Spatial Differentiation Effect of Rural Logistics in Urban Agglomerations in China Based on the Fuzzy Neural Network

Abstract

Rural logistics is particularly important for the sustainable development of Chinese urban agglomeration, which features the coexistence of urban circles and vast countryside. However, the existing literature generally focuses on urban logistics while ignoring rural logistics. Taking the Chengdu-Chongqing agglomeration as an example, this study constructed a rural logistics index system and proposed a new dynamic assessment model for rural logistics development using a fuzzy neural network, Moran index, and Kernel density estimation. The results are as follows: the development of rural logistics has been enhanced, and gaps among cities have gradually narrowed over the past decade. In particular, the spatial distribution of rural logistics showcases a dual-core structure in the Chengdu-Chongqing agglomeration, which is different from the unipolar structure manifested in other urban agglomerations. Because of administrative barriers, the impact from the dual-core cities is very different: Chengdu has a significant spillover effect on its surrounding cities, which is not the case for Chongqing. The findings are of great significance for local governments to provide decision-making support for the sustainable development of urban agglomerations.

1. Introduction

As a new form of regional spatial organization [1], urban agglomeration has become a global trend in sustainable development [2,3]. Some famous urban agglomerations include the Atlantic coastal urban agglomeration in the northeastern United States [4,5], the Great Lakes urban agglomeration in the United States [6,7], the Pacific coastal urban agglomeration in Japan [8], the urban agglomeration in England with London as its center [9], the Paris-centered northwest Europe urban agglomeration [10], and the Yangtze River Delta urban agglomeration in China [11]. By publishing policies on new urbanization and rural revitalization [12], the Chinese government has focused on developing four urban agglomerations from 2021 to 2025: the Yangtze River Delta, the Pearl River Delta, the Beijing-Tianjin-Hebei regions, and the Chengdu-Chongqing region. Logistics is a key link for the development of urban agglomeration [13,14]. According to data from the China Post Bureau, China’s express deliveries reached 108.3 billion pieces in 2021, exceeding 100 billion for the first time, with the above four urban agglomerations accounting for more than 70%, at a growth rate of 22.9% (Data are from the 2021 China Post Bureau. https://www.spb.gov.cn/, accessed on 13 May 2022). The integration degree of the logistics industry continues to improve for sustainable economic and social development. Compared with other countries, China’s urban agglomerations have shown some special characteristics. Due to low urbanization rates [15], there are still huge rural areas in the urban agglomerations across China. By the end of 2020, in fact, 36.11% of China’s population still lived in rural areas (Data are from the 2021 China Statistical Yearbook. http://www.stats.gov.cn/tjsj/ndsj/2021/indexch.htm, accessed on 13 May 2022). Therefore, rural logistics has become a new problem driving Chinese urban agglomeration.

Most of the existing literature focuses on urban logistics, including evaluation of urban logistics levels [16], exploration of the impact of urban logistics on citizens’ life quality [17,18], and examination of sustainable development of urban economy [19]. In contrast, few studies have been made on rural logistics, with only sporadic research discussing route optimization in managing agricultural logistics supply chains [20,21,22]. Research on how to evaluate the development of rural logistics is scarce. Therefore, it is necessary to further explore how to evaluate rural logistics in the context of urban agglomeration. This paper constructed a rural logistics index system and proposed a new dynamic assessment model for rural logistics development using a fuzzy neural network. The Chengdu-Chongqing agglomeration, the most important urban agglomeration in inland China, was chosen as the case study. The rural logistics comprehensive index of each city in the urban agglomeration from 2010 to 2020 has been calculated, and the spatial distribution of rural logistics in the Chengdu-Chongqing agglomeration has been further analyzed.

The contributions of this paper are: First, the sustainable development of urban agglomeration was analyzed in rural logistics, a perspective different from prior research that generally focused on the logistics among metropolitan areas in urban agglomerations. Second, it constructed a new dynamic assessment method for rural logistics development in urban agglomerations based on fuzzy neural network, Moran’s Index, and Kernel density estimation. This method differs from the qualitative description of rural logistics as shown in the existing literature. The quantitative approach can avoid the shortcomings of subjective assignments in the evaluation process when pinpointing the spatiotemporal evolution characteristics of rural logistics development in urban agglomerations.

According to the Ministry of Transport of the People’s Republic of China, rural logistics directly serves the production, life, and other economic activities of rural residents, thus becoming an important guarantee for the circulation of industrial products and agricultural produce between urban and rural communities. Rural logistics is an important foundation for agricultural modernization as well as an important way to improve the living standards of both urban and rural residents; and developing rural logistics is an effective measure to reduce the logistics cost of the whole society (Ministry of Transport of the People’s Republic of China. https://www.mot.gov.cn/zhengcejiedu/nongcunwuliujkfz/, accessed on 1 June 2022). To measure the development levels of rural logistics in urban agglomerations, this study establishes an urban-rural logistics index system that makes trial calculations of a comprehensive index for urban logistics development based on the existing literature on logistics evaluation in four aspects: rural logistics demand, agricultural production capacity, rural infrastructure, and rural informatization. On this basis, a spatial and temporal evolution of rural logistics in urban agglomerations was conducted.

The structure of this paper is as follows: Section 2 provides a literature review; Section 3 proposes a rural logistics index system for urban agglomerations; Section 4 describes the methodology of this study; Section 5 showcases the results of this study; Section 6 makes some discussions, and Section 7 gives the conclusion.

2. Literature Review

2.1. The Importance of Logistics

The existing literature is mainly focused on the importance of logistics in urban development, given that urban logistics has a great impact on the sustainable development of cities [23]. Taniguchi put forward the concept of urban logistics in 1999, maintaining that urban public logistics nodes could be established to alleviate urban traffic congestion and promote urban economic growth [24]. Based on the implementation experience in the first phase of the C-LIEGE project in Poland, Iwan proposed that urban logistics should adapt to the economic development of cities, while logistics development plans should be formulated according to the actual conditions of each city to improve the overall urban service efficiency [25]. Schliwa identified urban freight and logistics as the core of the British economy and laid out a sustainable urban logistics framework for the operation of the logistics industry and future research [26]. Rześny found that urban logistics was particularly important for local residents and enterprises in Tricity due to its unique geographical advantage [27]. According to Russo, urban logistics forms the cornerstone of social development and has become one of the most important research fields in recent years [28]. Kang and Pang found urban logistics crucial to e-commerce trades of fresh agricultural produce, so it plays a leading role in enhancing the competitiveness of online sales [29].

In summary, strong logistics have very important functions in the social and economic development of urban agglomerations. Nevertheless, the existing literature mainly focuses on urban logistics or the logistics in metropolitan areas while ignoring rural logistics. Accordingly, the existing research rarely analyzes the features of rural logistics in urban agglomerations. In fact, an effective supply of agricultural produce is a foundation for the normal operation of cities, so rural logistics and metropolitan logistics are equally important for the social and economic development of urban agglomerations. Therefore, this study chooses rural logistics in an urban agglomeration as its research object.

2.2. Evaluation of the Logistics Development

When evaluating logistics development, most existing literature focuses on urban logistics in two main categories. One is to evaluate urban logistics development from the perspective of efficiency improvement. For example, Morfoulaki has introduced specific policies and measures to strengthen the development of logistics in small- and medium-sized cities and evaluated the sustainable development of urban logistics in Ceres, Greece, through multi-standard analysis [30]. Viana has established a multi-criteria evaluation based on GIS to seek a balance between the convenience of life brought by urban logistics and the social costs incurred, including traffic congestion and environmental pollution [31]. Juvvala and Sarmah have proposed a model to evaluate the deployment of electric vehicles in urban logistics to reduce the carbon pollution caused by trucks [32]. Zhao has appraised the transit capacity of subway stations in four network centrality indexes, with an evaluation system constructed for urban subway logistics based on the hub-and-spoke network model [33].

Another category is to evaluate urban logistics development from the perspective of risk management. Considering the impact of a flood on urban logistics, Oliveira has introduced an intelligent modeling method for urban logistics in an environment of vulnerability assessment [34]. Based on the social network analysis, Liu has explored the relationship among multiple risk factors in the ecological chain of smart logistics while verifying the proposed research framework and evaluation system by taking the RRS logistics company as an example [35]. Qazi has developed a probabilistic network model to analyze the country’s risk factors that influence logistics performance [36].

Over recent years, some scholars have begun to evaluate the development of urban logistics in terms of urban agglomeration. Zheng has evaluated logistics efficiency and performance in China under the Belt and Road Initiative based on comprehensive DEA and hierarchical regression analysis with carbon constraints [37]. By using the three-stage Super-SBM model to eliminate environmental factors and random errors, Liang introduced the Malmquist index model to measure the low-carbon logistics efficiency of 13 cities in Jiangsu Province, China [38]. Zhuang has established an evaluation system for logistics input and economic output in urban agglomerations based on data-driven analysis to measure the logistics economic benefits in major first-tier cities across China [39].

In summary, as can be obtained from

Table 1. Comparison between this paper and existing literature.

Perspective	Indicators	Methods	Source
Efficiency improvement	Cost; Implementation time; Specialized technical requirements; Social reaction, a requirement for synergy between all stakeholders; Exploitation of existing infrastructure, policies, and actions.	Multi-Criteria Analysis	Morfoulaki et al., 2016 [30]
	Frequency of merchandise delivery; Time of loading and unloading of merchandise; Typology/size of the establishments; Type of vehicle used; Location and offer of dedicated spaces for loading/unloading; Street design and geometric characteristics associated with the quality of urban logistics operations; Degree of saturation of the street (service levels) associated with the quality of urban logistics operations.	Multi-Criteria Evaaluation in GIS	Viana and Delgado, 2019 [31]
	Vehicle capacity; Customer demand; Distance between two node points; Fixed cost of the vehicle; Subsidy on the purchasing price of the vehicle; Annual circulation tax of the vehicle; Entrance fee paid by the vehicle; Energy price for the vehicle; Energy tax for the vehicle; Energy efficiency for the vehicle; The amount of carbon emits; Carbon tax on the vehicle; A sufficiently large number; The speed limit of the vehicle.	Ant Colony Optimisation	Juvvala and Sarmah, 2021 [32]
	Degree centrality; Betweenness centrality; Closeness centrality; Network efficiency centrality.	Entropy-weighted TOPSIS	Zhao et al., 2021 [33]
Risk management	Demand for daily delivery; Daily route; Opening hours of the establishment; NOx count; Complaint count; Occurrence and duration time; Travel time information; Speed information; Pollutant emission parameters.	Multi-Agent Modeling	Oliveira et al., 2017 [34]
	Internal stakeholder risks; External stakeholder risks; Indirect stakeholder risks; The risk of disruptive technology upgrades; The risk of technological route changes; Government management risks; Industry management risks; Intermediary service risks; Industrial policy risks; Legal and regulatory risks.	Social Network Analysis; TOPSIS	Liu et al., 2020 [35]
	Business Environment Risk; Corruption Risk; Economic Risk; Environmental Risk; Financial Risk; Health and safety Risk; Political Risk; Customs; Infrastructure; International Shipments; Logistics Competence; Timeliness; Tracking and Tracing.	Probabilistic network model	Qazi, 2022 [36]
Urban agglomeration	Investment in fixed assets; Length of logistics network; Postal outlets; Terminal energy consumption; Cargo volume; Gross product of logistics industry; Carbon emissions.	Data envelopment analysis	Zheng et al., 2020 [37]
	Input and output indexes; Total mileage; Capital stock; Number of employees; Freight volume; Cargo turnover; GDP of the logistics industry; CO2 emission; Environmental variable index; Logistics industry density; Urbanization level; Logistics specialization level.	The three-stage Super-SBM model	Liang et al., 2021 [38]
	Number of people employed in logistics; Ownership of civil trucks; Total logistics investment in fixed assets; Total of Post business; Road/highway freight turnover; Added-value of the tertiary industry; GDP per capita; Total national investment in fixed assets; Total retail sales of consumer goods; Resident population; Household consumption; Public income.	Data envelopment analysis	Zhuang et al., 2021 [39]
Rural logistics from the perspective of urban agglomeration	Per capita GDP; Per capita disposable income of urban residents; Total retail sales of social consumer goods; Total sown area of crops; GDP of agriculture, forestry, animal husbandry, and fishery; Total power of agricultural machinery; Total grain output; Highway mileage; Highway freight turnover; Highway density; Internet broadband access users.	Fuzzy neural network	This paper

, the existing literature is concentrated on evaluating the development levels and influencing factors of urban logistics. Recently, urban logistics, especially in metropolitan areas, has attracted increasingly more attention; however, the vast rural areas in urban agglomerations are basically ignored.

2.3. Rural Logistics Related Research

With “rural logistics” and “rural logistics evaluation system” as keywords, this study retrieved the following relevant research efforts from PaperDigest (Paper Digest. http://www.paperdigest.org/, accessed on 5 June 2022) and Connected Papers (Connected Papers. https://www.connectedpapers.com/, accessed on 5 June 2022). On the one hand, Lan has proposed a development strategy for China’s rural logistics market [40]. Yan has proposed a location model for rural logistics centers based on the theory of intuitionistic fuzzy TOPSIS [41]. Jiang has uncovered valuable information for decision-makers to develop proactive strategies and reinforcement policies in improving rural last-mile deliveries, thus promoting the sustainable development of rural logistics [42]. On the other hand, Yuan has analyzed the current situation of logistics enterprises and their development opportunities in the environment of the Internet of Things while presenting a development strategy for rural logistics in Hunan by constructing a common logistics system for rural areas in such an environment [43]. Jiang has applied the rough set theory to analyze the evaluation index system of modern rural logistics by specifically setting up a modern rural logistics system in seven aspects: logistics infrastructure, logistics information, logistics support system, constitution of logistics enterprises, logistics planning, logistics outputs, and logistics costs [44]. Taking the rural e-commerce logistics service as the research object, Luo has constructed an evaluation system for the quality of rural e-commerce logistics services using the AHP and fuzzy comprehensive evaluation method, with an evaluation model established [45].

In summary, few studies have been made on rural logistics, and the existing research mainly focuses on site selections and distribution of rural logistics. Over recent years, scholars have begun to pay attention to the evaluation of rural logistics, but few evaluation systems for rural logistics have been proposed from the perspective of urban agglomeration. To address this issue, this study chooses the evaluation system of rural logistics in urban agglomeration as its research focus.

3. The Rural Logistics Index System under the Context of Urban Agglomerations

To measure the development of rural logistics in urban agglomerations, this study constructed an index system in four dimensions. Rural logistics demand can indicate the potential market scale of rural logistics in urban agglomerations. To assess such demand, three indicators are selected: per capita GDP, per capita disposable income of urban residents, and total retail sales of social consumer goods [46,47,48]. Agricultural production capacity can directly measure the overall development level of rural areas, and this study selected two indicators for it: the total sowing area of crops, and the total grain output [49,50]. Rural infrastructure provides the basis for developing rural logistics, and it can be assessed with highway mileage, highway freight turnover, and highway density [51,52,53]. Given the importance of information technology in the development of logistics, this study selected the number of Internet broadband access users to indicate the rural informatization levels [54,55]. The evaluation index system designed by this study for rural logistics development levels in urban agglomerations is shown in

Table 2. Index system of rural logistics development in urban agglomeration.

Level	Index	Variable	Attribute	Unit	Description	Source
	Per capita GDP	$x_1$	+	CNY	Regional economic scale	Yang, 2021 [48]
Rural logistics demand	Per capita disposable income of urban residents	$x_2$	+	CNY	Consumption demand of regional urban residents	Yang, 2021 [48]
	Total retail sales of social consumer goods	$x_3$	+	100 mn CNY	Realization degree of social commodity purchasing power	Lu et al., 2022 [47]
	Total sown area of crops	$x_4$	+	Hectares	Regional agriculture production scale	Wang, 2010 [50]
Agricultural production capacity	GDP of agriculture, forestry, animal husbandry, and fishery	$x_5$	+	100 mn CNY	Regional comprehensive agricultural production capacity	Wang, 2010 [50]
	Total power of agricultural machinery	$x_6$	+	10,000 kw	Regional agriculture development scale	Wang, 2010 [50]
	Total grain output	$x_7$	+	10,000 tons	Regional agricultural production capacity	Wang, 2010 [50]
	Highway mileage	$x_8$	+	Kilometer	Regional transportation infrastructure	Xie et al., 2022 [53]
Rural infrastructure	Highway freight turnover	$x_9$	+	10,000-ton kilometers	Freight transport efficiency	Xie et al., 2022 [53]
	Highway density	$x_{10}$	+	Km/100 square kilometers	Regional logistics circulation capacity	Zhang et al., 2016 [52]
Rural informatization	Internet broadband access users	$x_{11}$	+	Thousand households	Development degree of regional Informatization	Wang and Kang, 2020 [54]

.

4. Methodology

The dynamic assessment model for the assessment of rural logistics development is shown in Figure 1. Firstly, the T-S fuzzy neural network was used to calculate the development index of rural logistics in urban agglomerations. Then, a temporal variation of the rural logistics index was analyzed. Furthermore, Moran’s Index was used to analyze the spatial differentiation characteristics of such rural logistics. Finally, Kernel density estimation was used to explore the dynamic evolution of rural logistics in urban agglomerations. Figure 1 is from graphics software Visio.

4.1. The T-S Fuzzy Neural Network

Machine learning is widely adopted nowadays. For example, using an artificial neural network [56], Moayedi proposed a method to reduce the friction force in transportation pipelines while lowering transportation energy consumption [57]. Nasr presented a novel two-stage fuzzy supplier selection and order allocation model in a CLSC, purposed to minimize waste during the transportation of goods [58]. Hosseini and Vaferi tried to address the problem of gas hydrate formation by using a variety of machine learning algorithms [59]. A fuzzy neural network not only has the ability of neural network optimization and adaptive features, but also has the functions of fuzzy logic to deal with nonlinear and uncertain problems [60,61]. It has been shown that a fuzzy neural network only performs a deep learning algorithm once at the output layer and the rule layer. The blurred layer will directly connect the linear combination of input residuals to the rule layer. Thus, there is no threat of gradient diffusion in a fuzzy neural network [62,63]. In addition, the fuzzy neural network can illustrate the fuzzy relation between input distribution and output distribution through membership degree, making the predicted value smoother and more continuous in the field of time series prediction. Thanks to the advantages of fuzzy neural network methods, they have been widely adopted in the field of time series prediction, including traffic speed prediction [64], wind speed prediction [65], and machine failure prediction [66]. Therefore, to predict the development level of rural logistics in urban agglomeration more accurately, this paper used a fuzzy neural network prediction method in combination with the previous research results.

4.1.1. The Construction of Fuzzy Neural Network

T-S fuzzy system is a fuzzy system with a high adaptive capacity. It cannot only update itself automatically but can also constantly correct the affiliation functions of its fuzzy subsets. T-S fuzzy system is defined in the form of if–than rules. The principle of fuzzy inference in the case of a rule $R^i$ is as follows:

$$R^i: If\hspace{1em}{x}_1 is{ \mathrm{Q}}_1^i,x_2 is{ \mathrm{Q}}_2^i,...,x_k is{ \mathrm{Q}}_k^i, then{ \mathrm{z}}_i=p_0^i+p_1^i{x}_1+...+p_k^i{x}_k$$

where ${\mathrm{Q}}_j^i$ indicates a fuzzy set, $p_j^i(j=1,2,...,k)$ indicates the fuzzy system parameters, and $z_i$ indicates the output obtained according to the fuzzy rules. The input part is fuzzy, the output part is deterministic, and the fuzzy inference indicates that the output is a linear combination of the input. T-S fuzzy neural network is a neural network based on a T-S fuzzy system. The network structure is shown in Figure 2.

As seen in Figure 2, the T-S fuzzy neural network is divided into four layers: input layer, blurred layer, fuzzy rule calculation layer, and output layer. The input layer is connected to the input vector $x=\left[x_1,x_2,...,x_k\right]$, with the same number of nodes as the dimensionality of the input vector. In the blurred layer, the affiliation function of the variable $x_j$ is defined as:

$$\mu {\mathrm{Q}}_j^i=\exp (-{(x_j-c_j^i)}^2/b_j^i)\hspace{1em}\hspace{1em}\hspace{1em}i=1,2,...n;j=1,2,...,k$$

(1)

where $c_j^i$ and $b_j^i$ indicate the center and width of the affiliation function of variable $x_j$, respectively; $k$ indicates the number of indicators; and $n$ indicates the number of cities in an urban agglomeration. After fuzzifying $x=\left[x_1,x_2,...,x_k\right]$, the fuzzy affiliation value can be obtained. Further fuzzy calculation of each affiliation in the fuzzy rule calculation layer.

$${\omega }^i=u{\mathrm{Q}}_j^1(x_1)\ast u{\mathrm{Q}}_j^2(x_2)\ast ...\ast u{\mathrm{Q}}_j^k(x_k)\hspace{1em}\hspace{1em}\hspace{1em}i=1,2,...,n$$

(2)

In Equation (2), the fuzzy operator ${\omega }^i$ is a concatenated multiplicative operator. Then, the output value $z_i$ of the fuzzy neural network is calculated from the fuzzy calculation results.

$$z_i={\displaystyle \sum _{i=1}^n{\omega }^i}(p_0^i+p_1^i{x}_1+...+p_k^i{x}_k)/{\displaystyle \sum _{i=1}^n{\omega }^i}$$

(3)

4.1.2. The Algorithm of T-S Fuzzy Neural Network

To obtain effective training data and better classification results, this study counted the minimum, 20% quantile $Q_1$, 40% quantile $Q_2$, 60% quantile $Q_3$, 80% quantile $Q_4$, and the maximum values of the original data. The number of time series data is m. The quantile is calculated as follows.

$$\{\begin{array}{l}{Q}_1=1+(\mathrm{m}-1)\ast 0.2\\ Q_2=1+(\mathrm{m}-1)\ast 0.4\\ Q_3=1+(\mathrm{m}-1)\ast 0.6\\ Q_4=1+(\mathrm{m}-1)\ast 0.8\end{array}$$

(4)

Based on Equation (4), an interval ranking was performed to obtain the classification level of the output layer. Specifically, if the input layer data fall in the interval $[Q_{\min },Q_1)$, the output variable will be defined as Level I; if in the interval $[Q_1,Q_2)$, the output variable as Level II; if in the interval $[Q_2,Q_3)$, the output variable as Level III; if in the interval $[Q_3,Q_4)$, the output variable as Level IV; and if in the interval $[Q_4,Q_{\max })$, the output variable as Level V. In addition, the computational error of the fuzzy neural network is defined as:

$$e=\frac{1}{2}{(z_d-z_e)}^2$$

(5)

where $z_d$ indicates the desired output of the network, $z_e$ indicates the actual output of the network, and $e$ indicates the error between the desired output and the actual output. Furthermore, the network learning rate is valued as $\alpha$. According to the fuzzy system parameters $p_j^i$ and the input parameter affiliation ${\omega }^i$, the coefficient correction can be defined as:

$$p_j^i(k)=p_j^i(k-1)-\alpha \frac{\partial e}{\partial p_j^i}$$

(6)

$$\frac{\partial e}{\partial p_j^i}=(z_d-z_e){\omega }^i/{\displaystyle \sum _{i=1}^m{\omega }^i}\cdot x_j$$

(7)

Then, based on the center $c_j^i$ and width $b_j^i$ of the affiliation function, the parameter correction can be defined as:

$$c_j^i(k)=c_j^i(k-1)-\beta \frac{\partial e}{\partial c_j^i}$$

(8)

$$b_j^i(k)=b_j^i(k-1)-\beta \frac{\partial e}{\partial b_j^i}$$

(9)

The algorithm flow for rural logistics in urban agglomerations based on a T-S fuzzy neural network is illustrated in Figure 3 by Visio.

As shown in Figure 3, the fuzzy neural network determines the number of network input and output nodes based on the input and output dimensions of the training patterns. Since the input data have a dimension of 11 and the output data have a dimension of 1, this study set the number of input and output nodes of the network to 11 and 1, respectively. Also, according to the number of network input and output nodes, the number of membership functions is artificially fixed at 22. According to the convention, it is best to set the number as double that of the targets during training [67], so the network structure was constructed as 11-22-1. Besides, the center $c$, width $b$, and coefficients $P_0$ and $P_6$ of the fuzzy affiliation function were initialized randomly.

The fuzzy neural network was trained with training data. The maximum, 80% quantile, 60% quantile, 40% quantile, 20% quantile, and the minimum of the original data were divided into intervals. Training samples are generated in the linear interpolation method, and the network was trained repetitively 100 times. The trained fuzzy neural network was then used to evaluate the level and comprehensive index of rural logistics in urban agglomerations.

4.2. Moran’s I

Spatial autocorrelation can be used to reveal the spatial clustering and distribution characteristics of certain regions [68]. In this study, Moran’s Index was utilized to analyze the spatial correlation of rural logistics in Chengdu-Chongqing urban agglomeration through the following calculations:

$$I_i=\frac{(C{R}_i-\overline{CR})}{S^2}{\displaystyle \sum _{i1=1}^n{A}_{i,i1}}(C{R}_{i1}-\overline{CR})$$

(10)

$$S^2=\frac{1}{n}{{\displaystyle \sum _{i=1}^n(C{R}_i-\overline{CR})}}^2$$

(11)

where $S^2$ indicates the variance of the observed sample; $n$ indicates the total number of cities in the urban agglomeration; $C{R}_i$ and $C{R}_{i1}$ indicate the rural logistics comprehensive index of two random cities $i$ and $i1$, respectively; $\overline{CR}$ is the average of the rural logistics comprehensive index; $A_{i,i1}$ indicates a spatial adjacency matrix: when city $i$ is adjacent to city $i1$, $A_{i,i1}=1$; otherwise $A_{i,i1}=0$.

4.3. Kernel Density

Kernel density estimation demonstrates the distribution location, shape, and polarization of random variables. In this study, Kernel density estimation was used to describe the dynamic distribution evolution of rural logistics in the urban agglomeration, with the wave height and width reflecting the magnitude of differences in rural logistics development level and the number of waves reflecting the polarization. The formula of the empirical distribution is [69]:

$$F(y)=\frac{1}{nh}{\displaystyle \sum _{i=1}^{n}K\left(\frac{Y_i-\overline{Y}}{h}\right)}$$

(12)

where $n$ indicates the number of observations (the total number of cities), $h$ indicates the broadband, and $K$ indicates the Kernel density function, subject to the following conditions:

$$\{\begin{array}{l}\underset{y\to \infty }{\lim }K(y)\cdot y=0\\ K(y)\ge 0,{\displaystyle {\int }_{-\infty }^{+\infty }K(y)dy=1}\\ \sup K(y)<+\infty ,{\displaystyle {\int }_{-\infty }^{+\infty }{K}^2(y)dy<+\infty }\end{array}$$

(13)

In this study, the Gaussian Kernel function was adopted to estimate the dynamic evolution process of the distribution of rural logistics development levels in the urban agglomeration. The function is as follows:

$$K(y)=\frac{1}{\sqrt{2\pi }}\exp (-\frac{y^2}{2})$$

(14)

The research topic of this study is the spatial differentiation characteristics of rural logistics in the Chengdu-Chongqing urban agglomeration. Figure 4 provides a step-by-step summary of the above methods while introducing the software required to make the study more organized.

5. Results

5.1. The Study Area and Data Sources

This study selected the panel data from 16 prefecture-level areas in the Chengdu-Chongqing agglomeration from 2010 to 2020 as the research sample, including Chongqing, Chengdu, Zigong, Luzhou, Deyang, Mianyang, Suining, Neijiang, Leshan, Nanchong, Meishan, Yibin, Guang’an, Dazhou, Ya’an, and Ziyang. The original data were retrieved from the China Statistical Yearbook, China Rural Statistical Yearbook, and statistical yearbooks of various cities from 2011 to 2021. Figure 5 by ArcGIS 10.2. shows the location of the study area.

5.2. Evaluation Criteria of Rural Logistics in Urban Agglomeration

The maximum, 80% quantile, 60% quantile, 40% quantile, 20% quantile, and the minimum value of the original sample data were calculated to divide the intervals of rural logistics development. The rural logistics in the Chengdu-Chongqing agglomeration could be divided into five levels, as shown in

Table 3. Evaluation criteria of rural logistics in urban agglomeration.

Evaluation index	I	II	III	IV	V
Per capita GDP	12,638~23,769	23,768~30,806	30,905~38,712	38,846~49,376	49,830~85,679
Per capita disposable income of urban residents	12,708~19,386	19,451~24,565	24,619~28,851	28,920~34,371	34,549~48,592
Total retail sales of social consumer goods	98~283	285~420	422~580	586~1013	2473~117,872
Total sown area of crops	118~340	341~448	449~525	528~778	810~3372
GDP of agriculture, forestry, animal husbandry, and fishery	93~224	225~286	287~354	356~500	528~2749
Total power of agricultural machinery	84~152	153~193	194~230	231~281	10,591~825,062
Total grain output	35~127	127~165	166~216	217~258	268~1081
Highway mileage	5656~8160	8201~11,482	11,524~14,846	14,914~20,292	22,298~180,796
Highway freight turnover	240,303~423,410	424,931~545,112	546,691~671,405	677,515~1,160,247	1,597,072~36,106,277
Highway density	38~99	100~136	136~156	157~184	185~258
Internet broadband access users	88~268	270~410	413~646	653~1266	1421~13,724

, ranking from low to high.

5.3. The Comprehensive Index of Rural Logistics in Chengdu-Chongqing Agglomeration

The linear interpolation method was used in Table 3 to generate 400 groups of sample data. Among them, 350 groups were selected as the training samples, while the remaining 50 ones as the predicting samples. The proportion of the test data is 12.5%, which conforms to the convention standard—At least 10% of data should be used as test data for neural network training. In the training process of the fuzzy neural network, the learning rate was set at 0.001, the inertia coefficient at 0.05, and the evolutionary number at 100. Matlab2019b was used to train the fuzzy neural network. The prediction results from the training and test data are shown in Figure 6.

The fuzzy neural network was trained with MATLAB2019b software, and the rural logistics comprehensive index of the Chengdu-Chongqing agglomeration from 2010 to 2020 is demonstrated in

Table 4. Comprehensive index of rural logistics in Chengdu-Chongqing agglomeration.

City	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Chongqing	2.77	3.01	3.39	2.63	3.85	4.13	3.56	5.26	4.59	5.38	5.74
Chengdu	1.95	2.63	3.23	3.84	4.32	4.35	4.47	5.42	6.04	5.15	6.50
Zigong	0.51	0.95	1.38	1.82	2.09	2.54	2.80	3.31	3.83	4.25	4.70
Luzhou	0.56	0.96	1.40	1.74	2.13	2.20	2.75	3.22	3.67	4.16	4.52
Deyang	0.71	1.46	1.95	2.45	2.79	3.33	3.29	3.84	4.35	4.47	5.24
Mianyang	0.71	1.18	1.61	1.98	2.37	2.97	3.06	3.64	4.12	4.44	5.00
Suining	0.39	0.58	0.98	1.26	1.62	1.51	2.29	2.73	3.29	3.88	4.18
Neijiang	0.48	0.77	1.19	1.45	1.76	1.80	2.48	2.88	3.34	3.92	4.20
Leshan	0.57	1.05	1.50	1.95	2.31	2.98	2.92	3.39	3.95	4.35	4.93
Nanchong	0.62	0.63	0.98	1.17	1.52	1.86	2.16	2.60	3.04	3.71	3.87
Meishan	0.47	0.79	1.22	1.59	1.93	1.97	2.61	3.06	3.51	4.04	4.31
Yibin	0.60	0.98	1.43	1.80	2.18	2.46	2.72	3.22	3.90	4.34	4.91
Guang’an	0.46	0.78	1.21	1.53	1.83	1.47	2.37	2.77	3.17	3.69	3.91
Dazhou	0.54	0.61	0.95	1.12	1.46	1.74	2.16	2.57	2.94	3.54	3.73
Ya’an	0.38	0.75	1.18	1.60	1.94	1.88	2.57	2.95	3.38	3.94	4.25
Ziyang	0.45	0.78	1.20	1.43	1.73	1.05	2.32	2.65	3.00	3.38	3.65

.

According to the comprehensive index of rural logistics in the Chengdu-Chongqing agglomeration as shown in Table 4, the rural logistics development index of the 16 cities in the agglomeration increased rapidly from 2010 to 2020. The average of the comprehensive index went up from 0.76 in 2010 to 2.39 in 2015. In 2020, it rose to 4.6. Although the rural logistics development index of the 16 constituent cities had increased over time, the rural logistics in the Chengdu-Chongqing agglomeration developed in a very unbalanced manner. The levels of rural logistics in Chongqing and Chengdu have always been much higher than in other cities. Before 2013, Chongqing ranked first. After 2013, Chengdu had ranked first for seven years, except in 2019. Moreover, differences among the other 14 cities were relatively small. In addition, Deyang, Mianyang, Leshan, and Yibin, all of which are close to Chengdu, have developed well over the past five years. To further illustrate the changing trend of the rural logistics comprehensive index of the urban agglomeration, Origin2019b software was used to draw a dynamic change diagram of the index, as shown in Figure 7.

5.4. Spatial Distribution of Rural Logistics in Chengdu-Chongqing Agglomeration

The map of rural logistics in the Chengdu-Chongqing agglomeration further displays the level of the agglomeration from 2010 to 2020. In ArcGIS 10.2, the following figures are drawn. The base map showcases the Chengdu-Chongqing urban agglomeration, covering Chongqing as well as 15 cities of Sichuan province, acquired from the “National Basic Geographic Information System” of 14 million data entries. As shown in Figure 8, this study set up five levels to evaluate the development of rural logistics in the Chengdu-Chongqing urban agglomeration by using five colors: The darker the color, the higher the level. During the observation period, the city levels of the Chengdu-Chongqing agglomeration increased yearly. In 2010, the highest level of rural logistics was only shown in Chongqing at Level III, followed by Chengdu at Level II, and the other 14 cities were all at Level I (Figure 8a). In 2015, both Chongqing and Chengdu were upgraded to Level V, and the second on the list was Deyang at Level IV, a city near Chengdu, with no cities at Level I (Figure 8b). By 2020, except for Nanchong, Guang’an, Dazhou, and Ziyang, which were still at Level IV, the remaining 12 cities had all reached Level V, indicating that cities around Chengdu were developing rapidly. Except for Ziyang, the surrounding cities of Chengdu all reached Level V in 2020. This showcases an obvious spillover effect of Chengdu in recent years. However, Ziyang, which was supposed to be a bridge between Chongqing and Chengdu, was still at Level IV, further demonstrating the significant siphon effect between Chongqing and Chengdu (Figure 8c). In general, the rural logistics of cities in the Chengdu-Chongqing agglomeration showed a positive development trend, with the gaps between the cities narrowing yearly.

Through analysis and prediction using the fuzzy neural network, it can be concluded that during the observation period from 2010 to 2020, the overall rural logistics in the agglomeration had developed rapidly in terms of both the comprehensive index and the level. Chengdu and Chongqing, as the dual-core cities in the urban agglomeration, drive the overall development of rural logistics in their surrounding cities. Rural logistics is an important approach to improving the lives of urban and rural residents in the agglomeration. Therefore, promoting the prosperity of the rural economy and driving the sustainable and stable development of logistics in the Chengdu-Chongqing urban agglomeration is significant.

6. Discussion

To pinpoint the development characteristics of rural logistics, this study further uses Moran’s Index and Kernel density estimation to analyze the spatial differentiation effect and evolution process of rural logistics in the Chengdu-Chongqing agglomeration.

6.1. Differentiation Characteristics of Rural Logistics in Urban Agglomeration

The Moran’s I scatter diagram of rural logistics in the urban agglomeration in 2010 and 2020 is drawn using GeoDa software, as shown in Figure 8. As shown in this diagram, there is a positive correlation between the levels of rural logistics in the agglomeration. Chengdu and Chongqing form the main double-cores for the development of the urban agglomeration, but other cities failed to provide strong support, and the roles of the urban agglomeration had not been fully played.

By comparing Figure 9a,b, it can be observed that in this agglomeration, Chongqing, Chengdu, Deyang, and Mianyang were always in the “high-high” diffusion effect zone from 2010 to 2020, indicating that these four cities had a higher level of rural logistics than their neighboring cities, with a significant diffusion effect demonstrated to drive the development of the surrounding cities. In other words, a positive correlation was shown. Zigong and Yibin were in the “high-low” siphon effect zone. The rural logistics levels of these two cities were higher than their surrounding cities, with their siphon effect stronger than the radiation effect. Nine cities in the urban agglomeration, namely Luzhou, Suining, Neijiang, Nanchong, Meishan, Guang’an, Dazhou, Ya’an, and Ziyang, were in the “low-low” zone all year round, with relatively low rural logistics level. For Leshan, an important tourist city in the agglomeration, a noteworthy phenomenon is that it was in the “high-high” diffusion effect zone in 2010 but in the “high-low” siphon effect zone in 2020, indicating that with the development of tourism, Leshan’s rural logistics level has been improved compared to its neighboring cities. As a result, the siphoning effect was stronger than the radiation effect, showing a negative correlation.

6.2. Dynamic Evolution of Rural Logistics Distribution in Urban Agglomeration

According to Formulas (12)–(14), the Gaussian Kernel density function is adopted to analyze the dynamic evolution of rural logistics in the urban agglomeration, the analysis software is Matlab2019b, and the results are shown in Figure 10. As seen in Figure 10, in terms of distribution position, the main peak position of the agglomeration moves to the right, indicating an upward trend in the development level of rural logistics in the agglomeration. In terms of distribution form, the height of the main peak in the agglomeration experienced a “decline-rise-decline” process, and the width of the main peak became narrower, indicating a narrowing trend in the dispersion degree of the development level of rural logistics in the agglomeration, while the regional differences were narrowed on the whole. The main peaks represent the situation of the core cities, i.e., Chongqing and Chengdu, while the side peaks represent that of the emerging development cities, such as Deyang and Mianyang. In terms of polarization, the number of peaks in the Chengdu-Chongqing agglomeration gradually increased from a single peak over time, indicating a multi-polarization phenomenon in the urban agglomeration; and the distances between the main peaks and the side peaks gradually decreased, indicating a narrowed regional difference.

In summary, Chongqing, Chengdu, Deyang, and Mianyang, as rapidly developing high-level areas in the urban agglomeration, should give full play to their advantages while promoting the development of their surrounding cities. Leshan should launch more attractive tourism projects to secure its throne as a tourism city, thus driving the growth of the logistics industry. Relevant research has shown that the idea of polycentric city development has been revitalized in many rapidly urbanizing countries [70]. In addition, as pointed out by Marques, the main planning agenda in Europe is to direct the future of territorial organizations to an urban polycentric perspective to improve cohesion within regions [71]. After comparing single-center and multi-center systems in logistics activities, Heitz concluded that urban structures and spatial planning policies are critical to regional logistics development [72]. Moreover, in the Chengdu-Chongqing urban agglomeration, the gaps between development levels of rural logistics are narrowing each year, gradually moving towards regional integration and sustainable development.

6.3. Comparison between the Fuzzy Neural Network and the Traditional BP Neural Network

In this study, a neural network was used to evaluate the rural logistics comprehensive index of the Chengdu-Chongqing agglomeration from 2010 to 2020. As a data-driven methodology, machine learning can relieve subjective biases in the process of weighting while effectively diminishing classification errors. In addition, thanks to a combination of the structural knowledge expression ability of fuzzy logic reasoning with the self-learning ability of neural networks, fuzzy neural networks showcase more advantages than traditional BP neural networks. Matlab2019b software is used in this study to compare a traditional BP neural network and a fuzzy neural network, with a comparative analysis of the error curves shown in Figure 11. The average simulation error of the traditional BP neural network is 0.4460, but the prediction error of the fuzzy neural network is only 0.0746 (

Table A1. Prediction error table of BP neural network and fuzzy neural network.

Fuzzy Neural Network	BP Neural Network
0.1071	−0.5548
0.0496	−0.4788
−0.037	−0.0296
−0.092	−0.5013
−0.0534	−0.5449
−0.0088	−0.4233
0.0722	−0.5412
0.0102	−0.5409
−0.1002	−0.4441
−0.0581	−0.5626
0.0681	−0.2662
−0.0818	−0.4952
−0.0854	−0.7700
0.0997	−0.4294
−0.0737	−0.5409
−0.0072	−0.5441
0.1171	−0.5681
−0.0458	−0.1517
0.0872	−0.4917
−0.1166	0.0002
0.1282	−0.4068
−0.1385	−0.5474
−0.0902	0.1285
−0.0392	−0.4415
0.1423	0.1501
−0.0283	−0.5636
−0.0952	−0.4182
0.076	−0.8079
−0.112	−0.6168
−0.076	−0.7269
0.0947	−0.3827
0.1146	−0.8120
0.0311	−0.4626
0.0597	−0.5409
0.0414	−0.7154
0.0366	−0.5428
−0.0441	−0.1885
−0.0264	−0.5097
0.0972	−0.5462
0.0634	−0.4844
−0.0664	−0.0779
0.1096	−0.4576
−0.0865	−0.6770
0.1183	−0.5409
−0.0349	0.1628
−0.0516	−0.4653
0.0797	0.0226
−0.0749	−0.5415
−0.0629	−0.3301
−0.1401	0.1511

). Therefore, the latter can effectively enhance the accuracy of rural logistics classification and prediction.

7. Conclusions

Rural logistics is a key issue in the further development of Chinese urban agglomerations. By constructing a new dynamic assessment model for rural logistics development based on a fuzzy neural network, Moran’s Index, and Kernel density estimation, and taking the Chengdu-Chongqing agglomeration as a research case, this study delivers the following results: Firstly, this agglomeration exhibited a dual-core dominance structure, while producing a considerable siphon effect, as demonstrated by the empirical test findings. However, over recent years, rural logistics development in the urban agglomeration has been substantially enhanced, and the regional disparities have gradually shrunk, with a growing trend toward regional synergy. Secondly, the comprehensive index and level of rural logistics development in the urban agglomeration are increasing yearly, with the index average hiking from 0.76 in 2010 to 4.60 in 2020. Most cities advanced from Level I in 2010 to Level V in 2020. Thirdly, the cities of Deyang, Mianyang, Leshan, and Yibin experienced rapid development, while Chengdu showcased conspicuous spillover effects on its neighboring cities. Nonetheless, the development of rural logistics in Guang’an and Dazhou, both surrounding Chongqing, must be further improved.

Rural logistics, like logistics in urban regions, is a crucial component of urban agglomeration logistics. In addition, rural revitalization is an important strategy for promoting sustainable development. This study’s findings offer the following administrative insights: First, local governments in the agglomeration should optimize their regional industrial structures, strengthen industrial cluster cooperation, and integrate the industrial chains of Chengdu and Chongqing. Due to the siphoning effect and spillover impact, Chengdu and Chongqing should drive the development of rural logistics in their neighboring cities, such as Guang’an and Dazhou. Second, the integration of transportation between urban and rural regions must be boosted. To realize the integrated development of rural roads, industrial parks, tourist attractions, and key rural tourism sites, the construction of rural transportation infrastructure must be bolstered. Third, the cities should enhance the competitive advantages of their agricultural products; facilitate the integration of rural e-commerce systems; express logistics and distribution systems in counties, and construct convenient and effective two-way channels for industrial products to reach the countryside and for agricultural produce to be exported from the rural areas. In addition, the Chengdu-Chongqing urban agglomeration must weaken the concept of administrative regions but strengthen the concept of economic regions, consciously break administrative and institutional barriers, and promote the sustainable development of smooth and integrated logistics in the agglomeration.

Nonetheless, this study still has some limitations. Firstly, given that evaluation indicators for urban agglomeration logistics are diversified, the evaluation indicators selected in this study may not be the most accurate and perfect ones. In the follow-up research, a more necessary and reasonable index system should be designed from a more comprehensive perspective. Secondly, the Chengdu-Chongqing urban agglomeration was selected as the research object of this study, purposed to provide suggestions for the sustainable development of rural logistics in the agglomeration. Exploration of rural logistics development of urban agglomerations in different regions will be a focus of the follow-up work of this research team.