Partially ordered set evaluation of logistics competitiveness of coastal port cites considering carbon emissions

Abstract

Aiming at the problem of logistics competitiveness of coastal cities, a logistics competitiveness evaluation method based on weighted and partially ordered set combinations is proposed. Carbon emissions and inhalable pollutant concentrations are included in the evaluation scope, and an evaluation index system for the logistics competitiveness of 17 coastal port cities is constructed. The results show that: (1) the competitiveness of the logistics industry in 17 coastal port cities in China has been continuously improved, and the catch-up effect of logistics industry development in coastal port cities such as Shenzhen, Ningbo and Qingdao is obvious. The competitiveness level of the logistics industry shows an obvious spatial imbalance. (2) The competitiveness of the logistics industry in Yingkou, Beibu Gulf and other coastal port cities is low, and the difference in competitiveness of the logistics industry in coastal port cities is the main reason for the overall imbalance. (3) The technological innovation, openness and economic development level of the city and the hinterland have a positive impact on the competitiveness of the logistics industry, and the level of economic development has the greatest contribution to the variance of the competitiveness of the logistics industry. The logistics competitiveness of 17 cities is ranked and classified. The leading cities have core diffusion effects and promote the development of the competitiveness of each city. Suggestions on improving the competitiveness of cities are conducive to the high-quality development of China’s logistics industry.

Keywords

Green logistics partially ordered set combination weighting Hasse diagram

1. Introduction

According to the statistics of “Global Climate 2020”, the average temperature in 2020 is one of the three highest years in the history of human meteorology, and global warming is a common ecological problem facing the world. With the progress of human society, industrial production and people’s daily lives are inseparable from many fossil fuels. Due to the continuous consumption of fossil fuels, a large amount of carbon dioxide is emitted, and the global temperature continues to rise. In the face of global climate problems, China has taken control of carbon dioxide emissions as its responsibility and proposed at the United Nations General Assembly in September 2020 that it will complete the goals of “carbon peak” and “carbon neutrality” in the future to jointly cope with global climate change. China is at an essential stage of economic development. Industries such as construction and logistics consume a lot of energy, and carbon emissions continue to rise. According to the China Carbon Accounting Database (CEADS) and the World Resources Institute, China’s total carbon dioxide emissions rose from 1999 to 2018. It accounts for 27% of global carbon dioxide emissions [1].

China proposed implementing carbon emissions trading as early as 2011 to further reduce carbon emissions, trying to strictly control urban carbon emissions. As one of the main industries of China’s energy consumption, the logistics industry consumes about 94.57% of kerosene, 76.47% of fuel oil, 66.48% of diesel oil and 46.42% of gasoline every year, which is related to a large proportion of road transportation in China’s sub-mode transportation [2]. In 2019, China’s logistics industry’s carbon dioxide emissions reached 732.4793 million tons, ranking fourth in all industries in the country, indicating that the reduction of carbon emissions in the logistics industry is of great significance to China’s early realization of low-carbon emission reduction targets [3]. According to the existing data, China’s carbon dioxide emissions will continue to rise for some time. Therefore, it effectively integrated the existing logistics infrastructure and road network resources and actively built a national logistics hub-carrying city [4].

Combined with the “double carbon” background, China will continue to expand the scope of low-carbon pilot cities and promote the construction of national low-carbon pilot cities. Hence, the pressure on logistics hub cities is not small. Balancing the logistics industry’s development in hub cities and strictly controlling carbon emissions is a new topic. Therefore, it is necessary to explore the development direction and path of hub cities under the background of “double carbon”. The carbon emission and logistics development of hub cities under the constraints of low-carbon pilot policies have certain theoretical and practical research value.

With the city’s continuous development, more and more cities have spontaneously assumed some functions. For example, the city has good location conditions, so it has the endowment to develop the logistics industry. The academic community has also done a lot of research on evaluating logistics competitiveness. Jia et al. [5] established an index system for the comprehensive competitiveness of logistics in China’s inland urban agglomerations, evaluated Xi’an and Zhengzhou, respectively, and finally compared them. Blumenstock et al. [6] used the entropy weight-TOPSIS method to dynamically analyze and evaluate the provincial logistics competitiveness of the “New Silk Road Economic Belt” from 2005 to 2015. They analyzed the spatial spillover effects of logistics competitiveness in different types of agglomeration areas. Jean et al. [7] established the evaluation index system of logistics competitiveness in the Beijing-Tianjin-Hebei region from three aspects: logistics competitive strength, competitive potential and competitive environment. Hartmann et al. [8] selected indexes from two aspects of logistics competitive strength and logistics competitive potential, evaluated the logistics competition of coastal port cities and conducted cluster analysis. Xiong and Tang [9] constructed the evaluation index system of logistics competitiveness in the Yangtze River Economic Belt based on the diamond model and used the entropy weight TOPSIS method, exploratory spatial data analysis and spatial econometric model to explore the logistics competitiveness level, spatial evolution characteristics, influencing factors and spatial spillover effects of 11 provinces and cities in the Yangtze River Economic Belt.

The climate problem of global warming affects the hearts of all mankind. The implementation of China’s low-carbon pilot policy decomposes the task of low-carbon emission reduction in various cities, so the academic community has conducted a lot of research on evaluating low-carbon pilot policies. The impact of pilot low-carbon policies on cities is diverse. Some scholars have studied the impact of pilot low-carbon policies on urban carbon emissions and carbon intensity [10, 11] and the impact of low-carbon pilot policy on green technology, green lifestyle and green economy [12]. Scholars have also discussed the impact of urban industrial structures on carbon emissions from the perspective of the impact mechanism of low-carbon pilot policies [13].

In summary, in the existing research on logistics competitiveness, the academic community pays less attention to the logistics competitiveness of coastal port cities and more to the competitiveness and development model. The research on low-carbon pilot policies focuses more on the impact on the urban environment, innovation and economy. It does not consider the possible impact of low-carbon pilot policies on urban logistics development. As a logistics carrier city, the low-carbon pilot policy has put forward new requirements for urban low-carbon emission reduction to a certain extent. The state decomposes the big goals of “carbon peak” and “carbon neutrality” into provinces, autonomous regions and even prefecture-level cities. Therefore, it is necessary to explore the logistics competitiveness of coastal port cities and the impact of low-carbon pilot policies.

2. Materials and methods

This study uses entropy-CRITIC combination weighting and catastrophe progression methods to evaluate the performance of logistics competitiveness. Before using the catastrophe progression method to evaluate, entropy-CRITIC combination weighting is used to calculate the weight of each index.

2.1 Combination weighting model

Currently, most scholars use the Delphi or questionnaire survey method to rank control variables. Still, the ranking results are often subjective. They cannot be changed according to the relative change degree of each control variable, resulting in the evaluation results’ lack of objectivity and rationality. In this study, the entropy-CRITIC combined weight method is used to rank the importance of evaluation indexes, which ensures the objectivity and rationality of the performance evaluation index system of logistics competitiveness.

(1) Entropy method

The entropy method is an objective weighting method to judge the statistical dispersion of indexes. When the information is less, the greater the uncertainty, the greater the entropy. When there is more information, the uncertainty decreases, and the entropy decreases. The weight of the evaluation index is determined according to its entropy. The greater the relative change of the index, the greater the weight. The general procedure of the entropy method can be divided into the following steps.

1) It calculates the specific gravity $\gamma_{ij}$ of $x_{ij}$ . Among them,

$\displaystyle\gamma_{ij}=\frac{x_{ij}}{\sum\limits_{i=1}^{m}{x_{ij}}},(i=1,2,3% ,\ldots,m,j=1,2,3,\ldots,n)$ (1)

2) It calculates the entropy value $\rho_{j}$ of the $j^{\text{th}}$ index. where,

$\displaystyle\rho_{j}=-k\sum\limits_{i=1}^{m}\gamma_{ij}\ln\gamma_{ij},(i=1,2,% 3,\ldots,m,j=1,2,3,\ldots,n),$ (2) $\displaystyle k=\frac{1}{\ln m}\,(m\text{ is the number of samples})$

3) It calculates the difference coefficient $\mu_{j}$ of the jth index. where,

$\displaystyle\mu_{j}=1-\rho_{j}$ (3)

4) It calculates the weight $w_{j}$ of the $j^{\text{th}}$ index. where,

$\displaystyle w_{j}=\frac{\mu_{j}}{\sum\limits_{j=1}^{n}{\mu_{j}}}$ (4)

5) According to the above steps, the outermost index weight $W=(w_{1},w_{2},\ldots,w_{n})$ of the index system is determined, and the lower index weight value is added to obtain the upper index weight value. According to this method, the total weight value of the performance evaluation index of logistics competitiveness is decomposed into the bottom index.

6) According to the size of the weight vector $W=(w_{1},w_{2},\ldots,w_{n})$ , the importance of the performance evaluation indexes of logistics competitiveness is sorted, and the total ranking of the indexes is obtained.

(2) Objective weight calculation based on CRITIC method

The indexes for evaluating the performance of logistics competitiveness often have a certain correlation. This study uses the CRITIC method to calculate the objective weight. Supposing that there are $m$ schemes, each scheme has $n$ indexes, and the evaluation matrix $X$ can be expressed. The matrix elements evaluate the scheme’s value under the corresponding index, and the calculation is shown in Eq. (5).

$\displaystyle X=\left[{{\begin{array}[]{*{20}c}{x_{11}}&{x_{12}}&\ldots&{x_{1m% }}\\ {x_{21}}&{x_{22}}&\ldots&{x_{2m}}\\ \vdots&\vdots&&\vdots\\ {x_{n1}}&{x_{n2}}&\ldots&{x_{nm}}\\ \end{array}}}\right]$ (5)

The following steps calculate the objective weight using the CRITIC method.

1) The same direction processing of indexes

When determining risk assessment indexes, there may be some negative indexes, such as the quality of prefabricated parts. The greater the index value, the lower the risk, while the greater the positive index value, the higher the risk. When these two indexes exist simultaneously, it will increase the difficulty of calculation. Therefore, to facilitate the calculation, it is necessary to co-direct the indexes. The conversion is shown in Eq. (6).

$\displaystyle{x}^{\prime}_{ij}=\frac{1}{\lambda+\max\mid X_{i}\mid+x_{ij}}$ (6)

In the Eq. (6), the index value is represented by $x_{ij}$ . The index value of the same direction processing is represented by ${x}^{\prime}_{ij}$ . The maximum value of the $i$ index is represented by $\max|{X_{i}}|$ . The coordination coefficient is represented by $\lambda$ , which is generally set to 0.1. After the above processing, the positive evaluation matrix ${X}^{\prime}$ can be obtained.

2) Standardized treatment of indexes

Because the meaning and unit of each index in the evaluation matrix ${X}^{\prime}$ are different, it is necessary to convert the value of each index into the same standard, and the processing method is shown in Eq. (7).

$\displaystyle{x}^{\prime\prime}_{ij}=\frac{{x}^{\prime}_{ij}-\min({x}^{\prime}% _{ij})}{\max({x}^{\prime}_{ij})-\min({x}^{\prime}_{ij})}$ (7)

In the Eq. (9), ${x}^{\prime\prime}_{ij}$ is the standardized index value.

3) Index objective weight calculation

Through the standard matrix ${X}^{\prime\prime}$ , the standard deviation $\sigma_{i}$ of each index and the correlation coefficient $\rho_{ij}$ between the indexes can be obtained, and the calculations are shown in Eqs (8) and (9).

$\displaystyle\sigma_{i}=\sqrt{\frac{1}{m}\sum\limits_{j=1}^{m}{(x_{j}^{n}-\bar% {x}_{i}^{n})^{2}}},i=1,2,\ldots,n$ (8) $\displaystyle\rho_{ij}=\text{cov}(X_{i}^{n},X_{j}^{n})/(\sigma_{i}\sigma_{j}),% i=1,2,\ldots,n$ (9)

In the Eqs (8) and (9), the mean value of the $i^{\text{th}}$ index is represented by ${x}^{\prime\prime}_{i}$ . The covariance of the $i^{\text{th}}$ index and the $j^{\text{th}}$ index is represented by $\text{cov}(X_{i}^{n},X_{j}^{n})$ . The amount of information contained in each index $G_{i}$ , as shown in Eq. (10).

$\displaystyle G_{i}=\sigma_{i}\sum\limits_{j=1}^{n}{(1-\rho_{ij})},i=1,2,% \ldots,n$ (10)

Among them, the larger the $G_{i}$ , the higher the relative importance of the $i$ index, and the greater the amount of information contained. According to this value, the objective weight $\beta_{i}$ of the $i^{\text{th}}$ index is calculated, and the calculation is shown in Eq. (11).

$\displaystyle\beta_{i}=\frac{G_{i}}{\sum\limits_{j=1}^{n}{G_{j}}}$ (11)

(3) Determination of comprehensive weight

The subjective weight vector $\alpha$ and the objective weight vector $\beta$ are obtained by the entropy method and the CRITIC method respectively. The comprehensive weight is composed of these two weights, and the weight of each index in the evaluation process can be fully reflected by their complementarity. In order to make the comprehensive weight $\omega_{i}$ of the index as close as possible to $\alpha_{i}$ and $\beta_{i}$ , the principle of minimum distinguishing information can be used to obtain the comprehensive weight $\omega_{i}$ . The objective function is as shown in Eq. (12).

$\displaystyle\left\{{{\begin{array}[]{l}{\min J(\omega)=\sum\limits_{i=1}^{n}% \left(\omega_{i}\ln\frac{\omega_{i}}{\alpha_{i}}+\omega_{i}\ln\frac{\omega_{i}% }{\beta_{i}}\right)}\\ {\text{s.t. }\sum\limits_{i=1}^{n}{\omega_{i}}=1,\omega_{i}\geqslant 0\quad i=% 1,2,\ldots,n}\\ \end{array}}}\right.$ (12)

By solving this optimization model, the comprehensive weight is obtained, as shown in Eq. (13):

$\displaystyle\omega_{i}=\frac{\sqrt{\alpha_{i}\beta_{i}}}{\sum\limits_{j=1}^{n% }{\sqrt{\alpha_{i}\beta_{i}}}}$ (13)

A comprehensive weight vector, as shown in Eq. (14).

$\displaystyle\omega=[\omega_{1},\omega_{2},\ldots,\omega_{n}]^{T}$ (14)

2.2 Partially ordered set theory

Partial ordered set evaluation is a very attractive evaluation method, which reveals the hierarchical relationship between the elements in the set. Under this method, there is no need to assume that there is no linear correlation between the data, and there is no need to assume that the data distribution characteristics. It can be applied only by understanding the ordinal nature of the index weight, which avoids the influence of subjectivity to a certain extent, and then ensures the objectivity and robustness of the high standard. The poset is defined as follows.

Let $R$ be a binary relation on a set $A$ . If $R$ satisfies spontaneity, anti-symmetry and transitivity, then $R$ is called a partial order relation on $A$ .

(1)
Reflexivity: For any $x\in A$ , there is a relation to xRx.
(2)
Anti-symmetry: For any $x$ , $y\in A$ , if xRy and yRx, then $x=y$ .
(3)
Transitivity: For any $x$ , $y$ , $z\in A$ , if xRy and yRz, then xRz.

In the process of application, “ $\underline{\prec}$ ” is usually used to represent the partial order relationship. The partial order relationship $\underline{\prec}$ and the set $A$ together form the partial ordered set, denoted by $(A,\underline{\prec})$ . For the decision-making problem with m samples and n indexes, based on the importance of each index (i.e., the weight order $\omega_{1}\geqslant\omega_{2}\geqslant\omega_{3}\geqslant\ldots\geqslant\omega% _{n}$ of $(A,\underline{\prec})$ internal criterion), the decision-making problem with weight information is expressed in the form of a matrix, shown as Eqs (15)–(17).

$\displaystyle Q=D\cdot I=\left[{{\begin{array}[]{{20}c}{a_{11}}&{a_{11}+a_{12% }}&{a_{11}+a_{12}+a_{13}}&\ldots&{\mbox{a}_{11}+a_{12}+\ldots+a_{1n}}\\ {a_{21}}&{a_{21}+a_{22}}&{a_{21}+a_{22}+a_{23}}&\ldots&{a_{21}+a_{22}+\ldots+a% _{2n}}\\ \vdots&\vdots&\vdots&&\vdots\\ {a_{m1}}&{a_{m1}+a_{m2}}&{a_{m1}+a_{m2}+a_{m3}}&\ldots&{a_{m1}+a_{m2}+a_{m3}% \ldots+a_{mn}}\\ \end{array}}}\right]$ (15) $\displaystyle D=\left[{{\begin{array}[]{{20}c}{a_{11}}&{a_{12}}&\ldots&{a_{1n% }}\\ {a_{21}}&{a_{22}}&\ldots&{a_{2n}}\\ \vdots&\vdots&&\vdots\\ {a_{m1}}&{a_{m2}}&\ldots&{a_{mn}}\\ \end{array}}}\right]$ (16) $\displaystyle I=\left[{{\begin{array}[]{{20}c}1&1&\ldots&1\\ 0&1&\ldots&1\\ \vdots&\vdots&&\vdots\\ 0&0&\ldots&1\\ \end{array}}}\right]$ (17)

If the data of the $i^{\text{th}}$ row in the matrix $Q\geqslant$ the data of the $j^{\text{th}}$ row, $A_{i}\underline{\prec}A_{j}$ can be obtained, that is, the former is better than the latter corresponding to $i$ and $j$ . Thus, the hierarchical relationship between the schemes can be obtained. According to the accumulation transformation of Eq. (15), the iterative comparison of each row is carried out, and the partial order relationship with weight information is constructed, that is, the given partial ordered set $(A,\underline{\prec})$ . For $\forall a_{i},a_{j}\in A$ , if $a_{j}\underline{\prec}a_{i}$ , it is recorded as $r_{ij}=1$ . If $a_{j}$ and $a_{i}$ are not comparable or $r_{ij}=0$ , it is denoted as $r_{ij}=0$ , and $r_{ij}=0$ is called the comparison relation matrix of $(A,\underline{\prec})$ . The Hasse matrix is obtained by comparing the relationship matrix by retaining the maximum path. For the exclusion of the non-maximum path problem, the conversion formula between the comparison relationship matrix and the Hasse matrix is given, shown as Eq. (18).

$\displaystyle H_{R}=(R-I)-(R-I)\ast(R-I)$ (18)

In the Eq. (18), $H_{R}$ is Hasse matrix. $r$ is the relation matrix. $i$ is the unit matrix. is the Boolean operation, that is, $(1+1=1,1+0=1,0+0=0,1\times 1=1,1\times 0=0,0\times 0=0)$ . The multiplication in the matrix in the Boolean operation is equivalent to taking the intersection, and the addition is equivalent to taking the union.

After completing the above process, the Hasse diagram is drawn from the Hasse matrix. Hasse diagram is an extremely important tool to study the theory of posets. The information shown in the graph can fully reflect the correlation, transitivity and structure between samples, and help decision makers understand the hierarchical information and classification between schemes more accurately and intuitively. After obtaining the Hasse matrix, the Hasse diagram is obtained according to the Hasse matrix. Haas diagram can visually display the evaluation results and classify the schemes.

Based on the above analysis, this study combines the weighted set of China’s coastal port city logistics competitiveness evaluation steps:

(1)
The index set is constructed to determine the water quality classification standard.
(2)
Data preprocessing.
(3)
The entropy weight method is used to calculate the weight, and the evaluation indexes are sorted from large to small according to the obtained weight.
(4)
The Hasse matrix is obtained by data accumulation transformation.
(5)
The Hasse diagram is obtained to classify and compare the samples.
(6)
Finally, it’s results analysis. If the partial order satisfies the accuracy, the calculation is stopped. Otherwise, the approximate value of the rank mean is calculated by Eq. (19).

$\displaystyle\rho_{L}(x)=\frac{(m+1)|A_{x}^{-}|}{|A_{x}^{+}|+|A_{x}^{-}|}$ (19)

In the Eq. (19), $\rho_{L}(x)$ is the approximate value of the order value. $A_{x}^{+}$ is the number of sets better than $A_{x}$ . $A_{x}^{-}$ is the number of sets next to $A_{x}$ .
2.3 Construction of evaluation index system of logistics competitiveness

According to the above combing of the evaluation index of the logistics competitiveness, combined with the needs of practical work application, and personality characteristics of logistics competitiveness of coastal port cities, the primary index of logistics competitiveness performance evaluation is specially formulated.

Table 1
Evaluation index system of logistics competitiveness

	Primary indexes	Symbol	Secondary indexes	Symbol
Logistics	Economies of scale	A1	GDP	A11
competitiveness			Total retail sales of social consumption	A12
			Secondary industry added value	A13
	Infrastructure	A2	Wharf length c1/m	A21
			The number of berths is c2/unit	A22
			Cargo throughput c3/ten thousand tons	A23
			10,000 tons of berths c4/unit	A24
	Logistics scale	A3	Number of trucks	A31
			Added value of logistics	A32
			Volume of road haulage	A33
			Port capacity	A34
	Radiating capacity	A4	Fixed investment	A41
			Total export-import volume	A42
			The added value of the tertiary industry	A43
			Permanent population at the end of the year	A44
	Environment protection degree	A5	Carbon emission	A51
			Inhalable pollutants	A52

According to the “opinions on promoting the high-quality development of logistics and promoting the formation of a strong domestic market”, combined with the research of relevant scholars, considering the particularity of port cities, five primary indexes such as economic scale, infrastructure, logistics scale, radiation capacity and environmental protection degree, and 17 secondary indexes are selected to comprehensively evaluate the logistics competitiveness of 20 coastal port cities (Table 1). Carbon emissions are determined by the total energy consumption. The total energy consumption includes coal, oil, natural gas, primary electricity, net power and other energy, which is equivalent to 10,000 tons of standard coal per unit. Inhalable particulate matter, usually refers to the particle size below 10 microns, also known as PM10. The index statistics is used to evaluate the average concentration of PM2.5, and also shows whether the air quality is good or bad.

3. Result analysis and discussions

This study takes the logistics competitiveness of 17 coastal port cities as the research object, evaluates the logistics competitiveness by partial ordered set, and scores each equipment under different evaluation indexes based on cascade combination scoring method.

3.1 Weight of indexes at all levels

For the evaluation of logistics competitiveness of coastal port cities, it is necessary to comprehensively evaluate and determine the logistics competitiveness of coastal port cities from five aspects: economic scale, infrastructure, logistics scale, radiation capacity and environmental protection. According to the combined weighted-partial ordered set evaluation model established above, this study firstly uses the entropy-CRITIC group method to determine the weight of each index, and obtains the weight value of each third-level index by calculation (Table 2).

Table 2
Calculation results of entropy-CRITIC combination method

	Primary indexes	Symbol	Secondary indexes	Symbol	Entropy weight	Critic weights	Comprehensive weight	Bill-ing
Logistics	Economies	A1	GDP	A11	0.062	0.033	0.037	11
competitiveness	of scale		Total retail sales of social consumption	A12	0.033	0.072	0.032	9
			Secondary industry added value	A13	0.088	0.084	0.146	1
	Infrastructure	A2	Wharf length c1/m	A21	0.049	0.047	0.042	10
			The number of berths is c2/unit	A22	0.036	0.021	0.014	17
			Cargo throughput c3/ten thousand tons	A23	0.071	0.056	0.071	7
			10,000 tons of berths c4/unit	A24	0.016	0.084	0.024	12
	Logistics	A3	Number of trucks	A31	0.108	0.060	0.117	2
	scale		Added value of logistics	A32	0.068	0.074	0.091	5
			Volume of road haulage	A33	0.028	0.029	0.014	16
			Port capacity	A34	0.017	0.030	0.009	18
	Radiating	A4	Fixed investment	A41	0.019	0.062	0.022	13
	capacity		Total export-import volume	A42	0.095	0.054	0.093	4
			The added value of the tertiary industry	A43	0.067	0.090	0.108	3
			Permanent population at the end of the year	A44	0.016	0.071	0.021	14
	Environment	A5	Carbon emission	A51	0.091	0.051	0.085	6
	protection degree		Inhalable pollutants	A52	0.119	0.029	0.063	8

The index data of 17 cities in China’s coastal ports are directly or indirectly derived from China Statistical Yearbook and Provincial Statistical Yearbook, and 17 key coastal port cities such as Shanghai, Tianjin, Qingdao and Shenzhen are selected as sample cities. The data are standardized (Table 3). Among them, A11 $\sim$ A52 are 17 secondary indexes of the evaluation index system of logistics competitiveness of coastal port cities. A1 $\sim$ A14 represent the logistics competitiveness of Shanghai, Ningbo, Shenzhen, Qingdao, Guangzhou, Tianjin, Xiamen, Beibu Gulf, Rizhao, Lianyungang, Yingkou, Dalian, Yantai, Dongguan, Fuzhou, Tangshan and Jiaxing.

Table 3

Raw data normalization

City	Index
	A11	A12	A13	A21	A22	A23	A24	A31	A32	A33	A34	A41	A42	A43	A44	A51	A52
B1	1.00	1.00	1.00	0.55	0.10	0.02	1.00	1.00	1.00	0.99	1.00	0.61	1.00	1.00	0.23	1.00	0.38
B2	0.32	0.71	0.52	1.00	0.33	0.14	0.32	0.06	0.06	0.81	0.86	0.40	0.15	0.69	0.04	0.65	0.52
B3	0.70	0.37	0.99	0.04	0.13	0.28	0.25	0.83	0.77	0.54	0.63	0.34	0.46	0.60	0.15	0.20	0.95
B4	0.30	0.23	0.43	0.02	0.01	0.85	0.04	0.52	0.35	0.48	0.49	1.00	0.72	0.26	1.00	0.23	0.90
B5	0.64	0.40	0.66	0.26	1.00	0.89	0.21	0.69	0.35	1.00	0.51	0.41	0.12	0.63	0.17	0.57	0.24
B6	0.36	0.15	0.51	0.06	0.05	0.69	0.25	0.05	0.24	0.54	0.43	0.32	0.10	0.30	0.11	0.82	0.95
B7	0.15	0.10	0.26	0.47	0.41	0.53	0.44	0.02	0.08	0.80	0.25	0.32	0.10	0.12	0.03	0.05	0.10
B8	0.60	0.02	0.77	0.25	0.21	0.44	0.07	0.00	0.00	0.18	0.13	0.13	0.04	0.40	0.48	0.05	0.44
B9	0.02	0.02	0.05	0.01	0.02	0.76	0.10	0.09	0.00	0.09	0.10	0.14	0.01	0.02	0.01	0.34	0.57
B10	0.05	0.05	0.12	0.04	0.05	0.28	0.21	0.14	0.02	0.25	0.09	0.20	0.01	0.03	0.01	0.13	0.62
B11	0.00	0.01	0.03	0.08	0.04	0.18	0.23	0.13	0.00	0.36	0.08	0.04	0.00	0.00	0.00	0.03	0.71
B12	0.15	0.07	0.27	0.06	0.10	0.35	0.19	0.20	0.01	0.30	0.06	0.18	0.04	0.11	0.04	0.37	0.52
B13	0.19	0.13	0.33	0.14	0.26	0.58	0.59	0.18	0.14	0.30	0.07	0.69	0.05	0.13	0.05	0.28	0.33
B14	0.23	0.17	0.56	0.10	0.22	0.11	0.15	0.37	0.05	0.11	0.06	0.27	0.16	0.13	0.01	0.31	0.14
B15	0.26	0.18	0.39	0.29	0.14	0.21	0.16	0.20	0.12	0.29	0.05	0.70	0.04	0.20	0.06	0.29	0.10
B16	0.16	0.08	0.38	0.00	0.02	1.00	0.00	0.32	0.02	0.89	0.05	0.18	0.01	0.08	0.05	2.18	0.95
B17	0.12	0.09	0.28	0.18	0.06	0.05	0.28	0.00	0.02	0.29	0.04	0.29	0.02	0.07	0.03	0.25	1.00

The importance of the index can be known from the combined weight. The environmental protection index is regarded as a negative index. The larger the value, the lower the evaluation score.

A14 $>$ A31 $>$ A43 $>$ A42 $>$ A32 $>$ A51 $>$ A23 $>$ A52 $>$ A12 $>$ A21 $>$ A11 $>$ A24 $>$ A41 $>$ A44 $>$ A13 $>$ A33 $>$ A22 $>$ A34. The data are sorted in order from large to small according to the index, and the cumulative matrix $Y$ containing weight information is obtained (Table 4).

Table 4

Accumulative matrix containing weight information

City	Index
	A13	A31	A43	A42	A32	A51	A23	A52	A12	A21	A11	A24	A41	A44	A33	A22	A34
B1	1	2	3	4	5	6	6.02	6.4	7.4	7.95	8.95	9.95	10.56	10.79	11.78	11.88	12.88
B2	0.52	0.58	1.27	1.42	1.48	2.13	2.27	2.79	3.5	4.5	4.82	5.14	5.54	5.58	6.39	6.72	7.58
B3	0.99	1.82	2.42	2.88	3.65	3.85	4.13	5.08	5.45	5.49	6.19	6.44	6.78	6.93	7.47	7.6	8.23
B4	0.43	0.95	1.21	1.93	2.28	2.51	3.36	4.26	4.49	4.51	4.81	4.85	5.85	6.85	7.33	7.34	7.83
B5	0.66	1.35	1.98	2.1	2.45	3.02	3.91	4.15	4.55	4.81	5.45	5.66	6.07	6.24	7.24	8.24	8.75
B6	0.51	0.56	0.86	0.96	1.2	2.02	2.71	3.66	3.81	3.87	4.23	4.48	4.8	4.91	5.45	5.5	5.93
B7	0.26	0.28	0.4	0.5	0.58	0.63	1.16	1.26	1.36	1.83	1.98	2.42	2.74	2.77	3.57	3.98	4.23
B8	0.77	0.77	1.17	1.21	1.21	1.26	1.7	2.14	2.16	2.41	3.01	3.08	3.21	3.69	3.87	4.08	4.21
B9	0.05	0.14	0.16	0.17	0.17	0.51	1.27	1.84	1.86	1.87	1.89	1.99	2.13	2.14	2.23	2.25	2.35
B10	0.12	0.26	0.29	0.3	0.32	0.45	0.73	1.35	1.4	1.44	1.49	1.7	1.9	1.91	2.16	2.21	2.3
B11	0.03	0.16	0.16	0.16	0.16	0.19	0.37	1.08	1.09	1.17	1.17	1.4	1.44	1.44	1.8	1.84	1.92
B12	0.27	0.47	0.58	0.62	0.63	1	1.35	1.87	1.94	2	2.15	2.34	2.52	2.56	2.86	2.96	3.02
B13	0.33	0.51	0.64	0.69	0.83	1.11	1.69	2.02	2.15	2.29	2.48	3.07	3.76	3.81	4.11	4.37	4.44
B14	0.56	0.93	1.06	1.22	1.27	1.58	1.69	1.83	2	2.1	2.33	2.48	2.75	2.76	2.87	3.09	3.15
B15	0.39	0.59	0.79	0.83	0.95	1.24	1.45	1.55	1.73	2.02	2.28	2.44	3.14	3.2	3.49	3.63	3.68
B16	0.38	0.7	0.78	0.79	0.81	2.99	3.99	4.94	5.02	5.02	5.18	5.18	5.36	5.41	6.3	6.32	6.37
B17	0.28	0.28	0.35	0.37	0.39	0.64	0.69	1.69	1.78	1.96	2.08	2.36	2.65	2.68	2.97	3.03	3.07

The comparison relation matrix $R$ is obtained by comparing the row vectors according to the accumulation matrix. According to the comparison relationship matrix, the comparison relationship between the same kind is 1, such as the first row of the first column A1 and A1 comparison. The comparison between different classes, such as the first row and the second column are shown as 1, it is proved that A2 is better than A1 data, and vice versa. According to the comparison relation matrix, the Hasse matrix can be obtained (Table 5).

Table 5

Hasse matrix

City	Index
	A11	A12	A13	A14	A21	A22	A23	A24	A31	A32	A33	A34	A41	A42	A43	A44	A51	A52
B1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	1	0	1	0
B2	0	0	0	0	0	0	1	0	0	0	0	0	1	1	0	1	0	0
B3	0	1	0	1	0	1	0	0	0	0	0	0	0	0	1	0	1	0
B4	0	0	0	0	0	0	1	0	0	0	0	0	1	1	0	1	0	0
B5	0	1	0	1	0	1	0	0	0	0	0	0	0	0	1	0	1	0
B6	0	0	0	0	0	0	1	0	0	0	0	0	1	1	0	1	0	0
B7	0	0	0	0	0	0	0	0	1	1	0	0	0	1	0	0	0	1
B8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
B9	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0
B10	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0
B11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
B12	0	0	0	0	0	0	0	0	1	1	0	0	0	1	0	0	0	1
B13	0	0	0	0	0	0	0	0	1	1	0	0	0	1	0	0	0	1
B14	0	0	0	0	0	0	1	0	0	0	0	0	1	1	0	1	0	0
B15	0	0	0	0	0	0	0	0	1	1	0	0	0	1	0	0	0	1
B16	0	0	0	0	0	0	0	1	0	0	1	0	0	1	0	0	0	0
B17	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0

Figure 1.

Hasse diagram.

3.2 Result analysis

According to the Hasse matrix, the Hasse diagram is obtained, as shown in Fig. 1. The Hasse diagram can intuitively obtain the hierarchical relationship of logistics competitiveness of 17 port coastal cities. From Fig. 1, it can see the stratification and clustering information of logistics competitiveness of 17 coastal port cities, which are divided into 5 layers.

The first layer: the corresponding cities of b1, b3 and b5 are Shanghai, Shenzhen and Guangzhou.

The second layer: the corresponding cities of b2, b4, b6, b14 and b16 are Ningbo, Qingdao, Tianjin, Dongguan and Tangshan.

The third layer: the corresponding cities of b7, b12, b13 and b15 are Xiamen, Dalian, Yantai and Fuzhou.

The fourth layer: the corresponding cities of b9, b10 and b17 are Rizhao City, Lianyungang City and Jiaxing City.

The fifth layer: the corresponding cities of b8 and b11 are Beibu Gulf City and Yingkou City.

The evaluation method of the partial ordered set has the characteristics that the upper level is better than the lower level; that is, the more the upper level is, the stronger the logistics competitiveness is, and the more the lower level is, the worse the logistics competitiveness is. It can be expressed as (b1, b3 and b5) $>$ (b2, b4, b6, b14 and b16) $>$ (b7, b12, b13 and b15) $>$ (b9, b10 and b17) $>$ (b8 and b11). The development time of logistics industry in Beibu Gulf City and Yingkou City is relatively short. Although the state has strongly supported it in recent years, the infrastructure level is backward, and the scale of logistics is small. The most important factor is the insufficient support of the territorial economy. From the perspective of logistics scale, the investment in fixed assets, mileage, freight volume and turnover of Beibu Gulf City and Yingkou City are far below the average level. It can be seen that the development of industrial transportation has a certain negative effect on the local environment, and promoting the coordinated progress of the two can better promote the high-quality development of the economy.

4. Conclusions

(1) The combination weighting and partial ordered set evaluation model is constructed. This method can effectively overcome the limitation that other methods must give accurate weights, and provide a more objective and intuitive ranking for logistics competitiveness stratification.

(2) Based on the meaning of logistics competitiveness and the evaluation index system of logistics competitiveness of coastal port cities, this study gives a combination weighting method to determine the weight and puts forward the way to evaluate the logistics competitiveness, that is, the partially ordered set. Through the sample data of 17 cities, the hierarchical results are obtained.

(3) Through the evaluation and analysis of 17 coastal cities, the feasibility of the method is verified. Still, the use of “carbon emissions, inhalable pollutant concentration” instead of “total output value of the first and second industries” indexes, the scientific nature and rationality of the evaluation system need to be further verified.

Footnotes

Acknowledgments

This work has been supported by the Zhejiang Provincial Social Science Planning Project (No. 23NDJC408YBM).

Declarations of interest

None.

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Partially ordered set evaluation of logistics competitiveness of coastal port cites considering carbon emissions

Abstract

Keywords

1. Introduction

2. Materials and methods

2.1 Combination weighting model

(1) Entropy method

(2) Objective weight calculation based on CRITIC method

1) The same direction processing of indexes

2) Standardized treatment of indexes

3) Index objective weight calculation

(3) Determination of comprehensive weight

Table 1 Evaluation index system of logistics competitiveness

3.1 Weight of indexes at all levels

Table 2 Calculation results of entropy-CRITIC combination method

4. Conclusions

Footnotes

Acknowledgments

Declarations of interest

References

Table 1
Evaluation index system of logistics competitiveness

Table 2
Calculation results of entropy-CRITIC combination method