The entropy weight method is an objective assignment method which can objectively and realistically react to the information implied in the indicator data compared with other subjective assignment methods (Feng and Gong, 2020; Ouadfel and Abd Elaziz, 2021). Therefore, this paper uses the entropy weight method to determine the weights of indicators to provide a basis for comprehensive evaluation.

The first step is the standardization of indicator data. Given that there are certain differences in the evaluation index system among the indicators in terms of the outline, order of magnitude, etc., it is necessary to standardize the data to eliminate the impact of the differences in the indicators on the evaluation results to achieve comparability among the indicators. This paper adopts the method of polar deviation standardization to standardize the evaluation index data, and the calculation process is shown in Equations (1, 2): (1) Positive indicators Z i j t = X i j t − X j min X j max − X j min (2) Negative indicators Z i j t = X j max − X i j t X j max − X j min

where x_ijt is the original indicator value, i denotes the region (i = 1, 2,.., n), j represents the indicator (j = 1, 2,.., m), t represents the time (t = 1, 2,.., k), and Z_ijt is the standardized indicator value. X_jmax denotes the maximum value of the j-th indicator in all samples and X_jmin denotes the minimum value of the j-th indicator in all samples.

In the second step, we calculate the weight of the j-th indicator for the i-th region in year t [see Equation (3)]: (3) p i j t = Z i j t / ∑ i = 1 n ∑ t = 1 k Z i j t

In the third step, we calculate the information entropy of the j-th indicator [see Equation (4)]: (4) e j = − 1 In m × k ∑ i = 1 n ∑ t = 1 k p i j t In p i j t

If p_ijt = 0, then define lim p i j t → 0 p i j t In p i j t

In the fourth step, we calculate the j-th indicator’s weight [see Equation (5)]: (5) ω j = 1 − e j / ∑ j = 1 m 1 − e j

where ω j ∈ 0 1 ; ∑ j = 1 m ω j = 1

In the fifth step, we calculate the i-th region’s composite index in year t [see Equation (6)]: (6) E it or F it = ∑ j = 1 m ω j Z i j t

E_it and F_it are development indexes for agricultural and rural digital and sustainable food systems, respectively.

The coupling coordination degree (CCD) originates from the concept of physics, which characterizes the influence degree of two or more systems interacting. The coupling role and the degree of coordination determine the coupled system’s evolutionary development. The coupling degree, as an important indicator reflecting the degree of coupling between ARD and FSS, is of great significance in determining the strength of the coupling between the two, the time interval of the coupling action, and the development order of early warning of the two. However, the coupling degree in some cases is difficult to reflect the overall development level of ARD and FSS. For this reason, the ARD and FSS coupling coordination degree model is constructed to judge the high level of coordinated development of ARD and FSS. The CCD model of the two systems can be expressed as (Cheng et al., 2019; Li, 2022): (7) D it = C it × T it

Among them: (8) C it = E it × F it E it + F it / 2 2 1 / 2 (9) T it = α E it + β F it

In Equations (7)–(9), C_it is the degree of coupling. When C_it = 1, it indicates that the two systems are in the optimal coupling state; when C_it = 0, it indicates that the development between the two systems is irrelevant, i.e., the coupled system develops to disorder. The degree of coupling can only indicate the degree of system interaction, i.e., the consistency between the two systems, but cannot reflect the level of coordinated development of the system. E_it and F_it are development indexes for agricultural and rural digital and sustainable food systems, respectively. T_it is the comprehensive development index of the two systems. α and β are the undetermined coefficients, for the two systems are usually taken to be 0.5. D_it reflects the CCD of the two systems, the value of which ranges from 0 to 1. The bigger D_it is, the stronger the two systems’ coupling coordination is, i.e., the level of development of the two systems is high and coordinated. This paper draws on the “four-point method” of (Lai et al., 2020; Yan et al., 2021) to divide the CCD interval, shown in Table 3.

Coordinated development is an evolutionary process from low to high level, from disorder to order, from simple to complex, formed by mutual adaptation, collaboration, and promotion of the systems and their system elements. The coordinated development of the coupled system is closely related to the subsystems and their elements. To effectively promote the coupled and coordinated progression of ARD and FSS, we use the obstacle degree model to diagnose the obstacle factors affecting the coupled and coordinated development of the two. The equations for the model are as follows: (10) I i j t = 1 − Z i j t (11) h i j t = ω j I i j t ∑ j = 1 m ω j I i j t × 100 % (12) H i j ′ t = ∑ j h i j t

In Equations (10)–(12), Z_ijt is the standardized indicator value; I_ijt is the indicator deviation, i.e., the gap between the corresponding indicator’s standardized value and 1; ω_j is the factor contribution, i.e., the weight of a single indicator to the coupling coordination goal; h_ijt and H_ijt are the obstacle degree of the indicator layer indicator j and the factor layer indicator of the i-th region in the year t, respectively.

This paper takes 30 PAAs in China (excluding Tibet, Hong Kong, Macau, and Taiwan region) as the study area, with a sample period of 2011–2020 (given the availability of data). Raw data were obtained from the National Bureau of Statistics of China, China Statistical Yearbook, China Rural Statistical Yearbook, China Agricultural Yearbook, China Grain Yearbook, China Grain and Material Reserve Yearbook, China Taobao Village Research Report, Peking University Digital Inclusive Finance Index, Statistical Yearbooks of PAAs (provinces, autonomous regions, and centrally administered municipalities), and China’s provincial Food and Strategic Reserves Bureaus. Missing data for individual years are filled in by interpolation. We interpolate the missing data for individual years to fill in the gaps.

This paper first calculates the development indexes of agricultural and rural digital systems and sustainable food systems in each provincial administrative area (PAA) of China from 2011 to 2020. To clearly show the gap between the development indexes of the two systems, the two development indexes are written in fraction form. The numerator and denominator denote the ARD and the FSS development index, respectively. After entering the 21st century, China has divided the country into four major regions, namely, eastern, central, western, and northeastern regions, based on the natural conditions, economic foundation, development level, and opening degree to the outside world, to promote coordinated regional development. Therefore, this paper further averages the national, eastern, central, northeastern, and western regions, which can more clearly show the regional differences between the two development indexes (see Table 4).

At the national level, the ARD and the FSS Index are on an upward trend over the sample period. Although the ARD Index is generally smaller than the FSS Index, the gap between the two has gradually narrowed throughout the evolution. As of 2020, there are individual years and PAAs where the ARD is larger than the FSS development index. This phenomenon indicates that the growth rate of ARD is greater than that of FSS, and this development trend is conducive to the coupled system’s evolution to a higher order. However, both are generally low overall, and the growth rate is usually slow. For example, in 2020, the national averages of the ARD index and FSS indexes’ national averages are 0.190 and 0.350, respectively.

Locally, eastern China is leading the way in ARD. And the differences in FSS across regions are not noticeable. However, the growth rates show significant differences in different regions, such as the fast growth rate of ARD in the eastern region and FSS in the western region. This indicates that the evolution of ARD is synchronized with the evolution of FSS at different speeds, which may be due to the different foundations of ARD and FSS.

This section calculates the coupling degree and CCD of the agricultural rural digital system and sustainable food system in each PAA of China from 2011 to 2020. To be able to clearly show the gap between the coupled systems’ coupling degree and the CCD, this paper writes both in the form of a fraction. The numerator and denominator represent the coupling degree and CCD of the coupled system, respectively. In this paper, we further find the mean value for the whole country, the eastern, central, northeast, and western China, to show the regional differences between the coupling degree and the CCD (see Table 5).

At the national level, the coupling degree of the vast majority of Chinese PAAs has been stabilized above 0.8, which is at a high level of coupling. This phenomenon indicates that there is a close interdependence and interaction between China’s agricultural and rural digital system and the sustainable food system, i.e., there is a strong correlation between the two systems. However, having a high coupling level does not mean a high level of coordination between the two. From the Equations (7–9), the CCD is not only related to the coupling degree but also closely related to the comprehensive development index of the two systems. Therefore, when the development index of both systems is high, i.e., when the CCD is high, the high-level coordinated development of ARD and FSS can be realized. As can be seen from Table 5, the CCD of Chinese PAAs is generally low; the vast majority of PAAs are in the low and medium coupling coordination range, and a few PAAs have barely reached the high coupling coordination range in individual years. The CCD is about half of the coupling degree. Still, the CCD has increased at a faster rate, indicating that the coordinated development level of ARD and FSS has been significantly improved. This is mainly due to the relevant policy drivers of the digital economy and the safeguarding of food security in rural areas in recent years (Du et al., 2022; Lv et al., 2022).

From a localized point of view, the coupling degree, and the CCD of the northeastern, western, central, and eastern China are all increasing in turn. This indicates that the correlation between the ARD and the FSS in the northeast, west, central, and east regions is gradually increasing in that order, and the coordinated development level is also gradually increasing. The coupling degree in the central region increased the fastest, and the CCD in the eastern region increased the fastest. This phenomenon indicates that the coordinated development level of both ARD and FSS in the eastern region is ahead of other regions. The possible reason for this is the favorable geographic conditions in eastern China. Eastern China is flat (Wang et al., 2023), and the limited arable land is mainly concentrated in the plains of the monsoon zone in eastern China (Chen et al., 2023). In contrast, the geography of the central and western parts of the country is more diverse and complex. The complex geographical environment is unfavorable to food production and limits the promotion and popularization of digitization. For example, suppose the government needs to install a 5G communication base station at a high altitude. In that case, the tower firmware of the base station weighs several 100 kg, and the poor traffic conditions often limit the use of transportation or even the use of workforce to carry these bulky components. Even after the installation of the base station, preventing the climate from interfering with the signal and the maintenance of the room at a later stage is very difficult (Pangestu, 2022). This reason is why the first high-altitude 5G base station in Xinjiang was not set up until the end of 2021 in the Hotan region, which is 3,700 meters above sea level. In comparison, China opened its first 5G base station in Guangzhou, Guangdong Province, in 2017 (Liu et al., 2018). The northeast has the slowest growth rate in both coupling and coupling coordination, with the region lagging behind the other regions in both coupling and coupling coordination by 2020. This may be because the northeast has experienced significant population loss and aging in recent years, causing the rural digital economy and food system sustainable development to lag other regions (Mitra et al., 2021; Zhou et al., 2022).

In order to explore which indicators are obstacle factors affecting the development of agricultural and rural digital system and sustainable food system, we use Equations (10)–(12) to calculate the obstacle degree of each indicator in the indicator layer of the ARD and FSS evaluation index system. The obstacle factors are ranked according to the size of the obstacle degree. In this paper, the top 3 ranking obstacle factors in each PAA and each year are called the main obstacle factors, and the screening results are shown in Table 6. Where E_i is the obstacle factor (indicator) affecting the development of ARD and F_i is the obstacle factor (indicator) affecting the development of FSS. In Table 6, we use “forward slash” to separate the different factors.

As far as the indicator layer is concerned, the main obstacle factors vary from province to province and year to year. Still, they can reflect the main obstacle factors of the coordinated evolution of the system to a certain extent. For the agricultural and rural digital system, the top three major obstacle factors in 2011–2020 are the level of rural digital platform construction, the digital degree of agricultural products trading, and the level of rural residents’ consumption of digital products and services. The main obstacle factors to this system are relatively stable in time and space, showing differences only in individual PAAs and individual years. As seen in Table 6, the obstacle factors of the four large economic and population PAAs, Beijing, Shanghai, Zhejiang, and Guangdong, differed from those of the other PAAs in individual years. For example, Beijing’s ranking of major obstacle factors was E₇/E₅/E₈ in 2011, E₇/E₈/E₅ in 2015, but evolved to E₇/E₈/E₁ in 2020, which may be inextricably linked to the basis of digital development in different districts. For sustainable food systems, overall, the top 3 main obstacle factors for 2011–2020 are per capita food possession, governance level of soil erosion, and the effective irrigation of farmland. Per capita food possession has always been the primary factor impeding the FSS in space and time. This result suggests an urgent need to address the generally low per capita food possession in China on the way to achieving FSS. The second-and third-ranked obstacle factors vary across provinces and years, suggesting that the remaining ones are not static but constantly adjusted as the system evolves.

As far as the factor level is concerned, the main obstacle factors of the agricultural and rural digital system are, in descending order, rural digital industrialization, agricultural digitalization, and rural digital infrastructure. This ranking is stable in both time and space, indicating that China’s current ARD is still in its infancy, and there is still much room for the development of digital industrialization (Chen et al., 2022; Lee et al., 2023).

The main barriers to the sustainable food system are, in descending order, food stability, environmental and resource sustainability, food production security, economic and social sustainability, and food accessibility. Among them, food stability and resource and environmental sustainability have always been the top two obstacles in different times and spaces. Food accessibility was the third most obstacle factor for most PAAs in 2011. Still, by 2020 it had improved and had become the least obstacle factor for most PAAs. This phenomenon is due to the gradual realization of China’s poverty eradication task, the living standards of rural residents have been improving (Gao et al., 2019), and their purchasing power for food is increasing. In contrast, food production security became the third-ranked obstacle in most PAAs in 2020, indicating that China’s food production security has deteriorated recently. This may be due to the overuse of agrochemicals such as pesticides and fertilizers in the agricultural production process, which threatens food production security (Kopittke et al., 2019).

In this study, based on the theoretical connotation and practical operability of the ARD and FSS, the evaluation indicator system of the development level of the two was constructed, respectively. It also takes Chinese PAAs as the research object and measures the comprehensive development index of each PAA from 2011 to 2020, respectively, using the entropy weight method. The results show that the development indexes of ARD and FSS in most Chinese PAAs have gradually increased during the sample period, but the levels are still low overall. The ARD is generally smaller than the FSS development index, but the gap between the two gradually narrowing during evolution. The results of this paper’s ARD measurement validate existing studies’ findings (Tang and Chen, 2022; Xu et al., 2022). For the measurement of FSS, existing studies mainly focus on economically developed countries, including the United States (Heller and Keoleian, 2003), the United Kingdom (Yakovleva, 2007), Japan (Tsuchiya et al., 2021), and Germany (Keuter et al., 2021), etc., while studies for developing countries are still scarce.

In addition, existing measurement studies on the ARD mainly focus on a local area (Zhao and Li, 2022; Zhu et al., 2023) and regions (states, provinces, or cities, etc.) within a country (Tang and Chen, 2022; Xu et al., 2022), and there is a lack of comparative studies on different regions within a country. In contrast, current measures of FSS tend to be based on characteristic facts and national policies from a holistic perspective but do not specifically address FSS in regions (states, provinces, cities, etc.) within countries. The coarse granularity of the existing studies does not consider the characteristics of different regions within the country. It cannot provide precise and objective countermeasure recommendations for establishing a sustainable food system for smaller research objects (states, provinces, cities, etc.). This paper thus further explores the developmental heterogeneity between regions. The results show that the eastern region of China is leading in the ARD. FSS does not differ significantly across China’s regions, but growth rates show significant differences. The growth rate of ARD is faster in the eastern region, while FSS grows faster in the western region. The research in this paper contributes to a comprehensive understanding of the evolutionary trends of ARD and FSS in the country as a whole and within the country.

This paper further analyzes the relationship between the roles of agricultural and rural digital systems and sustainable food systems. Unlike existing studies focusing only on the unidirectional impact of agricultural or rural digitization on FSS, this study approaches from a system-coupling perspective. It innovatively explores the coupled and coordinated progression degree of ARD and FSS. In our work, the coupling degree and CCD of the agricultural rural digital system and sustainable food system in each PAA of China from 2011 to 2020 are calculated using the CCD model. The results show that the coupling degree of the vast majority of Chinese PAAs has been stabilized above 0.8, which is at a high level of coupling stage. However, the CCD of Chinese PAAs is generally low, and the vast majority of PAAs are in the low and medium coupling coordination intervals, with a few PAAs barely reaching the high coupling coordination interval in individual years. This phenomenon suggests a close interaction between China’s agricultural and rural digital systems and sustainable food systems. However, the two systems have not achieved a high level of coordinated development. Further analysis shows that the coupling and CCD in northeast, western, central, and eastern China all increase in sequence, meaning that regions with a high level of development of both systems have a higher coupling degree than regions with a low level of development. This phenomenon indicates that both in time and space, the role of the agricultural and rural digital system and the sustainable food system increases as the development level of the respective systems rises, i.e., the coupling and CCD of the two systems show a positive feedback relationship. This suggests that China has now united the two important goals of ARD and FSS, and this finding is of great significance for realizing the two’s high-level coordinated development in the future.

Using the obstacle degree model, this paper analyzes the main obstacle factors affecting the coupled and coordinated development of agricultural and rural digital systems and sustainable food systems. The results show that in terms of the indicator level, the top 3 main obstacle factors of the agricultural and rural digital system are the level of rural digital platform construction, the digital degree of agricultural products trading, and the level of rural residents’ consumption of digital products and services. The top 3 major obstacle factors of the sustainable food system are per capita food possession, governance level of soil erosion, and the effective irrigation of farmland. At the element level, the main obstacles to the agricultural and rural digital system are, in descending order, rural digital industrialization, agricultural digitalization, and rural digital infrastructure. The main obstacles to a sustainable food system are, in descending order, food stability, resource and environmental sustainability, food production security, economic and social sustainability, and food accessibility. The ARD and FSS both belong to the concept of conformity. It is difficult to accurately grasp the internal structure of their development by only analyzing the total development level index, so analyzing the obstacle factors can help us understand the main bottlenecks restricting the development of the system coupling and coordination at a more specific level.

Our study combines with the research findings and puts forward the following countermeasure suggestions. First, the Chinese government should continue to improve agricultural digitization, including the application of technologies such as the Internet of Things in agriculture, big data, and artificial intelligence. The government should strengthen the construction of rural information infrastructure, including network coverage and IT training, to promote farmers’ application and acceptance of digital technologies. The Government should formulate and improve policies to encourage agricultural enterprises and farmers to adopt digital technologies by providing financial support, tax incentives, and other incentives.

Secondly, government departments should formulate comprehensive plans to promote the coordinated development of agricultural and rural digital systems and sustainable food systems. Moreover, the government should actively establish cross-sectoral and cross-regional coordination mechanisms to facilitate the synergistic development of agricultural and rural digital systems and sustainable food systems among different regions. The government and enterprises should increase training and support for research institutions and farmers to improve their understanding and application of digital technology and the concept of sustainable food development, to promote the coordinated development of the two systems.

Thirdly, in response to the main obstacle factors in the agricultural and rural digital system, the government and relevant departments should increase investment to promote the construction of rural digital platforms, enhance their coverage and functions, and provide farmers with more digital services and support. The government should encourage the digital development of agricultural markets, promote the establishment of electronic trading platforms for agricultural products, improve the transparency and efficiency of agricultural transactions, and reduce information asymmetry. The government should strengthen digital literacy training for rural residents, promote digital products and services, and facilitate rural residents’ participation in the digital economy to improve their quality of life and economic income.

Fourthly, in response to the major obstacles to a sustainable food system, the government should increase food production, including improving agricultural technology, strengthening farmland management, and improving the cropping structure to raise the per capita food share. It should also increase investment in soil erosion management and the construction and maintenance of farmland irrigation facilities to improve land-use efficiency and farmland production capacity.