USING AN ENTROPY-GRA, TOPSIS, AND PCA METHOD TO EVALUATE THE COMPETITIVENESS OF AFVs – THE CHINA CASE

With the increase in severe environmental problems associated with fossil fuel vehicles, the development of Alternative Fuel Vehicles (AFVs) has led to their promotion and use in Chinese provinces and cities. The comprehensive evaluation of competitiveness of the AFV industry in Chinese cities is beneficial to analyse the effects and relationships of different factors to promote the sustainable development of the AFV industry and guide the growth paths of the cities. An industrial competitiveness evaluation index system is established based on the characteristics of AFVs, and the development of the AFV industry in ten typical cities in China is comprehensively evaluated based on the Grey Relative Analysis (GRA) Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) and Principal Component Analysis (PCA) methods. To evaluate the results, the entropy weighting method is used for the weight distribution, and the industrial competitiveness rankings of ten cities are obtained by the entropy-GRA, TOPSIS, PCA (EGTP) method. The results show that Beijing is ranked first, followed by Shanghai, and Qingdao is ranked last. By analysing the correlation between the evaluation methods and indicators, it is found that EGTP has a high correlation with the other three evaluation methods, which proves the rationality of the weighted linear combination of GRA and the other three methods. Indices C5 (pure electric car proportion) and C13 (average concentration of PM2.5) were outliers due to the small number of samples.


INTRODUCTION
With socio-economic development and increases in consumer material consumption, the global car ownership is increasing, and the resulting environmental problems have attracted worldwide attention. Because emissions from the transport sector are growing faster than those from other sectors and are expected to double by 2050, the transport sector is of critical importance in mitigating the climate change [1]. Therefore, clean-energy vehicles must be promoted to reduce these environmental problems. Alternative fuel vehicles (AFVs) have attracted extensive attention since their emergence, due to their reliability, environmental friendliness and pollution-free characteristics.
In China, a survey found that 42% of air pollution comes from the transportation sector, and only 99 of China's 338 cities at or above the prefectural level meet the environmental air quality standards [2]. Because exhaust emissions from traditional automobiles are the primary source of these pollutants, clean AFVs are able to mitigate these environmental problems. In recent years, many cities in China the AFV industry based on relevant guidance documents and use the improved GRA, TOPSIS and PCA methods -EGTP -to comprehensively evaluate the competitiveness of the Chinese urban AFV industry, which can reveal the overall development level of a country at the micro-level and provide policy enlightenment and rules for the development of AFVs in the future.
The rest of the paper is organized as follows. Section 2 establishes an evaluation index system for the competitiveness of the AFV industry with six first-level and 14 second-level indicators and completes the data collection from China. Section 3 introduces three evaluation methods and constructs the EGTP method according to the entropy weighting method. In Section 4, the results of various evaluation methods are analysed, and correlation analysis is carried out to illustrate the application of the proposed approach. Section 5 provides the conclusions.

Research object
This paper is a comprehensive evaluation of the industrial competitiveness of AFVs in Chinese urban cities. In total, 88 cities in China have been selected for AFV pilot work, and excellent results have been achieved. This paper selects ten typical cities for the exploration and analysis because they cover most of China's provinces and cities with AFV promotion policies, and they are also the most mature cities with the most comprehensive collection of relevant data. Since the economic development in each city is not the same, the popularity of AFVs has varied considerably. Only the development situations in ten cities with relatively mature development histories are comprehensively evaluated in this paper. The ten typical cities and their corresponding identification numbers are shown in Table 1.
Beijing, Shanghai, Guangzhou and Shenzhen, which are the four cities with the most influential traditional economies among the selected cities, are also at the forefront of the industrial competitiveness of AFVs in China. Chongqing and Tianjin, which are municipalities directly under the central government, have played an exemplary role in promoting AFVs nationwide. Hangzhou, Changsha and Hefei, which are the famous provincial capitals, and Qingdao, a have actively promoted AFVs, hoping to alleviate the environmental and energy problems through the popularization of AFVs. Therefore, studying the development scale, level and industrial competitiveness of AFVs in Chinese urban cities will be conducive to promoting China's economic growth and the essential strategic adjustment of the automobile industry for a country with a population of nearly 1.4 billion and more than 200 million passenger cars.
Many experts and scholars have conducted extensive studies of AFVs, which has helped drive a rapid development of AFVs in recent years. However, most existing studies focus on the environment, policy, consumer behaviour and infrastructure of AFVs but seldom make a comprehensive evaluation of the development within some countries' cities [3][4][5][6]. The competitiveness of the AFV industry reflects the development of urban AFVs. In this research area, Ruan and Shi [7] constructed an AFV industry competitiveness evaluation system and used the grey correlation model to conduct empirical research on the three provinces of Guangdong, Fujian, and Hubei. Xie et al. [8] used the new diamond model to evaluate the data related to the development of the AFV industry in typical provinces and cities, concluding that Guangdong's AFV industry has formed a large relevant industry support and technological innovation competitive advantage nationwide. Based on the analytic hierarchy process -fuzzy comprehensive evaluation method, Yan [9] evaluated the competitiveness of Beijing's AFV industry and proposed countermeasures and suggestions accordingly.
The main problems in the above literature are as follows: (1) The research on AFVs mainly focuses on the environment, policy, consumer behaviour and other aspects, lacking relevant research on the development of AFVs in different cities. This paper makes up for this research vacancy. (2) The evaluation methods are relatively singular, and there are no multiple evaluation methods for correlation analysis to make up for the errors between different models. (3) The evaluation method has a significant degree of subjectivity, and there is little research on the weight between evaluation methods.
In summary, there are few studies on the competitiveness of the AFV industry, and most are macro qualitative analyses, while some quantitative evaluation studies are deficient in terms of methods and index selection. Therefore, the aim of this paper is to establish a competitiveness evaluation system of follows. Generally, the more significant the benefit-type index, the better the evaluation result. Besides, the smaller the cost-type index, the better the evaluation result.
The scale development (B 1 ) mainly measures the sales volume, growth rate, ownership and number of significant brand dealers of AFVs in a city, directly reflecting the scale development status and promotion development degree of AFVs in a city. C 1 , C 2 , C 3 and C 4 are benefit-type indices.
The allocation proportion (B 2 ) mainly includes the pure electric car proportion and individual proportion. The former is the most significant and most representative proportion of AFVs in the local market, and the latter is the difference in the promotion of AFVs between individuals and units. The index can reflect the different allocation proportions of AFVs among cities and different development levels. The literature [10] proposes that pure electric driving is the primary strategic orientation for the development of new energy vehicles. Therefore, this paper considers that pure electric vehicles are the mainstream for AFVs, with better energy-saving effects and lower costs. A more significant proportion of pure electric cars reflects a higher degree of urban AFV development. At the same time, the greater the individual proportion, the higher the AFV penetration rate of urban residents, so C 5 and C 6 are benefit-type indices.
The popularization of AFVs is generally associated with the development level of local cities, including the total car ownership, economic strength and total urban population. Thus, a city's development strength (B 3 ) reflects the level of automobile development, along with the economic index and population size of a city. C 7 , C 8 and C 9 are benefit-type indices.
The development of AFVs in various cities is closely related to the infrastructure construction (B 4 ), such as charging piles and public charging facilities, which are required for the growth of AFVs. C 10 is a benefit-type index.
The local government's policy support (B 5 ) is essential for AFVs, including subsidies for AFVs and license limits. The earlier the start time of the license limit, the larger will be the scale of urban car ownership. Additionally, the higher the demand for AFVs, the more rapid will be the development of AFVs. C 11 is a benefit-type index, while C 12 is a cost-type index. city representative of the entire country, have all employed AFVs models. Because the development of AFVs in the above ten cities is relatively mature, by studying the industrial competitiveness in each area, it is possible to better understand and learn from the overall development situation in China.

Industrial competitiveness indicator system of urban AFVs
In 2014, the China State Council enacted the Guiding Opinions on Accelerating the Promotion and Application of New Energy Vehicles by the State Council of the People's Republic of China (2014, Number 35) [10]. Based on the AFVs industrial development plans of all provinces and cities in China, this guidance puts forward the requirements for accelerating the application of AFVs. It involves the scale, economy, policy and environment indicators of urban AFVs development, which can provide a reference for the construction of the index system in this paper. Additionally, the literature [11] pointed out that the factors restricting the development of urban AFVs include the status of local AFVs, the proportion of allocation, and the policy of purchasing restrictions. In summary, by referencing the literature [10,11] and based on the scientific, representative and developmental principles of indicator selection, we have constructed a rigorous industrial competitiveness evaluation index system for urban AFVs development, which is divided into six first-level indices (B 1~B6 ) and 14 second-level indices (C 1~C14 ). The above indicators are representative and simultaneously take into account the convenience of data collection, which can comprehensively and systematically reflect the development trends of AFVs in various cities. The specific meaning of the first-level indicators is as in China. Most cities are in the growth stage, with an average sales growth rate of 33.71%. Qingdao, which is the only city with a negative growth rate, may be influenced by the government subsidy policy change in 2018. Beijing and Shanghai, which are the two cities with the largest numbers of AFVs, observed a decrease in the average PM 2.5 concentration compared to those in previous years, partly due to the extensive promotion of AFVs.

METHODS
Through investigation and data collection, the industrial competitiveness of AFVs in typical Chinese urban cities was comprehensively evaluated. The original evaluation matrix collected was analysed using the GRA, TOPSIS and PCA methods, and the final sequencing result was obtained using the EGTP method.
The environmental impact (B 6 ) is the environmental quality level of local cities, and the average concentration of PM 2.5 is taken as the corresponding evaluation index. Moreover, changes in pollutant concentrations can be regarded as effects of AFV promotion on the environment. C 13 and C 14 are cost-type indices.
In summary, a comprehensive evaluation system is established, as shown in Table 2.

Raw data collection and analysis
With the help of the Economic and Information Commission (EIC), we have collected the specific data in 2018 from the indicator system constructed in this paper as the input for the AFV industrial competitiveness evaluation. The raw data are listed in Table 3.
Step 4: Calculate the grey-weighted relational degree: where r i is the grey-weighted correlation degree of the i-th evaluation object.
Step 5: According to the evaluation analysis of the grey-weighted correlation degree, the evaluation result is denoted by y 1 =[y 11 , y 12 ,..., y 1n ].

TOPSIS method
TOPSIS is an effective multi-index evaluation method that involves the construction of positive and negative ideal solutions to an evaluation problem. These solutions represent the optimal solution and the worst solution for each index. The relative closeness of each scheme to the ideal scheme is calculated to sort the schemes and select the optimal one [13]. The specific steps in this approach are as follows: Step 1: Obtain the canonical decision matrix by vector programming. We establish the index matrix A=(a ij ) m×n of the original problem and the normalized matrix B=(b ij ) m×n , where

GRA method
The GRA model is used as an evaluation tool to measure the degree of similarity or dissimilarity among the development trends of different factors [12]. This approach comprehensively evaluates a multi-index problem. The specific steps are as follows: Step 1: Determine the evaluation objects and evaluation criteria. Let there be m evaluation objects and n evaluation indices. The original data are standardized. The sequence of the best index values in each index is called the reference sequence, and the remaining values form the comparison sequence. The reference number column is x 0 ={x 0 (k)|k=1,2,...n}, and that of the comparison sequence is Step 2: Determine the corresponding weight of each index value. The corresponding weights w=[w 1 ,w 2 ,...,w n ] are given by the method of expert analysis.

EGTP method
Based on the GRA, TOPSIS and PCA methods, the EGTP method uses the entropy method to weight the above three evaluation methods and obtain the final evaluation results. This approach reduces the errors among different evaluation models. The entropy method is an objective weighting method that uses the real relationships among data to determine the relevant weights, thereby avoiding the subjectivity and arbitrariness of subjective weighting [15]. The steps in this process are as follows: Step 1: The results obtained by the three evaluation methods form the set Y=[y 1 , y 2 , y 3 ], and X (2) =(x ij ) m×n is the input vector of the entropy weighting method after standardization; Step 2: Index translation processing is conducted. There are some negative numbers in the standardized data, and data translation processing sets the maximum negative number to a value greater than 0 after the standardization process (for ease of calculation, we set the minimum precision to 0.001). The smaller the translation value, the smaller will be the effect on the result. We let the data after translation processing be y ij , and if A j is the absolute value of the minimum of x ij , then the calculation formula of y ij is as follows: .
Step 3: Ratio p ij associated with x ij in this index is calculated using the translated data. Step 4: The entropy value of index j is calculated as follows: At this time, this index does not provide any information. When p ij =0, let p ij · (ln p ij )=0 to ensure that E j ![0,1].
Step 5: The weight of index j is calculated. Step 2: Establish the weighted norm matrix C=(c ij ) m×n . The weight vector w=[w 1 ,w 2 ,...,w n ] is given by the decision maker to obtain the following equation. Step 4: Calculate the distances s i * and s i 0 of each scheme from the positive and negative ideal solutions. , , , , Step 5: Calculate the comprehensive evaluation index of each scheme as follows.

PCA method
PCA uses the concept of dimensionality reduction to convert multiple indices into a few comprehensive indices, and each principal component reflects a large portion of the information associated with the original variable [14]. This method not only eliminates many variables but also reduces various complex factors into several principal components to effectively obtain relevant information in a simplified manner. The specific steps in this process are as follows: Step 1: Standardize the original data and record them as X (1) =(x ij ) m×n ; Step 2: Calculate the correlation coefficient matrix R=(r ij ) m×n .
The EGTP method uses the entropy weighting method to distribute the weights of the results of the first three evaluation methods. After the three sets of results were standardized and combined, the weights were determined. The results are listed in Table 5.
The weights of the three evaluation methods, as determined by the entropy weighting method, were 0.335, 0.29, and 0.375. In summary, the industrial competitiveness rankings of AFVs in the Chinese cities are shown in Table 6. Moreover, the variation trends of the results of the four evaluation methods are shown in Figure 1. It can be seen that the four evaluation results are highly consistent.
The presented results indicate that the industrial competitiveness levels of AFVs in Beijing and Shanghai are the highest in the country. The sales volume, vehicle ownership level, policies, economy and other factors considered in the index system To more intuitively reflect the differences among methods, the results are obtained by combining the GRA, TOPSIS and PCA models, and their weights are determined by the entropy weighting method. Then, the final evaluation results are obtained by EGTP as a linear combination of the GRA, TOPSIS and PCA methods.

Solutions based on various evaluation methods
By using MATLAB programming calculations, the evaluation values of the various methods were calculated in Table 4.

Correlation between different evaluation methods
The scatter distributions of the sorting results of the four evaluation methods obtained by MATLAB are shown in Figure 2.
It can be seen that the four evaluation results have a strong correlation. The last row is the scatter distribution between the EGTP method proposed in this paper and the results of the traditional GRA, TOPSIS and PCA methods. The strong linear correlation shows that the entropy method is reliable. At the same time, the correlation between the other three methods is also high, which indicates the rationality of the combination of multiple evaluation methods. The correlation coefficients between the methods were calculated, as shown in Table 7.
Most methods are highly correlated with each other, and only the correlation coefficient between TOPSIS and PCA is less than 0.8. Most correlation coefficients are above 0.8, which shows that most combinations are reasonable and that each evaluation result is highly correlated. The entropy weight method can be used for linear combination. At the same time, it should be noted that the ranking results obtained by TOPSIS are somewhat different from the other three results, which also explains the significance of the entropy weighting method in the weighting of the methods, as TOPSIS is given the lowest weight (0.29). Although the GRA, TOPSIS, and PCA methods are similar in overall ranking, it is impossible to achieve the same evaluation results. Due to the difference in calculation formulas, a certain degree of deviation is generated. Therefore, the entropy weight method is used to combine them, and lower weight is given to the method with larger bias.

Correlation between indices and ranking results
The original values of the 14 indicators in ten cities were correlated with the sorted result values obtained by the EGTP evaluation method, and the scatter plot distributions are shown in Figure 3. provide favourable conditions for the industrial competitiveness of AFVs. The evaluation results indicate that the license plate and driving restriction policies, i.e. new energy license plates and car purchase subsidies, were the main reasons for the differences in AFVs industrial competitiveness among cities. In contrast, the industrial competitiveness degree of AFVs in Changsha and Qingdao was relatively low, especially in Qingdao, where the sales volume in the first two years was high due to supportive policies, after which a reduction in the subsidy policy led to a stagnant development.  Some indices had little impact on the final results, such as C 2 , C 13 and C 14 , indicating a low degree of correlation between these indicators. Most of the other indicators have a good linear relationship with the final EGTP results, demonstrating that these indicators had a significant impact on the evaluation results, and the rationality of evaluating these indicators with the EGTP method has thus been verified. The correlation coefficients of the EGTP sequencing results were calculated as shown in Table 8.
We have observed an interesting phenomenon in that the correlation coefficients of some indicators for the ranking results are contrary to the index types shown. In general, the larger the value of a benefit-type index, the more favourable will be the evaluation result, and the ranking result should be smaller. Therefore, a benefit-type index shows a negative correlation with the ranking results, while a cost-type index shows a positive correlation. However, according to the correlation calculation, index C 5 (pure electric car proportion) is different from   combination of the three methods. At the same time, the correlation coefficients of the ranking results of indices C 5 and C 13 are opposite of their intuitive natures. This result was due to the data sample being too small, and some outliers led to biasing of the results; however, this problem can be mitigated by expanding the sample size of the evaluation cities. The limitation of this paper is that there are some deficiencies in the established indicator system. For example, the indicator system lacks resident satisfaction indicators. The citizens' degree of support for AFVs should be collected, and a questionnaire survey should be conducted appropriately. We believe that the satisfaction of the public will also promote the vigorous development of the AFV industry. Future research can further expand the evaluation system, and some indices that are not easy to be inductively calculated should also be taken into account, such as indicators of resident satisfaction, AFVs pulling index to the economy, and indicators for the upstream and downstream services of the AFV industry. The evaluation system should be applied to assess AFV industrial competitiveness in different countries and regions with the continuous advancement of global integration. The evaluation results are used to guide the countries around the world to promote the development of the AFV industry in order to achieve the purpose of saving natural resources. the other efficiency models, showing a positive correlation with the ranking. Index C 13 (average concentration of PM 2.5 ) is also different from other cost indicators, but its impact on the final evaluation value is negatively correlated. This result goes against common sense. This result was due to the data sample being too few (there are only ten sets of indices, and the evaluation matrix is 10×14). Some cities have an outlier bias, such as Changsha, Qingdao, Hefei and other cities ranked lower in terms of the overall industrial competitiveness level, but their pure electric car proportion indices are ranked first. The overall industrial competitiveness levels of Beijing and Tianjin are at the top, but their average concentrations of PM 2.5 are at the bottom, which has a misleading influence on the final result. In the correlation analysis of the indices and results, these outliers lead to deviation of the results, producing irregular phenomena.
This provides a direction for our future improvement, including screening outliers or expanding the sample size to evaluate better and show the actual industrial competitiveness level of each city AFVs. As the sample size increases, the outliers will decrease.

CONCLUSION
This paper proposes an evaluation method for the industrial competitiveness of urban AFVs based on the entropy-GRA, TOPSIS, and PCA methods. The following conclusions were drawn from the study: 1) For this case, the weights of the three evaluation methods (GRA, TOPSIS and PCA) obtained by the entropy weight method were 0.335, 0.29 and 0.375, respectively, among which the reference value of TOPSIS was the lowest; 2) The EGTP evaluation results indicate that the industrial competitiveness levels of AFVs in various cities in China are currently unbalanced and uncoordinated. Beijing, Shanghai, Tianjin and other cities have experienced rapid AFV development due to favourable political and economic conditions. However, the development in Changsha, Qingdao and other cities is relatively slow, especially in Qingdao, where changes to beneficial policies have hindered the production and sale of AFVs; 3) The correlation analysis of the evaluation results shows that GRA, TOPSIS, PCA and EGTP are highly correlated, which confirms the rationality of using EGTP for the weighted linear