Sage Journals: Discover world-class research

Abstract

The digital economy is developing rapidly worldwide, which is of great strategic significance in leading and driving the process of high-quality and high-efficiency development of the economy. It has gradually become a new engine to promote China’s economic growth. Therefore, it is vital to establish a digital economy indicator system. In this context, according to the connotation of digital economy, comprehensively consider the four dimensions of digital foundation, digital application, digital innovation and digital benefit, and build a full-scale digital economy indicator system. However, some previous literature proposed operating the K-means clustering algorithm in optimizing the index system. The algorithm, susceptible to the initial selection of cluster center, generates completely different clustering results with other random seed points and is thus unsuitable for optimizing the index system. Based on this, the advantages of GRA, SA, and K-means algorithms are combined to propose a K-means-SA algorithm that can obtain the global optimal solution. Then, by combining the K-means SA algorithm and the rough set algorithm, the constructed index system is further optimized. Ultimately, it establishes a set of all-round, multi-system and multi-dimensional digital economy index systems, which is of great reference significance for formulating relevant policies, provides scientific index support for the subsequent extension of digital economy theory, and promotes the benign growth of the worldwide economy.

Plain language summary

The importance of constructing and optimizing the digital economy indicator system

In today’s rapid development of the digital economy, a set of scientific, feasible, and practical application values of the digital economy evaluation index system is constructed to evaluate better and promote the development of the digital economy. Based on the four dimensions of digital foundation, digital application, digital innovation, and digital benefit, this paper constructs a comprehensive evaluation index system for the development level of the digital economy. In addition, by combining the advantages of GRA, SA, and K-means algorithms, a K-means SA algorithm can obtain the global optimal solution proposed. Then, the K-mean-SA algorithm is combined with the rough set algorithm to optimize the constructed index system further. Finally, a comprehensive, multisystem, and multi-dimensional evaluation index system for the development level of the digital economy is established, which provides scientific support for the development of digital economy theory and promotes the healthy development of the digital economy. Although this paper collects indicators related to the digital economy as comprehensively as possible based on existing studies, there are still some limitations in the selection of needles due to the strong integration of the digital economy.

Keywords

digital economy index construction K-means algorithm K-means-SA algorithm

Introduction

With the continuous development and popularization of digital technology, the digital economy has evolved into a new engine of the international economy, which has a significant position in fostering economic growth, social welfare, industrial upgrading, cultural exchanges, and other fields, and has gradually become the center force leading China’s economic growth, industrial change and the construction of a new international pattern (D. Shi, 2021; J. Wang et al., 2021). At the G20 Hangzhou Summit held in 2016, the leaders of the participating countries jointly signed the G20 Initiative on Digital Economy Development and Cooperation, and the digital economy was listed as an essential issue in the G20 Blueprint for Innovative Growth for the first time. Since then, the digital economy has evolved as a focus of awareness for all countries worldwide. Since the 18th Party Congress, the government has attached grand matter to developing the digital economy. In 2017, the word digital economy appeared for the first time in the report on the work of our government. 2019 to 2022, been noted in the national work report for four straight years and successively put forward to grow the digital economy, build a unique advantage in the digital economy, accelerate digital development, and form a digital China to promote the growth of the digital economy, strengthen the overall layout of the build of digital China and other development plans. In the past 5 years, the ranking of China’s digital economy has thrived, effectively hedging the economic downward pressure in the context of the epidemic. It has become one of the primary ambitious forces of financial increase and the core competitiveness of China to gain economic conversion and change the pattern of global competition. The digital economy has evolved a fresh focus of international attention and is the first significant new impetus to lead high-quality economic development (Cao, 2018; W. Sun & Liu, 2022). The 20th Party Congress also put forward more clear requirements for the digital economy, such as concentrating on promoting the integration of the digital economy with the actual economy and realizing the digital accurate twin technology (X. Jiang & Jin, 2022). According to the relevant information from the China Communications Research Institute, China’s digital economy gets 45.5 trillion yuan in 2021, up 16.2% year-on-year, indicating that China’s digital economy industry resumes to increase, the process of industrial digitization is accelerating, and the digital economy is showing a heightened rate of growth (Z. Li & Liu, 2021).

However, against the background of the overall trend of China’s digital economic growth, China’s digital economic development is still meeting the issue of the “digital divide,” and there is still a polarization of the station of digital economic expansion between regions. Therefore, In the background of the development of the digital economy, it is necessary to construct a set of comprehensive evaluation index systems for China’s digital economy (Pan et al., 2021; M. Zhang, 2017). To accurately estimate China’s digital economy growth and then accurately grasp the regional differences and non-equilibrium characteristics. There are moderately more studies on the indicator system of the digital economy, but the controversial differences are still prominent (Williams, 2021). At home and abroad, there have been many studies on the definition of the digital economy, statistical accounting, and the index system for measuring development. However, a uniformly recognized system of statistical indicators still needs to be (Cong et al., 2022; Guo et al., 2022). Furthermore, at present, the research ideas of academics and governmental departments are divided into two kinds: one is to directly measure the volume of scale created by a particular defined region at a specific point in term; the other is to, through the establishment of a set of multi-dimensional indicators to evaluate the system, to evaluation of development of a defined region at a specific point in term (Q. Y. Xu et al., 2018), such as the OECD, the European Union, the United States, Tencent, Saidi and other nations and related organizations have a statistical digital economy indicator system, but the difference between each other is relatively significant.

Given this, based on the research of existing scholars, this study offers a new K-means-SA algorithm by combining the advantages of GRA, SA, and K-means algorithms. Further, it optimizes the constructed index system by connecting with the rough set algorithm to build a set of multi-system, multi-dimensional evaluation index systems on the development of the digital economy, to help decision-makers better understand the expansion of the digital economy, to formulate more scientific and reasonable policies, and to infiltrate new kinetic power for the country’s economic growth.

Literature Review

This section first classifies the applications and effects of the digital economy, secondly organizes and reviews the present condition of study on evaluation indicators of the digital economy, and finally reviews and summarizes the evaluation and measurement strategies for the digital economy.

Research on the Application and Impact of the Digital Economy

The digital economy is a new type of economy based on digitization and networking, which uses advanced data technology and network technology to attain rapid access, processing and transmission of information and has an essential impact on the conversion and upgrading of enterprises (X. Jiang, 2020; Savina, 2018; Sturgeon, 2021). The digital economy involves many areas, including e-commerce, digital finance, cloud computing, significant data, and additional emerging economic fields (L. Shi & Chen, 2023). It has broad connotations and extensions (Xia et al., 2023). Regarding the application and effect of the digital economy, the publication of the 2017 China Digital Economy Index has made essential contributions to developing the digital economy. Subsequent scholars have provided insights on the evaluation of digital economy index from various angles or levels such as digital economy theory (Yao, 2020), macro and micro (Jing & Sun, 2019), value creation sources and economic scale (Pei et al., 2018), consumer rights and interests (Qi et al., 2020), and the implementation of digital economy in China’s small and medium-sized enterprises (Ren, Lee, & Hu, 2023; Y. Wang, 2021). Some scholars have also explored the connection with the digital economy in terms of the degree of industrial integration (Xin et al., 2023), the growth of regenerative energy (Hwang, 2023; B. Wang et al., 2023; Zheng & Wong, 2024), new government-business relations (Y. Chen et al., 2023), global energy transition (Onifade et al., 2021; Shahbaz et al., 2022), and reduce carbon emissions (Z. Li & Wang, 2022; Yan et al., 2022). Most scholars have specifically analyzed the application and influence of the digital economy from the perspectives of high-quality development, networking, and industrial conversion and upgrading (Han et al., 2022; Ren, Wang, & Liu 2023; X. Sun et al., 2022; Zhang, Zhao, & Cheng). However, more studies must evaluate the digital economy, especially in forming a digital economy index system. Therefore, this paper focuses on selecting and constructing an index for assessing digital economic development.

Research on the Index System for the Level of Development of the Digital Economy

In designing the index system for estimating digital economic growth, some students have attributed it to the digital scale and used the digital economy development index as a reference to determine the corresponding evaluation index (P. Chen, 2022; Z. Li & Liu, 2021; Sidorov & Senchenko, 2020). Domestic and foreign professionals, scholars, and organizations have guided numerous explorations on the level of digital economic development and have constructed an indicator system for evaluating the level of digital economic development from multiple dimensions (Belanova et al., 2020). Foreign scholars primarily study the development trends and mechanisms of the digital economy to construct an indicator system for evaluating various aspects such as government digital transformation, innovation projects, and the development of smart cities (Basol & Yalcın, 2021; Ivanova et al., 2019). Another aspect is that domestic scholars focus more on establishing a more scientifically grounded indicator system to assess digital economy development. Founded on the Organization for Economic Co-operation and Development (OECD) digital economy research framework, Xiang and Wu (2018) used officially published foreign data to estimate the digital economy and set forward suggestions. J. Liu et al. (2020) discussed the relationship between information, networking, and digital transactions and constructed eight secondary and 17 tertiary indicators. They operated the SAR ideal to measure China’s digital economic expansion from 2015 to 2018. Pan et al. (2021) constructed 20 evaluation indicators from four levels and used the entropy method to comprehensively score China’s digital effect level from 2012 to 2019. Y. Sun et al. (2022) combed through the current evaluation theories and modes of the digital economy and constructed an evaluation system consisting of seven dimensions and 26 primary indicators. Based on this, Scholars have analyzed the evaluation index system of the digital economy and high-quality development and green innovation by constructing the evaluation index system and empirically analyzing the role mechanism between the two (Luo et al., 2023; Tao et al., 2022; W. Zhang et al., 2021; Zhao et al., 2019). Zhou and Liu (2022) constructed 15 secondary and 35 tertiary indicators from five dimensions of innovation, governance, economy, security, and service and analyzed the regional digital competitiveness development trend. L. Wang (2022) constructed an indicator system consisting of 19 primary and 44 secondary indicators from six dimensions of the digital economy. Lian et al. (2022) constructed five primary indicators and 20 secondary indicators from the viewpoints of digital governance, digital infrastructure, digital invention, industrial digitization, and digital automation and measured the digital economic development level of 19 Chinese cities using methods such as the Dagum Gini coefficient. Du, Huang, & Dong (2022) constructed four primary indexes and 22 secondary indexes from the perspective of the coordinated coupling of rural revitalization and the digital economy. Infrastructure development is essential. That is, the development of the digital economy must be reinforced by a digital foundation and fueled by digital innovation (Onifade, Ay, et al., 2020). The China Academy of Information and Communications Technology (ICT) estimated the ranking of China’s digital economy from multiple perspectives (Wu & Wang, 2012). Some scholars have also constructed a digital economy development indicator system established on the inter-provincial level (Z. Wang & Shi, 2021).

Through the above analysis, it is not difficult to find that domestic and foreign scholars, when constructing the index system for the digital economy, pay more attention to considering the demand side or using a single dimension to estimate the level of development and lack a comprehensive measurement of the digital economy. Based on existing research, this article adopts the literature analysis approach, based on the frequency of evaluation indexes, screening and integrating the existing evaluation indexes, and initially constructs a set of more complete and feasible digital economy index systems.

Research on the Evaluation Method of Digital Economy Development

In terms of evaluating the level of development of the digital economy, most scholars operate the K-means algorithm to optimize the indicator system, and some scholars use the entropy weight mode, gray correlation analysis, and factor analysis method (Y. Xu & Li, 2022; Y. Yang & Dong, 2022; S. Yang & He, 2022). The K-means algorithm is a widely used clustering algorithm. After years of research, the K-means algorithm has been employed in multiple areas, such as text data mining, genetic data recognition, and speech recognition (Abdullah et al., 2021; Dong & Zhu, 2020; Özöğür Akyüz et al., 2023). However, in practical applications, different cluster centers can lead to fluctuations in the clustering outcomes, and the number of groups is challenging to determine. When implementing the K-means algorithm, researchers operated the most straightforward explanation and randomly selected the initial cluster center points several times to find the local optimum solution. However, later studies found that the initial cluster number of the traditional K-means algorithm is determined randomly, and the algorithm is sensitive to cluster center abnormalities, resulting in clustering results that are different for different cluster centers (F. Li & Nong, 2013; H. Du et al., 2018; M. Li et al., 2020; X. Wang & Bai, 2016). In other words, the K-means algorithm is a greedy algorithm that tends to obtain stuck in local optimal solutions (Pham et al., 2004). To solve these shortcomings, scholars have proposed various improved algorithms, such as the DMK-Kmeans (H. Jiang et al., 2018), K-means- PSO-SVR (P. Liu et al., 2022), DIC-DOC- K-means algorithm (Lakshmi & Baskar, 2019). DMK-Kmeans algorithm strives to unravel the issue of local optimality of clustering results generated by the traditional K-means algorithm’s random initial cluster center selection. The K-means-PSO-SVR algorithm is a local modeling method, and the DIC-DOC-K-means algorithm is established on the dissimilarity of initial centroids selection to enhance reader document clustering. With the development of deep learning and deep learning, scholars have proposed a CMFGN clustering algorithm based on multi-layer features and graph attention net and have demonstrated the efficiency of the CMFGN algorithm through many experiments (Hou et al., 2023). In addition, H. Du et al. (2018) used the improved density peak algorithm (DPC) to select the initial clustering center. Some scholars have replaced the traditional Euclidean distance with other distances to calculate the space between sample points and have demonstrated through experiments that the enhanced k-means algorithm has a more acceptable clustering result and intersection than the traditional one (Zhu et al., 2021). Although scholars have improved the traditional K-means algorithm from different angles, most improvements are limited to the random selection of initial cluster centers and do not fundamentally solve the problem of getting stuck in locally optimal solutions.

In summary, current research on the digital economy’s development level by both domestic and foreign scholars has yielded fruitful results. However, there are also the following areas for improvement. Firstly, these traditional research models only analyze the development of the digital economy from a one-sided and localized perspective through theory or other aspects. They cannot effectively combine the indicator system with the model. Secondly, The evaluation indicators for the level of digital economic development currently have a narrow scope of coverage, and most studies are considered from the demand side, resulting in a limited evaluation of the level of digital economic development. Finally, Some scholars use the K-means algorithm to screen digital economy indicators. However, the K-means algorithm has inherent flaws and cannot find globally optimal solutions, so it is unsuitable for optimizing the evaluation indicator system of digital economic development.

Construction of the Evaluation Index System

In this paper, the steps for selecting the evaluation index system of the digital economy are “literature collection—index selection— preliminary construction of the index system.” Based on the regulations of scientific, representative, orientation, and comparability, it aims to construct an index system that combines the existing research and the wisdom of authoritative experts and scholars so that the constructed evaluation index system tends to be reasonable and universally applicable (Onifade, Cxevik, et al., 2020; Y. Sun & Chen, 2018).

Consider the conditions and application environment of the digital economy in the context of sustainable development scenarios based on the connotations and elements of the digital economy (Jin et al., 2019). This paper takes “digital economy indicator system” as the keyword. It manually screens out 40 documents (the selected documents are all published in well-known and authoritative journals or publishers, with high citation counts and high academic level and value, including 28 documents in Chinese and 12 in foreign languages). The indicators contained therein were collected manually, and after collating, summarizing, and counting, Table 1 displays the indicators with a frequency share more significant than 7%

Table 1.

Frequency Statistics.

Indicator	Frequency/times	Scale/%	Indicator	Frequency/times	scale/%
Mobile phone penetration rate	22	55	The amount of IPV4	8	20
Mobile broadband penetration rate	20	50	R&D funding	7	18
Number of Internet port access	20	50	GDP per capital	6	15
Internet penetration rate	20	50	Digital Life Index	6	15
Number of employees in related industries	19	48	Technology market turnover	5	13
E-commerce sales volume	18	46	Online retail sales	4	10
Total telecommunications business	17	43	Total express business	4	10
Software service revenue	17	43	Value-added value of the tertiary industry	4	10
E-commerce sales volume	17	43	Proportion of computer services and software practitioners	4	10
E-commerce purchase volume	17	43	Number of mobile phone users	4	10
Optical cable density	16	40	Number of web pages	3	8
The number of websites	15	38	Number of patent applications	3	8
Domain name number	14	35	Number of computers used by the Enterprises	3	8
Education level	12	30	Value added	3	8
The China Digital Financial Inclusion Index	10	25	Education spending	3	8
Number of Internet enterprises	9	23	Advanced industrial structure	3	8
Investment in fixed assets in the ICT industry	9	23	Rationalized the industrial structure	3	8
Mobile phone exchange capacity	8	20

Source. Summarized by the author.

To provide the comprehensiveness and fullness of the selection of indicators, this study selected 19 indicators with a frequency greater than or equal to 8 times and added the indicators that ranked lower in frequency and were not filtered for the first time, resulting in the selection of 28 indicators. Indicators are classified based on existing research. The development of the digital economy relies on “four needs,” that is, the need for the growth and advancement of the digital basis, the need for the evolution and deepening of digital applications, the need for the increase and service of digital innovation, and the need for the conversion and upgrade of the digital enterprise, thereby achieving the enhancement of the benefits of the whole industry and society. Thus, based on the connotation of the digital economy and concerning the evaluation index system for the level of development of the digital economy established by scholars and third-party institutions at home and abroad, four first-level indicators, namely, digital foundation, digital application, digital innovation, and digital benefit, were constructed from the four levels of infrastructure, application, innovation, and benefit (Ji & Zhu, 2022; Shen & Zhou, 2023; X. Xu & Zhang, 2020; X. Zhang & Jiao, 2017).

Digital infrastructure is an essential element in the digital age and is the prerequisite for developing and improving the digital economy. It is also the foundation for realizing a digital society. Referring to studies by scholars such as Lv and Fan (2023), Huang et al. (2023), Wan and Luo (2022), and Y. Li et al. (2023). Segment the digital infrastructure into device infrastructures such as mobile, fixed, and network. Digital application refers to various business processes and information management through digital technology to achieve efficient, convenient, accurate, and sustainable business operations. Referring to research by Wen et al. (2020) and Zhang , Dong, & Wang et al. (2022). The digital application was divided into personal and enterprise applications, laying the foundation for promoting digital innovation. Digital innovation is based on digital applications and explores new business, commercial, and management models. It is the key to achieving digital benefits. Referring to research by Zhang, Dong, & Wang et al. (2022), Zhou and Liu (2022), and Du, Zhang, & Xia (2022). Segment the digital innovation into two indicators: innovation input and innovation output, injecting new innovative power into enterprise development. Digital benefits are achieved through digital technology and tools, increasing operational efficiency, reducing costs, and enhancing innovation capabilities, according to studies by Shen and Zhou (2023) and Y. Sun et al. (2022). Segment the digital benefits into economic benefits and social benefits. Based on the analysis above, this research is an constructed an evaluation indicator system for the digital economy development, including four primary, nine secondary, and 28 tertiary indicators (Table 2).

Table 2.

Evaluation Index System for the Development Level of Digital Economy.

Primary indicator	Secondary indicator	Tertiary indicator (Unit)	Code
Digital infrastructureA	Mobile device infrastructureA₁	Mobile phone exchange capacity (10,000 households)	A₁₁
		Mobile phone penetration rate (number of mobile phones per 100 people)	A₁₂
		Mobile broadband penetration rate (%)	A₁₃
		Number of mobile phone users (10,000 households)	A₁₄
		The rate of decline in mobile data tariff (%)	A₁₅
	Fixed equipment infrastructureA₂	Fixed telephone penetration rate (number of fixed telephones per 100 people)	A₂₁
		Number of domain names (10,000)	A₂₂
		Number of websites (10,000)	A₂₃
		Long-distance optical cable (kilometers)	A₂₄
	Network equipment infrastructureA₃	Number of internet enterprises(unit)	A₃₁
		Number of internet port accesses (10,000)	A₃₂
		Internet penetration rate (%)	A₃₃
Digital applicationB	Personal applicationB₁	Number of TV sets (10,000)	B₁₁
	Personal applicationB₁	Digital life index (%)	B₁₂
	Enterprise applicationB₂	Number of enterprise-owned websites(unit)	B₂₁
		Proportion of e-commerce transaction enterprises (%)	B₂₂
		Number of digital cultural and creative enterprises (unit)	B₂₃
Digital innovationC	Innovation inputC₁	R&D expenditure internal support (10,000 yuan)	C₁₁
		R&D investment (10,000 yuan)	C₁₂
		Public security expenditure (10,000 yuan)	C₁₃
	Innovation outputC₂	Number of patent applications (unit)	C₂₁
	Innovation outputC₂	Technology market turnover (10,000 yuan)	C₂₂
Digital benefitsD	Economic benefitsD₁	Software service revenue (10,000 yuan)	D₁₁
		E-commerce transaction amount (10,000 yuan)	D₁₂
		E-commerce sales (10,000 yuan)	D₁₃
		Per capital disposable income (yuan)	D₁₄
	Social benefitsD₂	Employment structure (%)	D₂₁
	Social benefitsD₂	China’s digital inclusive finance index (%)	D₂₂

Methodology

K-means-SA Algorithm

The immediate purpose of this paper is to construct a set of indicators that accurately measure the level of digital economic development through indicator screening, clustering, and optimization. The purpose of clustering is, on the one hand, to find out whether the information of the selected set of indicators is overlapping and to eliminate it, and on the other hand, to perform an accurate cluster analysis for each set of indicators after removing one secondary indicator at a time. Currently, the clustering algorithm commonly used in academic research is the K-means algorithm. However, despite its many advantages, it affects the clustering results due to its sensitivity to the initial clustering center and anomalous data and its tendency to fall into a local optimum. While some studies have also found that the K-means algorithm has deficiencies, and academics have made different degrees of improvement, most scholars only improve the K-means algorithm initial clustering center randomly selected and did not fundamentally solve the defects that easily fall into the local optimum. The final effect of constructing indicators in this paper is to seek the optimal result. That is, the existing improved K-means algorithm does not apply to the screening of indicators in this paper. However, the SA algorithm is an improved optimization algorithm based on the hill-climbing algorithm, and its most prominent feature is that it satisfies the Monte Carlo criterion and can obtain the global optimal solution. If the benefits of the SA and K-means algorithms are combined efficiently and used for the dynamic clustering process, it could overcome the early clustering occurrence witnessed in the conventional K-means algorithm. At this point, the procedure and the fitness function are designed based on the actual situation of different clustering problems so that the algorithm converges to the global optimal solution more efficiently and avoids falling into the local optimum. The rough set algorithm estimates the established indicator system, creating a more precise one.

In this paper, we use the idea of K-means clustering to determine the objective function. That is, divide the sample data into K clusters, each with its own centroid (center of mass), and minimize the sum of the distances between the sample data and the corresponding center of mass points to find an optimal clustering scheme, which determines the objective function. Since the gray correlation coefficient formula is highly similar to the distance formula, and the larger the gray correlation coefficient is, the better the result is, the paper sets the distance formula as the inverse of the gray correlation coefficient. The weighted sum of the inverse of the gray correlation coefficient is the objective function.

The K-means-SA algorithm is a search process for new solutions based on the initial solution. That is, under the premise of specifying the initial solution of the original problem, it randomly generates new solutions within the proximity of the initial solution and carries out the subsequent optimization process on top of it. The specific implementation steps of the K-means-SA algorithm are as follows:

Step 1: Set the algorithm parameters and initialize the solution vector.

Set the initial temperature to T₀ = 1 × 10¹, the current temperature to T = T₀, the terminal temperature to T_end = 1 × 10⁻⁵, the cooling rate to q = 0.9, LL = 100 represents the number of iterations, the current iteration number K = 1, assume that the current global optimal solution is X = X₀, and import the number of clusters as num, which has different value ranges due to different numbers of indicators.

Step 2: Construct a new solution.

Based on the existing solution, randomly search for a new solution X_new in the neighboring area and check whether the new solution X_new meets the conditions. If not, it keeps looping and searching for a new solution again until it gets a feasible one.

Step 3: Comparison and judgment

Calculate the objective function values of the initial solution X₀ and the new solution X_new, represented as F(X₀) and F(X_new), respectively. If F(X_new)>F(X) = F(X₀), set X₀ = X = X_new, and jump to Step 5. Otherwise, jump to Step 4.

Step 4: Metropolis criterion

Calculate the cost of the new solution PF, let PF = F(X₀)-F(X_new), and accept X_new as the current new solution with a probability P(A) = EXP(−PF/T).

Step 5: The number of iterations K = K+1. If K > 1, jump to Step 6. Otherwise, return to Step 2.

Step 6: Temperature decreases, and the current temperature decreases to T = T × q. If T<T_end, the algorithm ends, the optimization process terminates, and the optimal solution X, the optimal clustering result determined by the number of clusters, is obtained. Otherwise, return to Step 2.

Model

Combining the K-means-SA algorithm, we select evaluation indicators from five aspects: constructing a scoring matrix, indicator normalization, gray dynamic clustering analysis, calculating F-statistics, and rough set indicator reduction (Su et al., 2022).

(1) Constructing a scoring matrix

We are inviting seven experts engaged in research in the field of digital economy to hold a symposium on the constructed digital economy indicator system, including three who worked in different companies related to digital technology and four senior professors or associate professors from different universities’ digital economy research fields. The scoring matrix is the data source for system optimization.

(2) Indicator normalization

Because the indicators involved in this paper are benefit type due to the standard 0 to 1 transformation of the initial sample data without loss, high degree of reduction, and the method in various types of research in a wide range, this paper uses this method to achieve the normalization of the data (G. Chen et al., 2022; Hong & Huang, 2021; F. Liu et al., 2021; Wu et al., 2022; L. Zhang & Gao, 2020), the standardization of the formula as the Appendix of the formula 1.

(3) gray dynamic clustering analysis

For the attribute set obtained after the first screening (Table 2), the gray Relational Analysis (GRA) algorithm can overcome the limitations of the number and distribution patterns of research objects and has a significant advantage in representing information overlap using a gray relational matrix. Equation 2 in the Appendix is the formula for the gray correlation coefficient, and Equations 3 and 4 in the Appendix is the formula for the gray correlation matrix.

(4) Calculation of F-statistic

The large number of clusters generated during the clustering process can lead to inconsistent clustering results, necessitating a scientific method for finding the optimal number of classifications. As is known from mathematical statistics, the value of F in the F-statistic directly represents the distance between two categories. The greater the value, the greater the distance between different categories, and the closer the classification is to being optimal, resulting in a more perfect classification performance. Therefore, the advantage of using the F-statistic is that it encourages more scientific and reasonable classification results. This paper calculates the optimal number of classifications using the F-statistic, calculated as Equation 5 in the Appendix.

(5) Rough set index reduction

The attribute reduction process in this paper compares the initial attribute set and the clustering results after successive deletion of attributes. Suppose there is a difference between the two clustering results. In that case, it indicates that the deleted attribute significantly impacts the clustering type of the attribute set and is a necessary index, so this attribute should be retained. Conversely, exclude the attribute.

Based on the detailed description of the index screening process in the previous section, a flowchart for index screening can be drawn as shown (Figure 1).

Figure 1.

Flowchart for index screening.

K-means-SA Empirical Analysis

Based on the research design. Scores were given for “typicality, scientific, systematic, and sustainability,” with 25 points assigned to each category and a perfect score of 100. The expert scoring data is shown (Table 3). Furthermore, the expert scoring data was normalized using formula 1, shown (Table 4).

Table 3.

Expert Scoring Data.

Indicators	y₁	y₂	y₃	y₄	y₅	y₆	y₇
A₁₁	87	65	89	93	77	65	88
A₁₂	63	63	80	72.5	82	77	69
A₁₃	89	85	74	66.5	88	91	65
A₁₅	77	61	82.0	81	73	92.5	60
A₂₁	78	72	69	94	70.5	69	81
A₂₂	65	91	85	83	89	81	92
A₂₃	87	97	94	72	85	92	95.5
A₂₄	69.5	94	81	91.0	66	73	71
A₃₁	77	73.5	68	80	62	76	82
A₃₃	96	74	64	76	70	81.5	91
B₁₁	86	82	91.0	90	90	92	86
B₁₂	84	73	83	79	82	73	90
B₂₁	77	91	72	83	85.5	86	86
B₂₂	69	74	85	81.5	86	71	90
B₂₃	78	83.5	91	64	72	80	78
C₁₁	82	90	72	82	74	92.5	77
C₁₂	60	81.5	61	93	82	71	81
C₁₃	85	78	86	80	91.5	84	73
C₂₁	94	93	86.5	79	75	80	65
C₂₂	75	82	93	88	61	67	93
D₁₁	90	79	71	61.5	93	88	71.5
D₁₂	69.5	77	66	81.5	72	71	89
D₁₃	86	85	90	75.5	81	73	86
D₁₄	70	91	74.5	86	64	73	94
D₂₁	93	64	88	90	88.5	71	76

Table 4.

Normalized Scoring Data.

Indicators	y₁	y₂	y₃	y₄	y₅	y₆	y₇
A₁₁	0.79	0.00	0.86	1.00	0.43	0.00	0.82
A₁₂	0.00	0.00	0.89	0.50	1.00	0.74	0.32
A₁₃	0.92	0.77	0.35	0.04	0.88	1.00	0.00
A₁₅	0.52	0.03	0.68	0.65	0.40	1.00	0.00
A₂₁	0.00	0.96	0.74	0.67	0.89	0.59	1.00
A₂₂	0.60	1.00	0.88	0.00	0.52	0.80	0.94
A₂₃	0.13	1.00	0.54	0.89	0.00	0.25	0.18
A₂₄	0.75	0.58	0.30	0.90	0.00	0.70	1.00
A₃₁	1.00	0.31	0.00	0.38	0.19	0.55	0.84
A₃₃	0.65	0.00	0.59	0.35	0.53	0.00	1.00
B₁₁	0.26	1.00	0.00	0.58	0.71	0.74	0.74
B₁₂	0.15	0.93	0.61	0.22	0.44	1.00	0.00
B₂₁	0.00	0.24	0.76	0.60	0.81	0.10	1.00
B₂₂	0.49	0.88	0.00	0.49	0.10	1.00	0.24
B₂₃	0.52	0.72	1.00	0.00	0.30	0.59	0.63
C₁₁	0.00	0.65	0.03	1.00	0.67	0.33	0.55
C₁₂	0.65	0.27	0.70	0.38	1.00	0.52	0.00
C₁₃	1.00	0.97	0.74	0.48	0.34	0.52	0.00
C₂₁	0.44	0.66	1.00	0.84	0.00	0.19	1.00
C₂₂	0.91	0.56	0.31	0.00	1.00	0.84	0.33
D₁₁	0.15	0.48	0.00	0.65	0.26	0.22	1.00
D₁₂	0.76	0.71	1.00	0.15	0.47	0.00	0.76
D₁₃	0.20	0.90	0.35	0.73	0.00	0.30	1.00
D₁₄	1.00	0.00	0.83	0.90	0.84	0.24	0.41
D₂₁	0.00	0.73	0.14	0.82	1.00	0.36	0.57

Based on normalized data, the screening of indicators shown in Table 2 with the three-level indicators C₁₁ to C₁₃ and C₂₁ to C₂₂ as examples, the screening process of the rest of the indicators is the same as this process, and the gray correlation matrix C of the scoring data according to Equations 24 is established.

$C = [\begin{matrix} 1.0000 & 0.6392 & 0.6962 & 0.6051 & 0.5087 & 0.6344 & 0.4703 \\ 1.0000 & 0.5256 & 0.6418 & 0.5292 & 0.6130 & 0.5989 \\ 1.0000 & 0.5748 & 0.5590 & 0.5699 & 0.5885 \\ 1.0000 & 0.5527 & 0.5977 & 0.6182 \\ 1.0000 & 0.5959 & 0.5950 \\ 1.0000 & 0.4700 \\ 1.0000 \end{matrix}]$

The K-means-SA algorithm is applied to search for the optimal clustering case for a different number of classifications (Table 5). There were many classification situations for scoring sub-indicators C₁₁∼C₁₃ and C₂₁∼C₂₂ by seven experts, but there were seven different classification scenarios. Each category contained multiple clustering situations except one scenario for classification numbers 1 and 7. Each category contained multiple clustering situations. The algorithm’s fitness function was obtained for the optimal clustering situation when the number of clusters was 2∼6 (Figure 2), with the horizontal axis representing the number of iterations and the vertical axis representing the objective function. As the number of iterations increased, the objective function value decreased continuously and eventually stabilized, demonstrating the validity and reliability of the clustering results.

Table 5.

K-means-SA Clustering Results.

Classification Number	Statistic	Optimal Clustering Results	Whether it is the Best Classification
7	-	{y₁},{y₂},{y₃},{y₄},{y₅},{y₆},{y₇}	No
6	1.436	{y₁,y₂,y₃,y₄,y₅,y₆},{y₇}	No
5	1.853	{y₁,y₃},{y₂,y₄},{y₅},{y₆},{y₇}	No
4	2.252	{y₁,y₇},{y₂,y₅,y₆},{y₃},{y₄}	No
3	2.667	{y₁,y₄},{y₂,y₅,y₆,y₇},{y₃}	Yes
2	1.367	{y₁,y₂,y₃,y₅,y₇},{y₄,y₆}	No
1	-	{y₁,y₂,y₃,y₄,y₅,y₆,y₇}	No

Figure 2.

Fitness function of different clusters numbers: (a) clusters is 6, (b) clusters is 5, (c) clusters is 4, (d) clusters is 3, and (e) clusters is 2.

The type of clustering can affect the final clustering results. The optimal number of classifications needs to be determined to obtain a more scientific clustering result. Formula 5 was used in this paper to calculate the F-values for each category. According to Table 4, when the number of clusters is 3, the F-value is the largest, suggesting that the best classification is {y₁,y₄},{y₂,y₅,y₆,y₇}, and {y₃}. On this basis, the indicators have rough sets to approximate them. Precisely, remove one indicator at a time, and the K-means-SA algorithm was operated to search for the optimal clustering results for three classifications and compared with the original clustering results to remove indicators that did not affect the clustering results. The set of all attributes is C. Clustering by deleting C₁₁∼C₁₃ and C₂₁∼C₂₂. The clustering results are shown (Table 6).

Table 6.

Dynamic Clustering Results.

No.	Indicator situation	Clustering results	Whether to reduce?
1	C	{y₁, y₄},{y₂,y₅,y₆,y₇},{y₃}	-
2	C-C₁₁	{y₁,y₂},{y₃,y₄,y₅,y₆},{y₇}	No
3	C-C₁₂	{y₁,y₂},{y₂,y₄},{y₅,y₆,y₇}	No
4	C-C₁₃	{y₁,y₅},{y₂,y₃,y₄},{y₆},{y₇}	No
5	C-C₂₁	{y₁,y₂,y₅},{y₃,y₆},{y₄,y₇}	No
6	C-C₂₂	{y₁,y₂},{y₂,y₄},{y₅,y₆,y₇}	No

From the dynamic clustering results of Table 5, we can see that the optimal clustering results after removing any indicator are different from the clustering results of all indicators. Explain that all indicators need to be retained in their entirety and not abbreviated. Similarly, we can reduce the third-level indicators belonging to other secondary indicators through the above steps. The specific results are as follows: the clustering results after removing A₁₄ and A₁₅ in Mobile Device Foundation A₁ are the same as the clustering results of all indicators, indicating that A₁₄ and A₁₅ have no impact on the comprehensive evaluation results, so these two indicators should be simplified; the clustering results after removing A₃₂ in Network Equipment Foundation A₃ are the same as the clustering results of all indicators, indicating that A₃₂ should be simplified; the clustering results after removing D₁₄ in Economic Benefits D₁ are the same as the clustering results of all indicators, indicating that D₁₄ should be simplified; the clustering results after removing D₂₁ in Social Benefits D₂ are the same as the clustering results of all indicators, indicating that D₂₁ should be simplified. For other secondary indicators, the optimal clustering results differ from all indicators’ clustering results after removing any indicator, so all indicators need to be retained without reduction.

The K-means SA algorithm optimizes the indicator system (Figure 1). Finally, an indicator system with four dimensions, nine secondary indicators, and 22 tertiary indicators comes into being, which evaluates the digital economy as more rational, comprehensive, and holistic and provides a scientific basis and reference for the government, enterprises, and society, which is conducive to the planning of policies and strategies related to the digital economy and the promotion of the high-quality development of the digital economy. The optimized digital economic evaluation indicator system is shown (Table 7).

Table 7.

The Optimized Digital Economic Indicator System.

Primary indicator	Secondary indicator	Tertiary indicator (Unit)	Code
Digital infrastructureA	Mobile device infrastructureA₁	Mobile phone exchange capacity (10,000 households)	A₁₁
		Mobile phone penetration rate (number of mobile phones per 100 people)	A₁₂
		Mobile broadband penetration rate (%)	A₁₃
	Fixed equipment infrastructureA₂	Fixed telephone penetration rate (number of fixed telephones per 100 people)	A₂₁
		Number of domain names (10,000)	A₂₂
		Number of websites (10,000)	A₂₃
		Long-distance optical cable (kilometers)	A₂₄
	Network equipment infrastructureA₃	Number of internet enterprises (unit)	A₃₁
	Network equipment infrastructureA₃	Number of internet port accesses (10,000)	A₃₂
Digital applicationB	Personal applicationB₁	Number of TV sets (10,000)	B₁₁
	Personal applicationB₁	Digital life index (%)	B₁₂
	Enterprise applicationB₂	Number of enterprise-owned websites(unit)	B₂₁
	Enterprise applicationB₂	Proportion of e-commerce transaction enterprises (%)	B₂₂
Digital innovationC	Innovation inputC₁	R&D expenditure internal support (10,000 yuan)	C₁₁
		R&D investment (10,000 yuan)	C₁₂
		Public security expenditure (10,000 yuan)	C₁₃
	Innovation outputC₂	Number of patent applications (unit)	C₂₁
	Innovation outputC₂	Technology market turnover (10,000 yuan)	C₂₂
Digital benefitsD	Economic benefitsD₁	Software service revenue (10,000 yuan)	D₁₁
		E-commerce transaction amount (10,000 yuan)	D₁₂
		E-commerce sales (10,000 yuan)	D₁₃
	Social benefitsD₂	Employment structure (%)	D₂₁

Discussion

Theoretical Contribution

The primary goal of this paper is to eliminate the overlap between attributes, making the constructed indicator system more precise. The main contributions of this article are the following: (1) Combining GRA, SA, and K-means algorithms, we propose a K-means-SA algorithm that can obtain the global optimal solution. It not only overwhelms the defects of the original K-means algorithm’s random selection of initial cluster centers but also solves the inherent defects of single algorithm convergence to local optimum and premature, thus making the clustering results more accurate and stable. This supplements and extends the theoretical basis of relevant algorithms. (2) By combing and reviewing the indicator system in the existing literature, we comprehensively consider the four needs for the development of the digital economy, namely, the need for the development and improvement of the digital foundation, the need for the expansion and deepening of the digital application, the need for the increase and service of digital innovation, and the need for the change and upgrade of the digital enterprise, which will in turn lead to the enhancement of the benefits of the whole industry and the whole society. Based on the four dimensions of digital foundation, digital application, digital innovation, and digital benefit, a set of all-round, multi-system, and multi- dimensional indicator systems is built. It aims to comprehensively evaluate the development level of the digital economy, enriching and promoting the research on the evaluation index system of the digital economy.

Limitations and Future Research

This paper also needs to include the following shortcomings that warrant further research in the future. (1) Combine and extend the advantages of the K-means-SA algorithm based on the digital economy evaluation index system formed in this article. Although the construction of the indicator system in this paper is relatively comprehensive, more is needed at the digital economic development applications, such as digital cities, digital education, and digital livelihoods, and there are fewer indicators at the level of digital governance. Subsequent research can continue to use relevant methods to streamline and supplement the indicators and replace the more difficult-to-measure indexes. It will also use China’s inter provincial time-series panel data to conduct empirical analyses to guarantee that the data can remember the actual case of digital economic development. (2) Although the proposed K-means-SA algorithm effectively optimizes the indicator system, it inevitably needs to be improved. The following research step will optimize and improve the algorithm to adapt to a more complex and variable digital economy development environment and improve the indicator system’s accuracy and comprehensiveness. In addition, it enriches the accumulation of actual data and cases to improve the indicator system’s applicability and provide more scientific, accurate, and feasible theoretical support for the fundamental operation and management of the digital economy.

Conclusion and Policy Recommendation

The digital economy is an essential part of the current direction of economic development., and assessing the level of digital economic development can deliver a scientific foundation and guidance for country departments to design digital economic policies, financial institutions to make investment decisions, and enterprises to make management decisions. Continue to promote the high-quality regional development of the digital economy. We are following the laws of development and the connotations of the digital economy. Using digital foundation, digital application, digital innovation, and digital benefit as the dimensions of analysis, it constructed a digital economy indicator system containing 9 secondary and 28 tertiary indicators. It is of outstanding academic and practical value to optimize the indicator system through the K-means-SA algorithm and rough set approximation to reduce the overlap to enhance the precision and strength of the digital economic development index system.

Policy Recommendation

The following policy recommendations are provided: (1) The digital economy is a new form of economy accompanied by continuous innovation in digital technologies. With the widespread use of big data, blockchain, artificial intellect, and 5G, the profound integration of the digital economy with the whole of economizing has made everything data-enabled, and data has become a new element of display after ground, capital, technology, and knowledge. With the full development of the digital economy and the in-depth development of the value of data elements, the value of data will occupy a paramount share of the digital economy in the future. Therefore, to further deepen the understanding of the digital economy, it is vital to increase research on the definition of the concept of the digital economy, industry classification, value-added accounting, the building of a comprehensive index system and other aspects of the digital economy, and to expand the authoritative classification and accounting standards, thereby unifying the caliber of the digital economy accounting and clarifying the scope of the digital economy accounting. (2) In constructing the indicator system, comprehensive consideration from 4 dimensions, namely, digital foundation, digital application, digital innovation, and digital benefits, is given. It lays a basis for the study of the digital economy theoretically and practically. It provides a referable indicator system for evaluating the consequence of China’s digital economy in this background to better exert the role and support of the digital economy for the high-quality and highly efficient development of the economy. Government departments should exercise their leading role and join forces with digital economy enterprises, universities, and research institutes to form a working group to conduct exchanges and discussions and analyze the current problems in measuring the digital economy. (3) The existing indicator system is relatively biased toward the supply side and pays less attention to the demand side. From the experience of different economies at home and abroad over the past few decades, the statistical indicator systems constructed for the digital economy and its related economic forms are mainly supply-side indicators favoring the industrial dimension, while the construction of demand-side indicators corresponding to consumption, investment, and export is very preliminary whether it is the level and secondary indicators of the digital economy indicator system constructed by the US, OECD, or the primary and second-level indicators of the EU’s Digital Economy and Society Index, as well as the indicators of the new economy, knowledge-based economy, information economy or digitization. The Digital Economy and Statistical Indicator System, released by China’s National Bureau of Statistics, are all obviously classified from the supply side of the different industries and sectors dimensions to define and count. Therefore, the construction of demand-side consumption, investment, and export indicators corresponding to supply-side industries is also an essential direction for improving the statistical indicator system of the digital economy in the present and future.

Footnotes

Thank editors and reviewers a lot for valuable suggestions and comments.

Abbreviations

T 0 : initial temperature

T : current temperature

T end : Cut-off temperature

q : cooling rate

LL: Iteration number

K : current number of iterations

num: cluster number

X 0 : initial solution

X : global optimum solution

X new : new solutions in the adjustment process

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

Ethics Statement

An ethics statement (including the committee approval number) for animal and human studies. If this is not applicable,please state this instead.

ORCID iDs

Changhong Dong

Ke Su

References

Abdullah

Susilo

Ahmar

A. S.

Rusli

Hidayat

(2021). The application of K-means clustering for province clustering in Indonesia of the risk of the COVID-19 pandemic based on COVID-19 data. Quality & Quantity, 56(3), 1283–1291.

Basol

Yalcın

E. C.

(2021). How does the digital economy and society index (DESI) affect labor market indicators in EU countries? Human Systems Management, 40(4), 503–512. https://10.3233/HSM-200904

Belanova

N. N.

Kornilova

A. D.

Sultanova

A. V.

(2020). Target indicators and directions for the development of the Digital Economy in Russia. In Digital transformation of the economy: Challenges, trends and new opportunities (pp. 111–118). Springer. https://doi.org/10.1007/978-3-030-11367-4_11

Cao

(2018). Research on new manufacturing model to promote high-quality development of Chinese industry under the background of digital economy. Theoretical Discussion, 201(02), 99–104. https://doi.org/10.16354/j.cnki.23-1013/d.2018.02.016

Chen

Jiang

Tang

(2022). Research on evaluation of scientific and technological innovation ability of universities under the background of construction of world-class universities with Chinese characteristics. Science and Technology Progress and Counter Measures, 39(24), 109–118.

Chen

(2022). Is the digital economy driving clean energy development? New evidence from 276 cities in China. Journal of Cleaner Production, 372, 133783. https://doi.org/10.1016/j.jclepro.2022.133783

Chen

Peng

(2023). Impact of new government–business relations on urban digital economy: Empirical evidence from China. Finance Research Letters, 58, 104325. https://doi.org/10.1016/j.frl.2023.104325

Cong

R. Y.

Gao

X. Y.

Huang

Z. H.

, et al. (2022). An overview of the progress of digital economy research. Contemporary Economy, 39(01), 15–19.

Dong

Zhu

(2020). A new K-means algorithm for selecting initial cluster center. Statistics and Decision, 36(16), 32–35. https://doi.org/10.13546/j.cnki.tjyjc.2020.16.007

10.

Zhang

Xia

(2022). Has China stepped into the ranks of innovative countries? A comprehensive study and judgment based on six authoritative evaluation index systems. Science and Technology Progress and Counter Measures, 39(15), 20–30.

11.

Bai

Zhu

(2018). K-means algorithm based on improved density peak algorithm. Statistics and Decision, 34(18), 20–24. https://doi.org/10.13546/j.cnki.tjyjc.2018.18.004

12.

Huang

Dong

Zhou

Wang

(2022). The measurement, sources of variation, and factors influencing the coupled and coordinated development of rural revitalization and digital economy in China. PLoS One, 17(11), e0277910. https://doi.org/10.1371/journal.pone.0277910

13.

Guo

H. M.

Wang

(2022). A review of research on digital economy accounting. Statistics and Decision Making, 38(09), 5–10. https://doi.org/10.13546/j.cnki.tjyjc.2022.09.001

14.

Han

Ding

Shi

(2022). The impact of digital economy on total factor carbon productivity: The threshold effect of technology accumulation. Environmental Science and Pollution Research International, 29(37), 55691–55706. https://doi.org/10.1007/s11356-022-19721-x

15.

Hong

Huang

(2021). Construction and evaluation of fair competition index system between state-owned enterprises and private enterprises. Shanghai Economic Research, 388(01), 66–77. https://doi.org/10.19626/j.cnki.cn31-1163/f.2021.01.006

16.

Hou

Ding

(2023). A novel clustering algorithm based on multi-layer features and graph attention networks. Soft Computing, 27(9), 5553–5566. https://doi.org/10.1007/s00500-023-07848-z

17.

Huang

Han

Chen

(2023). Can the digital economy promote the upgrading of urban environmental quality? International Journal of Environmental Research and Public Health, 20(3), 2243. https://doi.org/10.3390/ijerph20032243

18.

Hwang

Y. K.

(2023). The synergy effect through combination of the digital economy and transition to renewable energy on green economic growth: Empirical study of 18 Latin American and Caribbean countries. Journal of Cleaner Production, 418, :138146. https://doi.org/10.1016/j.jclepro.2023.138146

19.

Ivanova

Degtereva

Lukin

(2019). Evaluation of Digital Transform -ation of Government: Russian and international systems of indicators [Conference session]. Proceedings of the 2019 International SPBPU Scientific Conference on Innovations in Digital Economy (pp. 1–8). https://doi.org/10.1145/3372177.3373330

20.

Jiang

Wang

(2018). Anomaly detection of marine data based on improved K-means algorithm. Computer Engineering and Design, 39(10), 3132–3136. https://doi.org/10.16208/j.issn1000-7024.2018.10.023

21.

Jiang

Jin

(2022). Digital technology to improve economic efficiency: Service division, industrial collaboration and digital real twin. Management World, 38(12), 9–26. https://doi.org/10.19744/j.cnki.11-1235/f.2022.0173

22.

Jiang

(2020). Digital economy in the post-pandemic era. Journal of Chinese Economic and Business Studies, 18(4), 333–339. https://doi.org/10.1080/14765284.2020.1855066

23.

Jin

Chen

Wang

Guo

Dong

Yang

(2019). Trade-offs in land-use competition and sustainable land development in the North China Plain. Technological Forecasting and Social Change, 141, 36–46. https://doi.org/10.1016/j.techfore.2019.01.004

24.

Jing

Sun

(2019). Digital economy promoting high-quality economic development: A theoretical analysis framework. The Economist, 1(02), 66–73. https://doi.org/10.16158/j.cnki.51-1312/f.2019.02.008

25.

Zhu

(2022). Digital economy enables industrial structure upgrading: Demand traction and supply optimization. Academic Monthly, 54(04), 63–77. https://doi.org/10.19862/j.cnki.xsyk.000398

26.

Lakshmi

Baskar

(2019). DIC-DOC-K-means: Dissimilarity-based initial centroid selection for DOCument clustering using K-means for improving the effectiveness of text document clustering. Journal of Information Science, 45(6), 818–832. https://doi.org/10.1177/0165551518816302

27.

Lian

Wang

(2022). Research on measurement and spatial pattern of digital economy development in 19 national urban agglomerations. Science and Technology Progress and Countermeasures, 39(24), 29–39.

28.

Nong

(2013). Improved K-means algorithm based on vector semantic similarity. Information Science, 31(02), 34–37. https://doi.org/10.13833/j.cnki.is.2013.02.013

29.

Zhang

Zou

(2020). The seeding algorithms for spherical k-means clustering. Journal of Global Optimization, 76(4), 695–708. https://doi.org/10.1007/s10898-019-00779-w

30.

Liu

Cao

Zuo

(2021). Evaluation index system construction and empirical research of rumor-refuting platform. Journal of Information, 40(09), 95–100.

31.

Liu

Yang

Zhang

(2020). Research on measurement and driving factors of China’s digital economy. Shanghai Economic Research, 1(06), 81–96. https://doi.org/10.19626/j.cnki.cn31-1163/f.2020.06.008

32.

Liu

Zhang

, et al. (2022). Local modeling and optimization of K-means PSO-SVR for producing aromatic hydrocarbons from methanol. Chemical Industry Progress, 41(09), 4691–4700. https://doi.org/10.16085/j.issn.1000-6613.2021-2466

33.

Jiang

Zhang

, et al. (2023). Measurement and spatial-temporal evolution of high-quality development of China’s digital economy. Statistics and Decision, 39(04), 90–94. https://doi.org/10.13546/j.cnki.tjyjc.2023.04.016

34.

Liu

(2021). Research on the spatial distribution pattern and influencing factors of digital economy development in China. IEEE Access, 9, 63094–63106. https://doi.org/10.1109/access.2021.3075249

35.

Wang

(2022). The dynamic impact of digital economy on carbon emission reduction: Evidence city-level empirical data in China. Journal of Cleaner Production, 351:131570. https://doi.org/10.1016/j.jclepro.2022.131570

36.

Luo

Yimamu

Irfan

Hao

(2023). Digitalization and sustainable development: How could digital economy development improve green innovation in China? Business Strategy and the Environment, 32(4), 1847–1871. https://doi.org/10.1002/bse.3223

37.

Fan

(2023). Research on spatial -temporal differentiation and influencing factors of China’s digital economy development. Journal of Chongqing University (Social Science Edition), 29(03):47–60.

38.

Onifade

S. T.

Alola

A. A.

Erdoğan

Acet

(2021). Environmental aspect of energy transition and urbanization in the OPEC member states. Environmental Science and Pollution Research, 28, 17158–17169. https://doi.org/10.1007/s11356-020-12181-1

39.

Onifade

S. T.

Asongu

Bekun

F. V.

(2020). Revisiting the trade and unemployment nexus: Empirical evidence from the Nigerian economy. Journal of Public Affairs, 20(3): e2053, https://doi.org/10.1002/pa.2053

40.

Onifade

S. T.

Çevik

Erdoğan

Asongu

Bekun

F. V.

(2020). An empirical retrospect of the impacts of government expenditures on economic growth: New evidence from the Nigerian economy. Journal of Economic Structures, 9(1), 1–13. https://doi.org/10.1186/s40008-020-0186-7

41.

Özöğür Akyüz

Eygi Erdogan

Yıldız

Ö.

Karadayı Ataş

. (2023). A novel hybrid house price prediction model. Computational Economics, 62, 1215–1232. https://doi.org/10.1007/s10614-022-10298-8

42.

Pan

(2021). Spatial and temporal evolution and distribution dynamics of China’s digital economy. China Soft Science, 1(10), 137–147.

43.

Pei

(2018). Political economy analysis of digital economy. Finance and Trade Economy, 39(09), 5–22. https://doi.org/10.19795/j.cnki.cn11-1166/f.2018.09.001

44.

Pham

D. T.

Dimov

S. S.

Nguyen

C. D.

(2004). An incremental K-means algorithm. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 218(7), 783–795. https://doi.org/10.1243/0954406041319509

45.

Xiao

Cai

(2020). The digital reconstruction of industrial organization. Journal of Beijing Normal University (Social Science Edition), 1(02), 130–147.

46.

Ren

Lee

S. J.

(2023). Digitalization improves enterprise performance: New evidence by text analysis. Sage Open, 13(2), 21582440231175871. https://doi.org/10.1177/21582440231175871

47.

Ren

Wang

Liu

(2023). Impact of traditional and digital financial inclusion on enterprise innovation: Evidence from China. Sage Open, 13(1), 21582440221148097. https://doi.org/10.1177/21582440221148097

48.

Savina

T. N.

(2018). Digital economy as a new paradigm of development: Challenges, opportunities, and prospects. Finance and Credit, 24(3), 579–590. https://doi.org/10.24891/fc.24.3.579

49.

Shahbaz

Wang

Dong

Zhao

(2022). The impact of digital economy on energy transition across the globe: The mediating role of government governance. Renewable and Sustainable Energy Reviews, 166 112620. https://doi.org/10.1016/j.rser.2022.112620

50.

Shen

Zhou

(2023). Measurement and spatial-temporal pattern analysis of China’s digital economy development. Statistics and Decision, 39(03), 5–9. https://doi.org/10.13546/j.cnki.tjyjc.2023.03.001

51.

Shi

(2021). Evolution of industrial development trend under the conditions of digital economy. China Industrial Economy, 2022(11), 26–42. https://doi.org/10.19581/j.cnki.ciejournal.2022.11.001

52.

Shi

Chen

(2023). Research on mechanism and path of digital economy promoting common prosperity. Scientific and technological progress and Countermeasures. Retrieved January 23, 2023, from http://kns.cnki.net/kcms/detail/42.1224.G3.20221130.1432.003.html.

53.

Sidorov

Senchenko

(2020). Regional digital economy: Assessment of Development Levels. Mathematics, 8(12), 2143. https://doi.org/10.3390/math8122143

54.

Sturgeon

T. J.

(2021). Upgrading strategies for the digital economy. Global Strategy Journal, 11(1), 34–57. https://doi.org/10.1002/gsj.1364

55.

Wang

(2022). Evaluation of digital economy development level based on multi-attribute decision theory. PLoS One, 17(10): e0270859, https://doi.org/10.1371/journal.pone.0270859

56.

Sun

Liu

(2022). Digital economy, urbanization and farmers’ income increase: An empirical test based on the Yangtze River Economic Belt. Exploration of Economic Problems, 1(03), 1–14.

57.

Sun

Chen

Shi

Yang

(2022). Influence of digital economy on industrial wastewater discharge: Evidence from 281 Chinese prefecture-level cities. Journal of Water and Climate Change, 13(2), 593–606. https://doi.org/10.2166/wcc.2021.447

58.

Sun

Chen

(2018). Research on the establishment of local party organization political ecological assessment index system. Theoretical Investigation, 205(06), 127–133. https://doi.org/10.16354/j.cnki.23-1013/d.2018.06.020

59.

Sun

Hong

(2022). Construction of digital economy monitoring and evaluation system based on high-quality development: A case study of the construction of global digital economy benchmark city in Beijing. Bulletin of Chinese Academy of Sciences, 37(06), 812–824. https://doi.org/10.16418/j.issn.1000-3045.20220521001

60.

Tao

Zhi

Shangkun

(2022). Digital economy, entrepreneurship, and high quality economic development: Empirical evidence from urban China. Frontiers of Economics in China, 17(3): p393–426. 34p.

61.

Wang

Dong

(2023). Is the digital economy conducive to the development of renewable energy in Asia? Energy Policy, 173, 113381. https://doi.org/10.1016/j.enpol.2022.113381

62.

Wang

Zhu

Luo

(2021). The development level and evolution measurement of China’s digital economy. Quantitative Economy Technical Economy Research, 38(07), 26–42. https://doi.org/10.13653/j.cnki.jqte.2021.07.002

63.

Wang

(2022). Evaluation of high-quality development of Shaanxi’s economy based on digital economy based on machine learning algorithm. International Transactions on Electrical Energy Systems, 2022, 1–9. https://doi.org/10.1155/2022/6327347

64.

Wang

Bai

(2016). The global Minmax k-means algorithm. SpringerPlus, 5(1), 1665. https://doi.org/10.1186/s40064-016-3329-4

65.

Wang

(2021). Research on the impact of digital economy on the transformation of small and medium-sized manufacturing enterprises. Comparison of Economic and Social Systems, 215(03), 47–57.

66.

Wang

Shi

(2021). Research and analysis on the index system of digital economy in Anhui province. Complexity, 2021, 1–8. https://doi.org/10.1155/2021/5535864

67.

Wan

Luo

(2022). Measurement of the development level of digital economy and its impact on total factor productivity. Reform, 335(01), 101–118.

68.

Wen

Yan

Cheng

(2020). Research on the effect of digital economy driving innovation: Regression based on provincial panel data. Reform of Economic System, 1(03), 31–38.

69.

Williams

L. D.

(2021). Concepts of Digital Economy and Industry 4.0 in intelligent and information systems. International Journal of Intelligent Networks, 2, 122–129. https://doi.org/10.1016/j.ijin.2021.09.002

70.

Liu

, et al. (2022). Comprehensive evaluation of the quality of network geospatial intelligence service based on the cloud model. Information Theory and Practice, 45(04), 47–51. https://doi.org/10.16353/j.cnki.1000-7490.2022.04.007

71.

Wang

(2012). Measurement of digital economy development level based on the latest statistical classification standard. Statistics & Decisions, 38(03), 16–21. https://doi.org/10.13546/j.cnki.tjyjc.2022.03.003

72.

Xiang

(2018). Recent developments and implications of OECD digital economic accounting research. Statistical Research, 35(12), 3–15. https://doi.org/10.19343/j.cnki.11-1302/c.2018.12.001

73.

Xia

Wang

Ding

(2023). Evolution of digital economy research: A bibliometric analysis. International Review of Economics & Finance, 88, 1151–1172. https://doi.org/10.1016/j.iref.2023.07.051

74.

Xin

Song

Shen

Wang

(2023). Measurement of the integration level between the digital economy and industry and its impact on energy consumption. Energy Economics, 126,106988. https://doi.org/10.1016/j.eneco.2023.106988

75.

Q. Y.

San

Z. G.

C. J.

(2018). A review of research on digital economy measurement index system at home and abroad. Research World, 1(11), 52–58. https://doi.org/10.13778/j.cnki.11-3705/c.2018.11.008

76.

Zhang

(2020). Research on the scale measurement of China’s digital economy: From the perspective of international comparison. China Industrial Economy, 1(5), 23–41. https://doi.org/10.19581/j.cnki.ciejournal.2020.05.013

77.

(2022). Measuring digital economy in China. National Accounting Review, 4(3), 251–272.

78.

Yang

(2022). Analysis of digital economy development based on AHP-Entropy weight method. Journal of Sensors, 2022, 1–8. https://doi.org/10.1155/2022/7642682

79.

Yang

Dong

(2022). Evaluation Index System of China’s Digital Economy Development Level-based on factor analysis. Academic Journal of Business and Management, 4(18), 89–95. https://doi.org/10.25236/ajbm.2022.041815

80.

Yan

Deng

Peng

Jiang

(2022). Study on the impact of digital economy development on carbon emission intensity of urban agglomerations and its mechanism. Environmental Science and Pollution Research, 30(12), 33142–33159. https://doi.org/10.1007/s11356-022-24557-6

81.

Yao

(2020). Regional marketization level and digital economy competition: An analysis of inter-provincial spatial distribution characteristics based on digital economy index. Jianghan Forum, 1(12), 23–33.

82.

Zhang

Dong

Wang

(2022). High- quality development of China’s digital economy: Connotation, current situation and countermeasures. Journal of Humanity, 318(10), 75–86. https://doi.org/10.15895/j.cnki.rwzz.2022.10.009

83.

Zhang

Zhao

Cheng

, et al. (2022). The impact of digital economy on the economic growth and the development strategies in the post-COVID-19 Era: evidence from countries along the “Belt and Road. Frontiers in Public Health, 10, 856142. https://doi.org/10.3389/fpubh.2022.856142

84.

Zhang

Gao

(2020). Research on index screening method based on k-means clustering and rough set algorithm. Operations Research and Management, 29(12), 8–12.

85.

Zhang

(2017). Research progress of international new economy measurement and its reference to China. The Economist, 227(11), 47–55. https://doi.org/10.16158/j.cnki.51-1312/f.2017.11.006

86.

Zhang

Zhao

Wan

Yao

(2021). Study on the effect of digital economy on high-quality economic development in China. PLoS One, 16(9), e0257365. https://doi.org/10.1371/journal.pone.0257365

87.

Zhang

Jiao

(2017). Chinese digital economy development index and its application. Zhejiang Social Sciences, 1(04), 32–40. https://doi.org/10.14167/j.zjss.2017.04.005

88.

Zhao

Zhang

Liang

(2019). Digital economy, entrepreneurial activity and high-quality development: Empirical evidence from Chinese cities. Management World, 36(10), 65–76. https://doi.org/10.19744/j.cnki.11-1235/f.2020.0154

89.

Zheng

Wong

C. Y.

(2024). The impact of digital economy on renewable energy development in China. Innovation and Green Development, 3(1), 100094. https://doi.org/10.1016/j.igd.2023.100094

90.

Zhou

Liu

(2022). Evaluation of digital competitiveness of G20 countries and its implications. Reform of Economic System, 1(03), 164–171.

91.

Zhu

Hua

Shi

Tang

Miao

(2021). An improved K-means algorithm based on evidence distance. Entropy, 23(11), 1550. https://doi.org/10.3390/e23111550

Research on the Construction of Digital Economy Index System Based on K-means-SA Algorithm

Abstract

Plain language summary

Keywords

Introduction

Literature Review

Research on the Application and Impact of the Digital Economy

Research on the Index System for the Level of Development of the Digital Economy

Research on the Evaluation Method of Digital Economy Development

Construction of the Evaluation Index System

Methodology

K-means-SA Algorithm

Model

K-means-SA Empirical Analysis

Discussion

Theoretical Contribution

Limitations and Future Research

Conclusion and Policy Recommendation

Policy Recommendation

Footnotes

Abbreviations

Declaration of Conflicting Interests

Funding

Ethics Statement

ORCID iDs

References