Applied Mathematics and Nonlinear Sciences (aop) (aop) 1–17 Applied Mathematics and Nonlinear Sciences https://www.sciendo.com A comprehensive evaluation of county economies in the Beijing-Tianjin-Hebei Re- gion based on entropy TOPSIS analysis Lu Sen, Zhang Yang, Zhang Caihong†, Wu Chengliang Beijing Forestry University, Beijing 100083, P.R. China Submission Info Communicated by Juan Luis García Guirao Received February 7th 2021 Accepted March 25th 2021 Available online May 25th 2021 Abstract Although the economy of a county that is linked to surrounding towns and rural areas constitutes a multiple basic eco- nomic unit within China’s national economy, it usually exhibits independent characteristics and functions. Consequently, a county’s economy plays a critical role in the overall economic development of a country’s national economy. We created an evaluation index system based on entropy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to carry out a comprehensive evaluation of county economy across the entire Beijing-Tianjin-Hebei region. We found serious imbalances in the development of these counties, with county economies within Beijing and Tianjin being more advanced than those in Hebei Province. Furthermore, there were marked differences between county economies within prefecture- level cities of Hebei Province. The developmental level of counties in cities like Langfang, Tangshan and Chengde was relatively high. Conversely, the level of development of counties in Hengshui, Baoding, Xingtai and Handan was lower. Moreover, there were imbalances among cities in relation to county economic development, especially in Langfang, with smaller differences being found in Hengshui and Qinhuangdao. We analysed and identified the factors influencing differ- ences between counties before providing recommendations. Keywords: county economy, Beijing-Tianjin-Hebei region, entropy method, TOPSIS 1 Introduction The strategic location of the Beijing-Tianjin-Hebei region of China is of particular importance. The eastern portion of this region is located adjacent to the Bohai Sea, while the western portion is linked to the interior and the northern part borders the old industrial base in the northeast. Efforts to promote coordinated development of the region primarily aim to resolve the challenges facing Beijing’s urban regions. Other aims have included easing core non-capital functions to adjust and optimise the region’s urban layout and industrial structure [23], expanding the region’s environmental capacity, and promoting the sharing of public services [11,23]. At the end of 2015, the total permanent population of the Beijing-Tianjin-Hebei region was approximately 111 million, of †Email address: [email protected] ISSN 2444-8656 doi:10.2478/amns.2021.2.00014 Open Access. © 2021 Sen et al., published by Sciendo. This work is licensed under the Creative Commons Attribution alone 4.0 License. 2 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17 which the urban and rural populations, respectively, accounted for 67.48 million and 43.44 million. According to data published in the National Bureau of Statistics of China of 2016, the region’s gross domestic product (GDP) reached 6.94 trillion yuan, with machinery manufacturing, digital information technology, raw materials, logistics, and transportation constituting its main industries. Most of the country’s major high-tech industries and industrial bases are located in this region, with its three component sub-regions–Beijing, Tianjin, and Hebei- evidencing differences in their industrial structures, as depicted in Figure1. In 2015, the value of the output of Beijing’s primary industry accounted for <1% of the local GDP, and that of Tianjin accounted for 1.26%, while the output of Hebei Province was more than one-tenth of the GDP, at 11.54%. As Figure1 shows, the proportion of Beijing’s secondary industry was just under 20% in 2015, while Tianjin’s and Hebei’s secondary industries accounted for =∼50% of the GDP. Remarkably, the value of the output of Beijing’s tertiary industry accounted for the highest proportion of this sub-region’s total industry, at 79.65%, while the proportions of tertiary industry in Tianjin and Hebei Province in relation to the total industries in these sub-regions were 52.16% and 40.19%, respectively. Figure1 reveals that whereas tertiary industry was Beijing’s main industry type, Tianjin’s main industry types comprised a combination of secondary and tertiary industries. The primary industry in Hebei Province was more productive than the primary industries in Beijing and Tianjin, and the proportion of the other two industries accounted for =∼90%. The land area of the Beijing-Tianjin-Hebei region accounts for 2.3% of China’s total land area and supports 8% of the country’s entire population. Moreover, this land area contributes to 10.12% of the total value of China’s economy. Fig. 1 The proportions of the industries in the sub-regions of Beijing, Tianjin and Hebei Province in 2015. Consequent to significant internal disparities existing within the overall economic development structure of the Beijing-Tianjin-Hebei region, a number of issues need to be solved. These issues relate to the fast pace of population growth in Beijing, limited resources and environmental carrying capacities and their deterioration, marked differences in development within the region, inappropriate functional layouts and imbalanced urban and rural structures. Each city and county within the region exhibits a polarised state of development, and there are notable disparities between the levels of economic development and ecological environment in every region. Given its mediating role between urban and rural economic development, a county is a fundamental unit of the national economy and it is therefore influenced by the state of economic development characterising the nation as a whole and by urban and rural development strategies. Promoting coordinated development between counties in this region is perceptibly advantageous. Consequently, the question of how to coordinate the relationship between regional economic development and social development has been widely discussed within academic circles and within local governments. Evaluation of county economies by entropy TOPSIS analysis 3 2 Literature review Following the implementation of the reform and opening-up policy in the 1980s, China’s economy has grown rapidly. However, there has been a concurrent increase in gaps and disparities between regions, with the eastern, southern, and northeastern regions being more developed than the western region. In the 1990s, most discussions on regional economic differences occurred at the national level and focused on East-West, North- South, and coastal areas-inland differences [37]. Foreign scholars have used state-of-the-art research methods to investigate regional economic differences within China, and their studies provide useful references for domestic scholars. Rozelle’s decomposition of the Gini coefficient for the period 1984–1989 indicated that economic disparities between the eastern coastal provinces were rapidly expanding, mainly because of advancing rural industrialisation [16]. In 2002, county economies became national strategies aimed at economic reform, gradually evolving into a key research topic within the disciplines of Economics and Economic Geography. According to a clear admin- istrative system, China has a total of 1,470 counties – excluding county-level cities and autonomous counties – comprising one component of the Chinese national economy. The total area of all of the counties exceeds 90% of China’s entire territory (excluding the marine area), and more than 70% of the total population resides in counties, contributing more than 50% of the total GDP. Therefore, ensuring healthy economic development of counties is critical for sustaining efficient development of the country as a whole [7]. Development of county economies entails availing of the economic advantages of individual counties and carrying out appropriate plan- ning [25]. Existing studies about county economies mainly focused on eastern coastal areas and central regions: Henan Province [31], Hubei Province [29], and Anhui Province [27]. Studies that focused on western regions included those that concentrated their effort on the following regions: Shanxi Province [40], Gansu Province [6], Inner Mongolia [27] and the Xinjiang Autonomous Region [7]. There were a few studies on county economies in southwestern provinces such as Yunnan and Guangxi [3]. Foreign scholars have conducted some research on county-level differences within China. For example, Lyons, Long and Ng, selected the county as the unit of analysis in their study on internal economic differences within Fujian and Jiangsu Provinces. Their results indicated that economic differences between these provinces were expanding [10]. Moreover, in recent years, the Beijing-Tianjin-Hebei region has become a popular target for research because of the emphasis on coordinated development and strategic planning in this region. However, most of the existing research has focused on the provincial or municipal scale, there being a dearth of studies undertaken at the county level. An exception is Cui et al., who evaluated the industrial economies of counties in Hebei Province [1, 17]. Currently, two types of research methods were used in evaluations of the economic development of counties: the single index evaluation method and the comprehensive