Evaluation of Provincial Carbon Neutrality Capacity of China Based on Combined Weight and Improved TOPSIS Model

: It will be a huge challenge for China to achieve carbon neutrality by 2060. At present, China needs to understand its own carbon neutrality status and then scientiﬁcally plan a path to achieve carbon neutrality. In order to evaluate the carbon neutrality capacity of China’s provinces, this paper ﬁrstly constructs an evaluation indicator system, which includes 20 indicators at six levels. Then, a combination of subjective and objective weighting methods, as well as an improved technique for order preference by similarity to an ideal solution (TOPSIS) model, are used to calculate evaluation results. On this basis, the reasons for their different carbon neutrality capacities are analyzed. The results show that the use of renewable energy, maintaining ecological environmental quality, and low-carbon technology are important factors affecting China’s carbon neutrality capacity, and according to the evaluation results, China’s provinces are divided into three categories. Finally, corresponding suggestions for speeding up the pace of carbon neutrality are put forward.


Introduction
According to The Global Climate Report in 2015-2019, published by the World Meteorological Organization (WMO), with the rising concentration of greenhouse gases in the atmosphere, global temperature is rising continuously, and global problems such as melting glaciers and rising sea levels are becoming increasingly serious, so it is urgent to take effective measures to deal with the greenhouse effect. The main cause of the greenhouse effect is increasing carbon emissions. Currently, China is one of the world's largest carbon emitters [1], which has an impact on the global climate. In response, China has proposed to achieve the goal of carbon neutrality by 2060 [2] and actively participates in global climate governance. Carbon neutrality refers to greenhouse gas emissions that do not cause a net increase in the global greenhouse gas emissions into the atmosphere [3]. Under such circumstances, how to achieve the goal of carbon neutrality in China in the next 40 years and how to plan the carbon neutrality path scientifically are questions worth exploring. At the same time, due to the great differences in regional development in China, it is also urgent to evaluate the carbon neutrality capacity of all the provinces and put forward corresponding strategic suggestions.
In the beginning, most of the published literature focused on the study of the factors influencing carbon emissions [4,5] or on the evaluation of the ability to reduce carbon emissions [6,7]. With the introduction of the concept of carbon neutrality, some scholars began to assess the potential for carbon neutrality. The factors considered in the relevant articles mainly include sewage treatment plants [8], the carbon absorption and carbon emissions of urban forests [9], and the balance between carbon source/sink [10]. Then, based on a full consideration of various influencing factors, Huang (2020) proposed a comprehensive carbon assessment model to assess the carbon neutrality capacity of urban areas in terms of population change, redevelopment, and renewable energy [11]. However, on the basis of a carbon neutrality capacity assessment, it is also very important to formulate an appropriate carbon neutralization path policy. Sannamari et al. (2019) analyzed national and local ways to achieve carbon neutrality from the perspectives of technology, emissions, and resilience [12]. Karna et al., (2018) and Li et al., (2018) further analyzed the necessity of a renewable energy policy and carbon emission capacity for achieving carbon neutrality [13,14]. How to effectively achieve carbon neutrality has become an important issue.
Besides, evaluation methods have been extensively studied. Comprehensive evaluation methods include an objective weighting method, a subjective weighting method, and a combination weighting method. Objective weighting methods include the entropy weight method (EWM) [15], the principal component analysis (PCA) method [16], coefficient of variation [17], etc. Among them, the entropy weight method has the advantage of distinguishing between indicators. Subjective weighting methods include the analytic hierarchy process (AHP) [18], the Delphi method [19], the cloud model [20], etc. Compared with other subjective weighting models, the cloud model has the advantage of uncertainty transformation, which can maximize the retention of the inherent uncertainty in the evaluation process and improve the credibility of the evaluation results. However, a single weighting method has limitations: (1) The objective weighting method only depends on differences between attributes, which easily leads to one-sided results; (2) the subjective weighting method may lead to an unreasonable weight ratio due to a lack of experience. A combination weighting method is the weighted summation of the subjective weighting method and the objective weighting method and can comprehensively consider subjective and objective factors to ensure the rationality of the index weight [21,22].
In terms of decision analysis methods, technique for order preference by similarity to an ideal solution (TOPSIS), the Vikor method (VIKOR), and PROMETHEE-II are traditional analysis methods. The TOPSIS method is easy to understand and flexible in application, and it has been widely used in social economy, engineering technology, and other fields [23]. VIKOR is a typical multicriteria compromise method and requires the determination of a criteria weight coefficient and criteria value, which is difficult to achieve in actual decision making [24]. PROMETHEE-II introduces a dominance function to process the index information of samples, which can reflect the advantages of different samples under a certain index. However, there are also some problems, such as there being no definite index evaluation standard, and the subjectivity of the dominance function is strong [25]. In recent years, multicriteria decision-making methods have been improving. For example, stochastic algorithms such as a particle swarm optimization (PSO) algorithm and simulated annealing algorithm (SAA) have been introduced to evaluate a given scheme, similar to the unknown decision model [26]. The random forest (RF) algorithm optimized by smote method and contribution function was used to evaluate enterprise credit risk [27]. The introduction of these stochastic algorithms can optimize traditional decision-making evaluation methods, while the results are usually unstable.
In summary, recent studies have only researched carbon emissions. However, for the evaluation of carbon neutrality capacity, the evaluation of this aspect alone is not comprehensive enough. In addition, there has been no systematic and in-depth study of carbon neutrality capacity in China; a few studies are limited to small-scale carbon neutrality capacity. Therefore, this paper tries to evaluate the carbon neutrality capacity of provincial regions. In the selection of an evaluation weighting method, the combination weighting method containing the entropy weight method and the cloud model is selected to ensure the rationality of the index weight. At the same time, considering the large amount of data in this paper and the practicability of the decision-making method, the TOPSIS method is selected as the carbon neutrality capacity evaluation method.
The structure of this paper is as follows: In Section 2, this paper constructs a provincial carbon neutrality capacity evaluation system with 20 indicators in six dimensions. In Section 3, this paper introduces the cloud model, entropy weight method, and improved TOPSIS model. In Section 4, this paper calculates the neutrality capacity of each province and analyzes the reasons for the differences. In Section 5, this paper makes corresponding suggestions on how to achieve the 2060 carbon neutrality goal based on the results. The specific provincial carbon neutrality capacity evaluation process in this paper is shown in Figure 1.

Evaluation Indicator System of Carbon Neutrality Capacity
For the evaluation of carbon neutrality capacity, different indicators need to be selected from multiple perspectives to reflect the overall level. In fact, there are two ways to achieve carbon neutrality: carbon absorption and carbon emission reduction. Carbon absorption mainly uses forests and oceans to absorb carbon dioxide for carbon sequestration, so the evaluation of sink capacity is essential. For carbon emission reduction, carbon emission efficiency and technological progress are an important reflection of the emission reduction capacity. Economic growth is the main driving factor of the significant increase in carbon emissions in China in recent decades, so it is necessary to consider the social and economic development of each province. In addition, energy consumption, construction, and traffic are the main sources of carbon emissions. The utilization of renewable energy and the low-carbon development of construction and traffic can accelerate the pace of carbon neutrality in China. Therefore, the indicator system of this paper is composed of relative indicators, including carbon emission efficiency, carbon sink capacity, energy consumption, economic development of society, scientific and technological progress, and construction and traffic.

Carbon Emission Efficiency
Carbon efficiency can be reflected by the growth rate of carbon emissions, carbon emission intensity, and per capita carbon emissions [6].
(1) Growth rate of carbon emissions. The higher the growth rate of carbon emissions, the faster the growth of carbon emissions and the more difficult it is to achieve carbon neutrality.
Growth rate o f carbon emissions = Last year s carbon emissions This year s carbon emissions − 1.
(2) Carbon emission intensity. Carbon emission intensity is used to measure the relationship between regional economy and carbon emissions.
(3) Per capita carbon emissions. Per capita carbon emissions reflect the average level of regional carbon emissions.
Per capita carbon emissions = Carbon emissions Population .

Carbon Sink Capacity
A forest carbon sink is an important way to offset carbon emissions [28]. In this paper, the carbon sink capacity of a region is calculated by four indicators: afforestation area per capita, forest volume, forest coverage rate, and green coverage rate. Afforestation area per capita reflects the intensity and motivation of human afforestation. The other three indicators reflect the carbon absorption capacity of existing terrestrial ecosystems. Forest volume refers to the total volume of tree trunks in a certain forest area. Green coverage rate refers to the ratio of green coverage area and regional area in urban built-up area at the end of the report period.

Energy Consumption
Currently, fossil energy plays a leading role in China's energy structure. The reduction in energy intensity and the development of renewable energy will have a significant reduction effect on carbon emissions [29].
(1) Total energy consumption per capita. Currently, the main source of energy is still fossil energy, and higher energy consumption per capita means higher carbon emissions.
Total energy consumption per capita = Total energy consumption Population .
(2) Energy consumption intensity. Energy consumption intensity is the reflection of energy utilization efficiency. With the gradual improvement in energy utilization efficiency, society is moving towards low-carbon development.
Energy consumption intensity = Energy consumption GDP .
(3) The proportion of renewable energy power generation. The electric power industry is a major consumer of energy, and the proposal of carbon neutrality means that the electric power industry must accelerate the pace of clean energy development.

4.
Economic Development of Society Economic development will inevitably increase energy consumption and carbon emissions [30]. In this paper, the economic development of a region is measured from four indicators: the proportion of secondary industry, per capita GDP, GDP index, and urbanization level.

Scientific and Technological Progress
Scientific and technological progress will lead to the application of low-carbon technologies, the improvement in energy utilization efficiency, and the development of green electricity, which is an important way to increase carbon emission reduction and carbon absorption [31]. In this paper, scientific and technological progress is measured via three indicators: number of patents granted per capita, investment in R&D per capita, and waste disposal rate. Progress in technology can improve the efficiency of waste treatment, reduce carbon emissions from waste, and make full use of the biomass in waste to improve energy efficiency.

Number o f patents granted per capita =
Number o f patents granted Population . 6.

Construction and Traffic
In recent years, high energy consumption and emissions from the increasingly largescale construction industry and increasingly congested traffic have been a great hindrance to achieve carbon neutrality [32,33]. In this paper, construction and traffic are measured via three indicators: housing construction area per capita, gross output value of construction industry per capita, and ownership of vehicles per capita.
Housing construction area per capita = Housing construction area Population .
In summary, this paper selects 20 specific indicators, and the specific indicator system is shown in Table 1.

Cloud Model for Subjective Weights
The cloud model was proposed by Li D.Y. [34]. This method refers to the uncertainty transformation model between a qualitative concept and quantitative expression. The cloud model consists of three characteristic numbers of expectation, entropy, and super entropy, which are usually defined as C(E x , E n , H e ). The weights can be obtained through the following process.
Step . According to the one-dimensional normal cloud approximation representation of uncertain language evaluation scales introduced in [35], the one-dimensional normal cloud corresponding to the uncertainty evaluation in this paper is calculated as shown in Table 2. The composition of clouds satisfies the following equation, where k, l is a constant: Step 2: Calculation of Subjective Weights The initial subjective weights are calculated by converting the evaluation language of each expert on the indicators into a comprehensive cloud model and then using the cloud similarity to determine the subjective weights of each indicator. We suppose that there are s experts (k = 1, 2, · · · s) who evaluate the importance of the evaluation indicators A j (j = 1, 2, · · ·). The calculation steps are as follows: (1) According to Table 2, the expert's language evaluation is transformed into the corresponding cloud model: (2) Using the cloud composition equation, the comprehensive cloud model of evaluation indicators A j is constructed with the following equation: (3) According to the calculation method of cloud similarity in [36], the cloud model Z * corresponding to language evaluation V is taken as the cloud with an importance value of 1. Then, the similarity Similar Z j , Z * is calculated.
(4) The initial subjective weights of each evaluation indicator are obtained by normalization processing Similar Z j , Z * . The equation is as follows:

Entropy Weight Method for Objective Weights
Entropy was originally a thermodynamic concept. It was first introduced into information theory by Shannon [37]. The basic idea of the entropy weight method is to determine weight according to the amount of information on the indicators. Generally speaking, the lower the information entropy of an indicator, the more information it provides, so the greater the role it can play in the comprehensive evaluation and the greater its weight. The initial objective weights v j are obtained by normalizing the information entropy E j according to the steps of the entropy weight method algorithm in [38]. The equation is as follows: Finally, the initial subjective weights calculated by the cloud model are combined with the initial objective weights calculated by the entropy weight method to obtain the comprehensive weights of the indicators. In this paper, the importance of both subjective weights and objective weights are set to 0.5. The equation for calculating the combined weights is as follows:

Improved TOPSIS Model for Evaluation
The TOPSIS method is an analysis method that is applicable to the comparison of multiple evaluation objects by multi-attribute indicators. This method aims to choose alternatives that simultaneously have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution [39]. However, the traditional TOPSIS analysis method cannot distinguish between the advantages and disadvantages of the sample points in the vertical line of the positive ideal solution and the negative ideal solution. Therefore, this paper introduces an auxiliary negative ideal solution instead of a negative ideal solution to solve the above problems, which can make the evaluation results more convincing [40]. The algorithm of the improved TOPSIS model is to construct an auxiliary negative ideal solution on the basis of a traditional TOPSIS model. The steps are as follows: Step 1: Constructing a weighted judgment matrix: y 11 y 12 · · · y 1n y 21 y 22 · · · y 2n . . . . . . . . . . . .
In the above equation, S is the weighted judgment matrix, Y is the judgment matrix, W is the weight matrix; w ij is calculated by Equations (9)-(13).
Step 2: Constructing a positive ideal solution, negative ideal solution, and auxiliary negative ideal solution: In the above equations, S + is the positive ideal solution, S − is the negative ideal solution, and S * is the auxiliary negative ideal solution; J + is the set of benefit-based indicators, and J − is the set of cost-based indicators.
Step 3: Calculating the distance of the object to be evaluated to the positive ideal solution and the auxiliary negative ideal solution: In the above two equations, D + i is the distance from the object to be evaluated to the positive ideal solution and D * i is the distance from the object to be evaluated to the auxiliary negative ideal solution.
Step 4: Calculation of relative closeness: In the above equation, C i is the closeness degree of the object to be evaluated, and the greater the closeness, the better the evaluation results. Then, the closeness of the evaluated objects is ranked and the advantages and disadvantages are compared.

Case Analysis
In this section, this paper evaluates the carbon neutrality capacity of 30 provinces in China (except Tibet, Hong Kong, Macao, and Taiwan) based on the evaluation indicator system in Section 2 and the methods proposed in Section 3. The data were obtained from the National Bureau of Statistics of China, the China Energy Statistical Yearbook, and the China Emission Accounts and Datasets (CEADs) in 2017. And Some data are shown in Table A1 in the Appendix A.

Determination of Subjective Weights
A qualitative evaluation of the 20 indicators in Table 1 was performed by five experts, which were shown in Table A2 in the Appendix A. And the evaluation was converted into a corresponding cloud model according to Table 2. Then, the comprehensive cloud model of each indicator was calculated according to Equations (10) and (11) to obtain the initial subjective weight. The relevant data of the calculation process are shown in Table 3 (n = 2000).

Determination of the Combined Weights
Then, the entropy weight method was used to calculate the initial objective weight, and after combining the initial subjective weight and initial objective weight according to Equation (13), the final weight was obtained. The results of the weight calculation are shown in Table 4.

Comprehensive Evaluation Results
First, we calculated the positive and auxiliary negative ideal solutions according to Equations (14)- (17). Then, we calculated the distance of the object to be evaluated from the positive and auxiliary negative ideal solutions according to Equations (18)- (19). Finally, the relative closeness of each province was calculated by Equation (20). The results are shown in Table 5.

Analysis of Evaluation Results
The subjective weight is 0.5r j and the objective weight is 0.5v j in Figure 2. As can be seen from Figure 2, the six indicators that have the greatest impact on the evaluation of carbon neutrality capacity are forest volume, afforestation area per capita, proportion of renewable energy power generation, proportion of secondary industry, number of patents granted per capita, and investment in R&D per capita. Forest volume and afforestation area per capita are indicators of carbon sequestration capacity. It shows that natural carbon sequestration plays a key role in carbon neutrality. The number of patents granted per capita and the investment in R&D per capita are indicators of scientific and technological progress It shows that attention needs to be paid to the development of low-carbon technologies. In addition, accelerating the development of clean energy and controlling the energy consumption of high energy-consuming industries are also the key to accelerating the movement towards carbon neutrality. The objective weights of these six indicators are also the highest among all indicators, indicating that the differences among provinces are the greatest in these four aspects.
On the other hand, it is worth noting that the indicators with greater subjective weights are concentrated in two areas: carbon emission efficiency and energy consumption. Currently, fossil fuel consumption is the largest source of carbon emissions. Reducing the proportion of fossil energy, developing clean energy, and improving carbon emission efficiency are the main ways to improve carbon neutrality at this stage. Therefore, the importance of these two aspects cannot be ignored. In Figure 3, the 30 provinces can be divided into three categories. The first category has a carbon neutrality capacity value of 0.7 or higher and includes six provinces. The second category has carbon neutrality capacity values between 0.623 and 0.7 and includes 18 provinces. The third category has a carbon neutrality of less than 0.623 and includes six provinces. It can be seen that carbon neutrality capacity in the first category is mainly in some economically underdeveloped areas, for the following reasons. Firstly, the levels of transportation, construction, and energy consumption in economically developed areas are much higher than those in economically underdeveloped areas. Secondly, some provinces are rich in renewable energy, and the proportion of renewable energy power generation is very high, which makes the carbon emission level of the power industry very low. For example, the clean energy power generation of Qinghai Province and Yunnan Province accounts for more than 80%. Thirdly, the forest ecosystem of some provinces has a high greening level and strong carbon absorption capacity. For example, the forest volume and forest coverage of Sichuan Province, Yunnan Province, and Heilongjiang Province are at the top level in China. In order to further analyze the characteristics of provinces in different categories, the indicator data were first normalized, followed by further processing of the normalized values by the following equation: In the above equation, i indicates the indicator, j indicates the category, t j indicates the number of provinces belonging to category j, t indicates the province, u i,j (t) indicates the value of indicator i in province t, and − u ij indicates the average level of indicator i of provinces belonging to category j, where the higher the value of − u ij , the higher the level. As can be seen in Figure 4, the high level of the first category is mainly reflected in three aspects: economic development of the society, construction and traffic, and the proportion of renewable energy generation. This shows that most of the provinces in this category have good environmental quality and a high utilization rate of renewable energy, but their economic and social development is relatively backward. Therefore, for these provinces, the first thing is to maintain the advantage of renewable energy as the main energy consumption structure and a stable ecosystem. Future economic development should focus on a circular economy, developing green buildings and transportation, and avoiding weakening the capacity of these aspects in the process of development. The second group of provinces are relatively balanced in all aspects and have no outstanding advantages. This category of provinces should focus on their own strengths for development. The third category of provinces are mainly economically developed provinces. The advantages of these provinces lie in the level of scientific and technological progress. Therefore, they should first continue to develop carbon emission technology to further improve efficiency. After that, efforts should be made to make up for the shortcomings in the energy structure, optimize the industrial structure, and control the high carbon emissions of construction and transportation. In addition, there is little difference in carbon emission efficiency among the three categories of provinces, so China's overall carbon emission capacity needs to be improved. It is worth noting that Ningxia is in last place in the third category but does not have the general characteristics of the third category provinces. Most of its indicators are weaker than those of other provinces.

(1) Comparison between TOPSIS method and improved TOPSIS method
The TOPSIS method was compared with the improved TOPSIS method, as shown in Table 6. The two methods adopt the same weighting method, but the difference lies in the negative ideal solution. It can be seen from the table that the evaluation results of the two methods are similar, and the changes are basically in the same category. The main difference is that Liaoning and Anhui move up three places, while Henan moves down five places. Comparing the normalized indicator data of three provinces with the average level of the second category indicators, it can be seen that half of the indicators of Henan, including the five indicators with the largest weight, are lower than the average level. Most of the indicators with a high weight in Liaoning and Anhui are above the average level. Therefore, the change in ranking is reasonable. This shows that the improved TOPSIS method is effective. (2) Comparison between weighted RSR method and improved TOPSIS method In order to further analyze the accuracy of the improved TOPSIS method, this paper used the weighted rank-sum ratio (RSR) method [41] to evaluate carbon neutrality capacity and compared it with the improved TOPSIS method. The RSR method is an effective multi-index evaluation method which has the characteristics of simple calculation, no special requirements for data, and easy promotion [42]. The weight of weighted RSR is the same as the improved TOPSIS. The evaluation results are shown in Table 6. There are some differences between the evaluation results of the two methods. It is inevitable that the evaluation results of different methods are inconsistent. Through a careful comparison, it can be seen that the top provinces ranked by weighted RSR method are mainly economically underdeveloped with rich forest resources and a high proportion of renewable energy power generation. The provinces at the bottom are mainly economically developed with outstanding advantages in scientific and technological progress. This is consistent with the evaluation results of the improved TOPSIS method on the macro level.

Conclusions
China has a long way to go to achieve the goal of carbon neutrality by 2060. Under such circumstances, this paper constructs the first carbon neutrality capacity evaluation indicator system. Furthermore, the carbon neutrality capacity of 30 provinces in China is comprehensively evaluated by the combined weighting and improved TOPSIS model. The main conclusions are as follows: (1) The evaluation indicator system and comprehensive evaluation method established in this paper can effectively evaluate the carbon neutrality of a region. (2) The development of low-carbon and carbon sequestration technologies, energy cleanup in the power industry, and ecological improvements have the greatest impact on carbon neutrality. (3) The results in this paper are helpful to understand the carbon neutrality status of each region and can provide some information for the government to formulate a carbon neutrality strategy.
In addition, based on the evaluation results and the analysis of indicator weights, this paper puts forward some corresponding suggestions for a future carbon neutrality realization path.
(1) It is necessary to improve the environment. The government should increase afforestation efforts, improve forest ecosystems and urban greening programs, and protect marine ecosystems so as to reduce net carbon emissions. (2) The path to carbon neutrality after 2030 is mainly to reduce carbon emissions and develop artificial carbon sinks. A rapid reduction in carbon emissions with the goal of renewable energy becoming the mainstay of energy consumption will require the large-scale application of energy storage systems to reduce energy waste. Furthermore, we must vigorously develop Carbon Capture, Utilization, and Storage (CCUS). (3) Developing carbon-neutral demonstration areas is helpful to accumulate carbon neutral experiences. Achieving net carbon emissions close to zero in a small area requires low-carbon-intensive economic industries as the driving factor of economic growth. Energy consumption should be based on electricity generated from renewable energy sources and supplied in combination with energy storage systems. The construction and traffic demand should be met by intelligent low-carbon technology.
However, there are some shortcomings to this paper. The indicator system is constructed on the basis of data accessibility and provincial comparability, so the indicator system can be further improved. At the level of technological progress, indicators will be more relevant if based on energy storage costs, renewable energy generation costs, etc. As for carbon sink capacity, the carbon trading market is also an important way of achieving carbon neutrality which is not considered in this paper because the carbon market is currently in a pilot project stage in China. In addition, the development of vehicles relying on new energy sources has gained momentum in recent years, and their contribution to carbon emission reductions in transportation is also a positive driving factor of carbon neutrality.
Further research should be carried out in the following areas in the future: (1) We can study China's carbon neutrality-related policies to analyze whether the current policy system can reach the carbon neutrality target on time, as well as how we can improve the existing shortcomings. (2) It is necessary to study the costs of carbon capture technology and analyze how it can be made economical.
(3) Against the backdrop of peak carbon and carbon neutrality, how a decarbonization road map of China's power system could be designed is a problem worthy of study.   IV  IV  IV  IV  V  Forest volume X5  IV  III  III  IV  IV  Forest coverage rate X6  III  II  IV  III  III  Green coverage rate X7  II  II  III  III  III  Energy consumption per capita X8  IV  IV  IV  IV  IV  Energy consumption intensity X9  IV  V  IV  V  V  The proportion of renewable energy power generation X10  V  V  V  IV  V  The proportion of secondary industry X11  V  V  V  IV  V  Per capita GDP X12  III  III  III  III  III  GDP index X13  III  III  III  III  III  Urbanization level X14  IV  III  IV  IV  IV  The number of patents granted per capita X15  III  III  IV  IV  IV  The investment in R&D per capita X16  III  IV  IV  III  IV  Waste disposal rate X17  II  III  III  III  III  Housing construction area per capita X18  IV  IV  IV  V  IV  Gross output value of construction industry per capita X19  III  IV  III  III  IV  Ownership of vehicles per capita X20  IV  IV  IV  IV  IV