots & {\tilde{t}}_B^{\eta im}\\ ⋮& & ⋮& & ⋮\\ {\tilde{t}}_B^{\eta m1}& \dots & {\tilde{t}}_B^{\eta mj}& \dots & {\tilde{t}}_B^{\eta mm}\end{array}\right]$$

(15)

(ii) The fuzzy weighted super matrix ($\widetilde{W_{\eta }}$) was obtained by treating $\tilde{W}$ and ${\tilde{T}}_B^{\eta }$ with Equation (16).

$${\tilde{W}}_{\eta }=\tilde{W}\otimes {\tilde{T}}_B^{\eta }=\left[\begin{array}{ccccc}{\tilde{W}}_{11}\otimes {\tilde{t}}_B^{\eta 11}& \dots & {\tilde{W}}_{1j}\otimes {\tilde{t}}_B^{\eta 1j}& \dots & {\tilde{W}}_{1n}\otimes {\tilde{t}}_B^{\eta 1n}\\ ⋮& & & & \\ {\tilde{W}}_{i1}\otimes {\tilde{t}}_B^{\eta i1}& \dots & {\tilde{W}}_{ij}\otimes {\tilde{t}}_B^{\eta ij}& \dots & {\tilde{W}}_{in}\otimes {\tilde{t}}_B^{\eta in}\\ & & & & \\ {\tilde{W}}_{n1}\otimes {\tilde{t}}_B^{\eta n1}& \dots & {\tilde{W}}_{nj}\otimes {\tilde{t}}_B^{\eta nj}& \dots & {\tilde{W}}_{nn}\otimes {\tilde{t}}_B^{\eta nn}\end{array}\right]$$

(16)

Step 9: Calculate the limit value of the fuzzy super matrix, and perform a multiplication operation on the fuzzy weighted super matrix ($\widetilde{W_{\eta }}$).

When the elements of each row of the matrix were the same, it meant that the matrix had reached a stable state and convergence was over. The limiting fuzzy matrix ($\tilde{W}\ast$) was obtained. See Equation (17):

$$\tilde{W}\ast =\underset{k\to \infty }{\lim }{\tilde{W}}_{\eta }^k$$

(17)

Step 10: Defuzzify.

Equation (3) was employed to defuzzify, yielding a distinct influence weight, which was then used to determine the weight ranking of key factors affecting the sustainable development of the digital economy industry.

3.3. TOPSIS Method

The TOPSIS, also known as the ideal point method, was first proposed by Hwang and Yoon in 1981. This method comprises two primary concepts. One is the “ideal solution,” which represents the best conceivable scenario, where all attributes achieve their optimal values. The other is the “negative ideal solution”, signifying the worst-case scenario, when all characteristics are in their least favorable states among the possible options. The ranking is determined based on the distances between the evaluation subject and both the best and worst scenarios, employing the Euclidean distance to calculate the separation between each alternative and the positive and negative solutions, ultimately defining each alternative’s relationship with the ideal solution. If the target is closest to the optimal solution, it is deemed the best; conversely, if it is nearest to the worst-case scenario, it is considered the worst. For multiple alternatives, the distances between each evaluated entity and the positive and negative benchmarks are calculated separately, with rankings assigned according to proximity. The specific steps are as follows:

Step 1: Establish the decision feature matrix.

Typically, there are m evaluation goals ($D_1,D_2,\dots ,D_M$), each with n evaluation indicators ($x_1,x_2,\dots ,x_n$), and an evaluation scoring sheet is designed comprising both qualitative and quantitative indicators. Experts are invited to score these indicators, and the scores are then transformed into a mathematical matrix representation. A feature matrix (D) is established. See Equation (18):

$$D=\left[\begin{array}{ccccc}{x}_{11}& \dots & x_{1j}& \dots & x_{1n}\\ \dots & \dots & \dots & \dots & \dots \\ x_{i1}& \dots & x_{ij}& \dots & x_{in}\\ \dots & \dots & \dots & \dots & \dots \\ x_{m1}& \dots & x_{mj}& \dots & x_{mn}\end{array}\right]=\left[\begin{array}{c}{D}_1\left(X_1\right)\\ \dots \\ D_i\left(X_j\right)\\ \dots \\ D_m\left(X_n\right)\end{array}\right]$$

(18)

Step 2: Normalize the matrix.

The matrix (D) is normalized, and the normalized matrix of the normalized vector ($r_{ij}$) is established. See Equation (19):

$$r_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\displaystyle \sum _{i=1}^m{x}_{ij}^2}}}}, i=1,2,\dots ,m, j=1,2,\dots ,n.$$

(19)

Step 3: Construct the weight normalization matrix.

The weights of each indicator in the matrix are dot-multiplied by the elements in the normalized matrix to get the normalized value ($v_{ij}$), and the related normalized matrix is established:

$$v_{ij}=w_j{r}_{ij}, i=1,2,\dots ,m, j=1,2,\dots ,n$$

(20)

Step 4: Determine the positive and negative ideal solutions ($v_j^{*}$ and $v_j^{-}$) by Equations (21) and (22), where i = 1, 2, …, m.

$$v_j^{*}=\underset{\mathrm{i}}{\max }{v}_{ij}$$

(21)

$$v_j^{-}=\underset{\mathrm{i}}{\min }{v}_{ij}$$

(22)

Step 5: Calculate the Euclidean distances ($D^{+}$ and $D^{-}$) between each evaluation indicator and the positive and negative ideal solutions by Equations (23) and (24).

$$D_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{\left({\mathrm{v}}_{ij}-{\mathrm{v}}_j^{*}\right)}^2}}$$

(23)

$$D_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{\left({\mathrm{v}}_{ij}-{\mathrm{v}}_j^{-}\right)}^2}}$$

(24)

Step 6: As shown in Equation (25), calculate the approximation degree of the ideal solution. The evaluation goals are ranked according to the proximity of the ideal solution ($R_i$). The larger the $R_i$ value, the closer the evaluation goal is to the positive ideal solution.

$$R_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}}$$

(25)

3.4. Methodological Considerations and Limitations

The integration of the fuzzy DANP and the TOPSIS in this study provides a structured and systematic approach to handle the complexity and interdependence of indicators influencing digital economy sustainability. The fuzzy DANP effectively captures the causal relationships and relative importance of indicators during uncertainty, while the TOPSIS offers a clear ranking of alternatives based on their proximity to ideal solutions. However, it is important to acknowledge that these methods, while widely used in multi-criteria decision making (MCDM), are not without limitations. First, both the fuzzy DANP and the TOPSIS rely heavily on expert judgment, which may introduce subjective bias despite the use of fuzzy logic to mitigate uncertainty. Second, the methods assume linear relationships and compensability among criteria, which may not fully reflect the non-linear and dynamic nature of digital economy systems. Third, the selection of experts and the number of respondents may influence the robustness of the results.

Furthermore, while the combination of the fuzzy DANP and the TOPSIS is appropriate for exploratory and evaluative purposes, it may not be suitable for predictive modeling or real-time policy simulation. Future research could consider integrating machine learning techniques or system dynamics models to enhance predictive accuracy and capture dynamic feedback loops. Despite these limitations, the methodological framework adopted in this study is well-suited for identifying key indicators and evaluating the sustainability of the digital economy in developing nations, particularly in data-scarce contexts.

4. Data Analysis

In Section 2, this paper identified four dimensions and 14 indicators that affect the sustainable development of the digital economy industry, as shown in Table 1. This section reports the design of a questionnaire based on these indicators to investigate the causal relationships of the four dimensions and the indicators under them and to assess their relative importance to identify the key influencing indicators.

4.1. Questionnaire Design and Collection

The questionnaire indicators in this study were derived from a literature review of factors influencing the sustainable development of the digital economy. The questionnaire structure included five parts, namely a survey description, the personal information of the respondents, an indicator description, a filling method, and an evaluation table of the interactions between the indicators.

The questionnaire adopted a 14 × 14 matrix scoring method, using a 0 to 4 point scoring method to evaluate the influence of the different indicators from low to high. The survey was sent via email between 13 February and 28 March 2023, with 10 valid questionnaires returned. Expert information was mainly obtained by a keyword search in the National Knowledge Infrastructure (CNKI) database and a search engine for the official websites of their institutions. All experts who completed this questionnaire have conducted in-depth research in the field of the digital economy, and most of their research results have been published in authoritative journals such as those in the Chinese Social Sciences Index (CSSCI), so the data they provided is of important reference value.

In addition, the investigation set up a 10-member panel of experts, in which the members did not know each other’s information. The members of the expert group are listed in

Table 3. Background information of the 10 experts.

Experts	Working Experience (Years)	Work Unit	Education Level
Researcher	20	Internet Economy Research Institute	PhD in Economics
Director	20	Institute of Economic Development, Nanjing Academy of Social Sciences	PhD in Economics
Professor	20	Central University of Finance and Economics	PhD in Economics
Professor	15–20	Harbin University of Technology	PhD in Economics
Professor	15–20	Zhongnan University of Economics and Law	PhD in Economics
Professor	20	Kunming University of Science and Technology	PhD in Economics
Lecturer	10	Northwest University	PhD in Economics
Associate Professor	15–20	Xi’an University of Posts and Telecommunications	PhD in Economics
Professor	15–20	Anhui University of Finance and Economics	PhD in Economics
Operations Director	10	Xiamen Yilian Network Technology Co., Ltd.	Master of Computer Science

.

4.2. Data Processing

First, we constructed the fuzzy direct relationship average matrix ($\tilde{Z}$). During the survey, the experts were required to assess the interactions between the indicators by making pairwise comparisons to determine the relative influence of two indicators. The experts used precise numerical values in their assessments, enabling measurement of consensus levels. The extent of direct influence was evaluated using a 5-point scale, from “no influence” (0) to “extremely influential” (4). The average consistency gap, calculated using Equation (4) across the 10 questionnaires, was 4.1%, which was below the 5% threshold.

Following step 2 of Section 3, we converted the responses of the 10 experts into triangular fuzzy numbers. Subsequently, we aggregated these numbers to form the fuzzy direct relation mean matrix ($\tilde{Z}$). Second, we normalized $\tilde{Z}$ according to step 3 to obtain the fuzzy initial influence relationship matrix ($\tilde{P}$). Third, the fuzzy total influence relationship matrix could be calculated through Equation (8). The values in the matrix indicated the degree of the total fuzzy influence of one indicator on the other indicators and the degree of the total fuzzy influence of the other indicators on the other indicators.

Fourth, to obtain the R, D, R + D, and R − D values of each factor, Equation (3) was applied to the fuzzy total-impact matrix to defuzzify and form a clear total-impact matrix. Then Equations (9) and (10) were applied to calculate the impact degree (R), the affected degree (D), the centrality degree (R + D), and the cause degree (R − D) (see

Table 4. The centrality degrees and cause degrees of the dimensions and indicators.

Dimensions	R	D	R + D	R − D	Indicators	R	D	R + D	R − D
Society	1.45	1.35	2.80	0.10	S1	4.86	4.73	9.58	0.13
					S2	5.16	4.91	10.07	0.25
					S3	5.17	4.41	9.57	0.76
Economy	1.42	1.35	2.76	0.07	E1	5.05	5.07	10.12	−0.02
					E2	4.27	4.61	8.89	−0.34
					E3	5.56	4.29	9.85	1.26
Environment	1.23	1.31	2.53	−0.08	EN1	4.67	4.76	9.43	−0.09
					EN2	4.52	4.35	8.88	0.17
					EN3	4.01	4.43	8.44	−0.42
					EN4	3.94	4.57	8.51	−0.63
Technology	1.24	1.33	2.57	−0.09	T1	3.77	4.14	7.90	−0.37
					T2	4.59	4.74	9.33	−0.15
					T3	4.11	4.89	9.00	−0.78
					T4	4.85	4.63	9.49	0.22

). The degree of centrality (R + D) reflects the combined importance of an indicator, and the degree of cause (R − D) indicates its net impact.

Fifth, taking the degree of centrality (R + D) as the horizontal coordinate and the degree of reason (R − D) as the vertical coordinate, were drew a network relationship diagram of the factors affecting the sustainable development of the digital economy industry. See Figure 2.

As can be seen in the figure above, in terms of the dimensions, society and the economy influence technology and the environment. There is mutual influence between society and the economy. In addition, the dimensions of society and the economy have significant impacts on the remaining dimensions and hold a high level of importance within the system of indicators. The environment is the result indicator, and its role in the dimension system is weak, as it is mainly affected by the cause indicators. In the society dimension, human resource management has an impact on enterprise innovation culture and the digital divide. In the economy dimension, government fiscal and tax policies influence capital investment and the regional economic development level. The level of regional economic development is an outcome indicator influenced by other factors. The innovation level of business models plays a leading role in the environment system and has an impact on digital infrastructure, the business environment, and the government digital management level. In the technology dimension, data privacy protection dominates the technological innovation capability and core technology construction, as well as the enterprise digital transformation capability. The detailed management implications from the cause-and-effect analysis are discussed in Section 5.

Using Equations (11)–(17), we could obtain the weights of the dimensions and indicators.

Table 5. Dimension and indicator weights.

Dimensions	Weight	Rank	Indicator	Local Weight	Rank	Global Weight	Rank
Society	0.254	1	Digital divide	0.337	2	0.086	3
			Enterprise innovation culture	0.351	1	0.089	2
			Human resource management	0.312	3	0.079	5
Economy	0.253	2	Regional economic development level	0.365	1	0.092	1
			Capital investment	0.329	2	0.083	4
			Government financial and tax policies	0.305	3	0.077	6
Environment	0.244	4	Digital infrastructure	0.264	1	0.065	8
			Innovation level of business models	0.239	4	0.058	13
			Business environment	0.244	3	0.060	12
			Government digital management level	0.252	2	0.062	11
Technology	0.249	3	Technological innovation capability	0.222	4	0.055	14
			Core technology construction	0.258	2	0.064	9
			Enterprise digital transformation capability	0.267	1	0.067	7
			Data privacy protection	0.253	3	0.063	10

indicates that the weights of the dimensions ranked in descending order are society, the economy, technology, and the environment. The five highest weights among the indicators are the level of regional economic development, corporate innovation culture, the digital divide, capital investment, and human resource management. These top indicators all belong to the dimensions of society and the economy. Thus, the key to achieving sustainable development in the digital economy industry should be enhancing the levels of the society and economy indicators, specifically improving the levels of regional economic development and corporate innovation culture. Furthermore, while generating profits, companies should not overlook issues of technological innovation and environmental protection. They should aim to advance technological innovation and reduce costs and should actively explore innovative environmental strategies to minimize pollution.

4.3. Case Study

To justify the selection of cities A, B, and C as case studies, we provide socioeconomic profiles highlighting their comparability and representativeness. Cities A, B, and C are located within the same province and exhibit comparable levels of economic development, making them suitable for comparative analysis. City A is a mid-sized city with a balanced economic structure, relatively high government support for digital initiatives, and a growing number of internet-related enterprises, making it a regional hub for digital innovation. City B, an inland city, has a moderate GDP per capita but has shown rapid growth in digital infrastructure investment and human capital development. Its industrial structure is transitioning from secondary to tertiary, with increasing digitalization in manufacturing and services. City C is a coastal city with a GDP per capita above the provincial average and a high urbanization rate (over 75%). Its tertiary sector contributes more than 60% of its GDP, with a high concentration of producer services. All three cities have made significant strides in digital infrastructure, including internet penetration rates above the national average, high digital finance adoption, and expanding telecommunications and IT services. These socioeconomic and digital infrastructure indicators demonstrate the cities’ suitability for evaluating sustainable digital economy development.

Cities A, B, and C collectively represent a spectrum of development stages—advanced, transitional, and emerging—within a single provincial context. This diversity allowed this study to capture variations in digital economy sustainability across different urban development models. Their shared regional policy environment and comparable baseline conditions enhanced the internal validity of the comparative analysis using the TOPSIS method. By selecting these cities, this study ensured the practical relevance and reliability of the indicator system developed using the fuzzy DANP method. The findings can provide strategic references for sustainable growth of the Chinese digital economy, particularly for cities at different development stages.

This questionnaire survey is based on the indicators that affect the sustainable development of the digital economy listed in Table 1. The content includes the survey description, personal information, a detailed explanation of each indicator, the filling method, and an evaluation of the realization degree of the three cities according to 14 indicators on a scale of 1–5, where 1 represents a low level and 5 represents a high level. In particular, the digital divide is a very small indicator, where the lower the score the better, while the rest are very large indicators, where the higher the score the better. The expert group for the survey consisted of ten people, including four digital economy practitioners from Fujian, four professors from Fujian universities, and two finance master’s students from Fuzhou University. The questionnaires were distributed through a combination of email and personal recommendations. The process began on 21 April 2024 and ended on 28 April 2024, with a total of 10 valid questionnaires collected over a week.

We exported the collected original data to EXCEL and performed data processing according to the specific steps of the TOPSIS introduced in Section 3 of this paper. The specific process and results are as follows:

First, the decision feature matrix (D) was constructed according to Equation (17). Since the digital divide is a very small indicator, it needed to be transformed into an extremely large indicator by positive processing; that is, the score of the indicator was subtracted from the maximum value of the score. The positive decision matrix (Q) was obtained. Then, the normalized decision matrix was normalized according to Equation (19), and the normalized matrix of the normalized vector ($r_{ij}$) was established. The weights of each indicator (Table 5) obtained by the fuzzy DANP above were dot-multiplied with the elements in the normalized matrix, and the normalized weight matrix with the normalized weight value ($v_{ij}$) was established. According to step 4, the positive and negative ideal solutions ($v_j^{*}$ and $v_j^{-}$) were determined by Equations (21) and (22). Finally, through step 5, the Euclidean distances ($D^{+}$ and $D^{-}$) between each evaluation indicator and the positive and negative ideal solutions were calculated using Equations (23) and (24), the approximation degree of the ideal solution was calculated using Equation (25) based on the obtained $D^{+}$, and the evaluation target was sorted according to the value of $R_i$ of the approximation degree of the ideal solution. The greater the value of $R_i$, the closer the evaluation target was to the positive ideal solution. For details, see

Table 6. Ranking of Euclidean distance and ideal solution proximity.

	A	B	C
D+	0.032	0.040	0.007
D−	0.017	0.004	0.039
Ri	0.346	0.084	0.852
Rank	2	3	1

.

In summary, it can be seen in Table 6 that among the three cities, the sustainable development capability of the digital economy of city C ranks first, followed by A and then B. The evaluation goal of city C is the closest to the positive ideal solution, indicating that many enterprises in city C have given full play to their own advantages. Therefore, city C should continue to strengthen its advantages, maintain and improve this leadership level, and consider sharing its successful experiences and strategies to drive the development of the surrounding area. Although city A ranks second, there is still a gap between cities A and C, so city A needs to analyze and learn from the strategies of city C to improve its digital economy development. City B has the lowest ranking of the three cities. This could mean that the digital economy development of city B needs a major push to catch up with the other cities. City B should consider improving its digital infrastructure, enhancing digital skills training, encouraging the growth of innovation and technology enterprises, and developing favorable policies to attract digital industry investment, thereby driving the sustainable development of the digital economy in the province. Finally, all cities should pay attention to constantly updating technology, training professionals, and motivating enterprises to foster a culture of innovation, which are key indicators that promote the development of the digital economy.

5. Discussion

5.1. Practical Implications

To promote the sustainable development of the digital economy, this study proposes targeted strategies based on the analysis of four key dimensions: society, economy, environment, and technology. These recommendations are tailored to the roles and responsibilities of different stakeholders, including governments, enterprises, and educational institutions, to ensure practical implementation.

5.1.1. The Society Dimension: Strengthening Human Capital and Bridging the Digital Divide

As shown in Table 5, corporate innovation culture (8.9%) and the digital divide (8.6%) rank second and third in the society dimension system, while human resource management (7.9%) ranks fifth. To enhance innovation culture and human resource development and to reduce the digital divide, it is essential to attract innovative talent and improve digital infrastructure [41].

To effectively address the digital divide, governments should invest in expanding broadband infrastructure, especially in rural and underserved urban areas, and provide subsidies or low-cost options to improve affordability [42]. They can also implement digital literacy programs in schools and community centers to enhance digital skills. On the other hand, companies, particularly tech firms, can contribute by developing user-friendly platforms, offering digital skills training, and creating content in local languages to improve accessibility. Public–private partnerships are essential, combining government policy support with corporate innovation and resources to ensure inclusive digital access [43,44].

5.1.2. The Economy Dimension: Enhancing Regional Development and Capital Investment

The economy dimension ranks second (25.3%), with the regional economic development level (9.2%), capital investment (8.3%), and government fiscal and tax policies (7.7%) ranking first, fourth, and sixth, respectively. Capital investment, as a result indicator, plays a crucial role in the indicator system. Regional economic development is closely linked to infrastructure development, and cities with higher development levels are mainly distributed in economically developed areas such as the eastern coastal regions [45]. This indicates that digital infrastructure in the east is relatively advanced and that the application and innovation of digital technologies are more mature.

Therefore, governments should increase investment policies in the central and western regions to narrow regional gaps. In addition, if the Midwest wants to establish a competitive advantage, it should prioritize green technologies and seize opportunities in emerging high-tech fields such as blockchain and quantum communications. By promoting regional digital integration and exploring paths of digital transformation and innovation, comprehensively upgrading the regional economic structure can be achieved [46,47,48]. Government fiscal and tax policies play a pivotal role in shaping the extent of regional economic growth and the levels of capital investment. Notably, these policies have a profound effect, while capital investment outcomes are affected by various other determinants. The formulation of government fiscal policies is underpinned by several key factors, including fiscal health, international competitive dynamics, and political elements [49,50,51]. Establishing a regional cooperation mechanism based on resource sharing is imperative to enhance regional technological innovation capabilities [52].

5.1.3. The Technology Dimension: Advancing Innovation and Ensuring Data Privacy

The technology dimension ranks third (24.9%), with the enterprise digital transformation capability (6.7%), core technology construction (6.4%), data privacy protection (6.3%), and the technological innovation capability (5.5%) ranking 7th, 9th, 10th, and 14th, respectively. Although technology ranks lower in weight, it plays a vital role in the sustainable development of the digital economy. Technology not only promotes innovation in the digital economy industry but also improves enterprise operational efficiency and ensures data security.

To address data privacy, governments should establish clear legal frameworks and enforce compliance through audits and oversight [53]. In addition, the technological innovation ability, the core technology construction ability, and the enterprise digital transformation ability are affected by capital investment, the talent reserve, the policy environment, and other indicators. Therefore, enterprises need to comprehensively consider the above indicators and formulate corresponding strategies to improve the technological innovation capability and the digital transformation level [54]. Companies must adopt strong security measures, such as encryption and access controls, and must promote privacy awareness among employees. Both parties should collaborate to develop industry standards and ensure transparent data practices, balancing innovation with protection. Strengthening basic scientific research and promoting technological progress and innovation are crucial to supporting the national innovation strategy and building a strong country.

5.1.4. The Environment Dimension: Promoting Green and Sustainable Development

The environment dimension ranks fourth (24.4%), with digital infrastructure (6.5%), the government digital management level (6.2%), the business environment (6.0%), and innovation in business models (5.8%) ranking 8th, 11th, 12th, and 13th, respectively. With the rapid development of the economy and science and technology, the state has introduced a series of environmental protection policies. Although negative environmental outcomes are a result indicator, their influence on the development of the digital economy is significant [55,56]. Sustainable development of the ecological environment is the environmental basis for achieving sustainable development. Human use of natural resources should be carried out under conditions that allow for reasonable regeneration.

To achieve sustainable development in the digital economy, this principle should be followed to avoid irreversible environmental threats. Digital infrastructure can help reduce carbon emissions, and increased levels of government digital management and oversight will help create a better business environment. This will encourage us to strengthen government digitization, encourage enterprises to innovate green technologies, accelerate the integration of enterprise development and sustainable production, and facilitate harmonious coexistence between the economy and the environment.

5.2. Sensitivity Analysis

Experts selecting cities might inadvertently introduce bias into their holistic evaluations of urban economic sustainability potential if they fail to consider all indicators due to individual inclinations. To test the resilience of the evaluation framework and mitigate such biases, this study adopted sensitivity analysis techniques.

5.2.1. Sensitivity Analysis of Single Indicator

The pivotal parameter of the regional economic growth level was set as the variable, fluctuating between 0.05 and 0.95, while correspondingly adjusting the weights of the remaining thirteen criteria. Thereafter, this study employed the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) to hierarchically assess the sustainable development capabilities of the three cities under scrutiny. That is, when the weight of a certain indicator changed, the weight of the other indicators also changed, as shown in Equation (25), where $w$ is the weight of E1:

$$\left\{\begin{array}{c}w=\delta ,(\delta =0.05,0.1,0.15\cdots 0.95)\\ \delta +{\displaystyle \sum _{i=1,i\ne k}^m{\beta }_i}{w}_i=1\end{array}\right.$$

(26)

According to Equation (26), the changed weights were carried into the step of weighting the standardized decision matrix in the above case analysis, and the corresponding ranking of the sustainable development abilities of the three cities could be obtained. In order to facilitate a more intuitive display, the rankings were converted into line charts, as shown in Figure 3 below:

Upon examination of Figure 3, it becomes evident that the rankings of cities B, A, and C for their economic sustainability capabilities remained unchanged, with city C consistently topping the list, city A securing the second position, and city B ranking third. This consistency indicates that the choice of indicators for this research project was both judicious and resilient, thereby demonstrating the stability of the results when subjected to a range of hypothetical scenarios.

5.2.2. Multi-Indicator Joint Sensitivity Analysis

To address the limitations of the single-indicator perturbation analysis, this study adopted a combined approach using the One-At-a-Time (OAT) method and multi-indicator joint perturbation to systematically test the robustness of the model [57]. As seen in

Table 7. OAT sensitivity analysis results (city ranking changes).

Indicator	Weight Range	City A Rank Change	City B Rank Change
E1	0.05→0.95	2→1	3→3
S2	0.05→0.95	2→2	3→3
S1	0.05→0.95	2→3	3→2
E2	0.05→0.95	2→2	3→3
S3	0.05→0.95	2→2	3→3

, the top five weighted indicators—E1 (the regional economic development level), S2 (enterprise innovation culture), S1 (the digital divide), E2 (capital investment), and S3 (human resource management)—were selected for analysis. Each indicator’s weight was varied from 0.05 to 0.95 in increments of 0.1, while the remaining weights were proportionally adjusted to ensure the total sum remained 1.

In addition, a Monte Carlo simulation was conducted by randomly generating 1000 weight combinations for the five indicators. The resulting city rankings were recorded and analyzed to assess the model’s stability under multidimensional uncertainty, as shown in

Table 8. Monte Carlo simulation results.

City	Average Rank	Std. Deviation	Rank Range	Most Frequent Rank
City A	2.1	0.42	1–3	2nd (68%)
City B	2.8	0.38	2–3	3rd (72%)
City C	1.1	0.31	1–2	1st (89%)

.

5.2.3. Threshold Identification

Table 9. Threshold identification for key indicators.

Indicator	Critical Weight	Rank Change	Explanation
E1	>0.70	City A > City C	Economic level becomes dominant
S1	>0.65	City B > City A	Reduced digital divide boosts city B
S2, E2, S3	No clear threshold	No significant change	Limited impact on overall ranking

identifies the critical thresholds at which shifts in the city rankings occurred when key indicator weights exceeded specific values. When the weight of E1 (the regional economic development level) surpassed 0.70, city A overtook city C, indicating that economic strength became the dominant factor. Similarly, when the weight of S1 (the digital divide) exceeded 0.65, city B rose above city A, suggesting that narrowing the digital gap significantly enhanced its competitiveness. In contrast, indicators such as S2, E2, and S3 did not exhibit clear thresholds, as their variations did not trigger notable changes in the city rankings. These findings highlight the importance of prioritizing regional economic development and digital inclusion in policy design to influence urban digital sustainability outcomes effectively.

5.2.4. Implication for Policy Prioritization

The comparative analysis of cities A, B, and C revealed distinct development stages—emerging, transitional, and advanced—offering valuable insights for policy prioritization. City C, with its high GDP per capita and mature service sector, should focus on innovation-driven policies and digital finance expansion to sustain its competitive edge. City A, a mid-sized city with strong government support and a growing digital enterprise base, would benefit from policies that enhance digital infrastructure and attract talent. City B, which is still transitioning industrially, should prioritize investments in digital infrastructure and human capital to accelerate its shift toward a service-oriented economy. These targeted strategies align with findings that digital transformation enhances urban innovation resilience, particularly when tailored to local industrial structures and development levels.

6. Conclusions

Amidst the burgeoning growth of the digital economy, nations are leveraging it as a new impetus for economic expansion. This study investigated the pivotal indicators impacting the digital economy, as synthesized from prior studies, and drew the following conclusions: First, by focusing on keywords for the collection of domestic and international research, we devised an evaluation framework for the indicators influencing the sustainable progress of the digital economy. This framework predominantly includes technological, economic, environmental, and societal dimensions and features indicators such as the digital divide, corporate innovation levels, and financing, among others. Second, by employing the fuzzy DANP approach to dissect the indicator weightings, we proffer recommendations for the digital economy’s sustainable evolution. Third, by selecting three cities of comparable developmental stature, this study utilized the TOPSIS technique to further substantiate the reliability and practicability of the indicator system. Fourth, using the sensitivity analysis method, we verified that the indicator system and the integrated evaluation method of the fuzzy DANP and the TOPSIS used in this paper are suitable for studying the issue of achieving sustainable development in the digital economy industry.

Although this research has achieved preliminary strides in elucidating the indicators of sustainable development within the digital economy through the establishment of an evaluative model, it still confronts numerous challenges. Initially, the extant indicator system was chiefly derived from a literature review, so it may have neglected certain covert indicators; furthermore, the delineations of various indicators are overly broad and necessitate more precise refinement by the scholarly community. In addition, while the adoption of the fuzzy DANP method alongside expert evaluations mitigated the influence of uncertainties, it could not entirely obviate subjective biases. Additionally, while the fuzzy DANP-TOPSIS framework provided valuable insights, it is important to interpret the results within the context of its methodological limitations, particularly regarding expert subjectivity and the assumption of linearity among the indicators. Lastly, the macro-level perspective of this analysis does not adequately account for regional disparities; the critical influencing indicators could differ markedly across different areas. Subsequent research endeavors should scrutinize regional idiosyncrasies more scrupulously to foster balanced and sustainable growth of the digital economy in our nation. Future research should expand the sample size and geographic scope by including more experts and cities from diverse regions to enhance the generalizability and robustness of the findings.