EVALUATION OF THE BUSINESS ENVIRONMENT OF PARTICIPATING COUNTRIES OF THE BELT AND ROAD INITIATIVE

As an important indicator for measuring the quality of business environment of different countries, ease of doing business (EDB) issued by the World Bank (WB) provides an important reference for investors in making decisions on transnational investment. The calculation method for EDB issued by the WB is improved using a technique for order preference by similarity to an ideal solution (TOPSIS) method based on Mahalanobis distance. Based on various indicator data in 2019, business environments in 121 countries participating in “the Belt and Road Initiative (BRI)” were empirically analysed and compared through such models. The result showed that TOPSIS method based on Mahalanobis distance can more fully utilise information and take the effect of negative ideal points into account. Therefore, compared with ranking method by the WB, TOPSIS method based on Mahalanobis distance is more applicable for ranking BRI countries. The ranking results indicated significant geographical characteristics. The EDB rankings obtained through the WB overestimate the business environments of countries in Central and Eastern Europe while underestimate those in Southeast Asia, Africa, etc.


Introduction
"The Belt and Road Initiative" (BRI), as a major strategic measure for expanding openingup, was proposed by the Chinese Government in 2013. It aims to facilitate orderly and free flow of economic factors, efficient allocation of resources and deep integration of markets; drive coordination of economic policies of various BRI countries; carry out even boarder and more sophisticated regional cooperation; and foster a regional framework of open and inclusive economic cooperation (Yan et al., 2018). BRI has effectively facilitated China's in-vestment and cooperation with BRI countries (Huang, 2019;Cullinane et al., 2018); however, investment risk will increase due to some problems of business environments of some BRI countries (Li et al., 2019), including unstable political situations, disputes around resource utilisation and development, and frequent changes in regulations and policies (Qu & Yang, 2017). Therefore, conducting comprehensive evaluation on business environments of various BRI countries by utilising scientific methods provides reference for enterprises in making decisions on transnational investment and also promotes BRI countries to improve their business environments to some extent.
In terms of business environment, the World Bank (WB) will issue an annual Doing Business every year. The WB measures the ease of doing business (EDB) based on the whole life cycle of an enterprise, from the initial stage of entrepreneurship to acquisition of a business site, financing, daily operation, and operation in a safe business environment. To measure EDB of each country, the WB measures EDB scores of various indicators every year to calculate the sum based on a simple additive weighting method. In this way, the EDB rankings of 190 countries in the world are determined. Various indicators, based on which the WB calculates EDB ranking, are significantly correlated with one another, and various economies show a great difference in terms of various indicators; however, when calculating EDB ranking, the WB just calculates the gap between each country with the country with the frontier score. Moreover, the WB only performs simple additive weighting for various indicator data but also ignores the dependency of various indicators and the distance of various economies to negative ideal points. Obviously, the method for calculating EDB ranking remains to be modified. How best to evaluate the business environments of BRI countries has attracted attention of many scholars.
As for evaluation objects, existing research mostly only evaluates the business environments of a small number of BRI countries. For example, by investigating the business environment of Nepal, Shrestha (2017) found that although the economic growth potential of Nepal is high, there are a series of problems such as unsound rule of law and imperfect infrastructure. By analysing business environments of the five countries in Central Asia, Yue and Qian (2015) showed that the five countries have a significant difference, however, either at an infrastructural level and in terms of financial environment or in political environment and labour market contexts, Kazakhstan's EDB is optimal; Huang (2019) evaluated the business environments of 64 BRI countries and showed that Singapore, Bhutan, Nepal, Myanmar, Laos, and most countries in Central and Eastern Europe have the best business environment while India's business environment is the worst. Some scholars also explored business environments of a minority of BRI countries (Zhong & Fan, 2016;Xu et al., 2015;Du & Zhang, 2018). These scholars carry outed analysis mostly focusing on 64 countries. Among the 64 countries, Singapore and New Zealand exhibit a relatively favourable business environment; by contrast, business environments of Kyrghyzstan, Tajikistan, etc. are relatively poor.
In terms of evaluation method, scholars mostly apply extended gravity models and an analytic hierarchy process (AHP) or evaluate the business environment directly based on the WB's evaluation indicator system. By utilising an extended gravity model, Kong and Dong (2015) validated the promotion effect of trade facilitation on trade between BRI countries is more significant compared with regional economic organisations, national GDP (gross domestic product) brought about by import and export, tariff reduction and exemption, etc. Cui and Huang (2016) explored the evaluation indicator system for trade and investment facilitation of BRI countries by employing AHP and further measured the trade and investment facilitation levels of various BRI countries. Additionally, in the literature, business environments in different countries were measured mostly according to EDB rankings or EDB scores issued by the WB (Escaleras & Chiang, 2017;Lu & Chen, 2018;Corcoran & Gillanders, 2015). The WB's evaluation system is relatively comprehensive; however, the calculation method for EDB ranking issued by the WB fails to utilise fully raw data to reflect the gap between various countries on the one hand; on the other hand, the method often leads to the occurrence of problems such as information overlapping.
Above all, the existing research exhibits two drawbacks: firstly, scholars evaluate business environments mostly based on EDB rankings issued by the WB, which often causes information overlapping and insufficient information utilisation. Secondly, some 125 countries are participating in the BRI initiative while only a small number of them were systematically evaluated in the existing literature.
Ranking business environments of BRI countries belongs to a multiple attribute decision-making problem: among numerous methods for multiple attribute decision-making, the technique for order preference by similarity to an ideal solution (TOPSIS) method is widely applied to good effect due to its simple principle, intuitive geometrical significance, and imposing no special requirement on sample data (Dwivedi et al., 2018;Sirisawat & Kiatcharoenpol, 2018;Vidal & Sánchez-Pantoja, 2019). Numerous scholars have also improved the traditional TOPSIS method applied the improved method to empirical research. A summary of the literature on improved TOPSIS in recent years is given in Table 1.
By using Mahalanobis distance-based TOPSIS, the method for calculating EDB ranking issued by the WB is modified to solve a series of problems, including high dependency between various indicators and ignoring negative ideal points during calculation. Moreover, the business environments of 121 BRI countries are evaluated and ranked. The innovation in the research is as follows: 1) Based on data concerning all primary indicators in the WB's Doing Business database, the business environments of BRI countries are assessed by using traditional TOPSIS method to calculate the closeness of indicators of various countries. On this basis, all BRI countries are ranked, in expecting to solve the problem of only considering gap of each country to the country with frontier score while ignoring that to the country with the lowest score when calculating EDB scores. 2) By introducing the Mahalanobis distance, the traditional TOPSIS method is improved.
According to raw data pertaining to various indicators, the closeness of indicators of various countries is separately calculated by using Mahalanobis distance-based TOP-SIS. On this basis, all BRI countries are ranked. Mahalanobis distance considers the relationship between various indicators and is dimensionless. Therefore, it can solve the problem of information overlapping, which is not considered in traditional TOP-SIS methods or that used in EDB ranking. 3) All BRI countries are ranked separately according to results of similarity obtained by using the traditional TOPSIS method and Mahalanobis distance-based TOPSIS. Additionally, from the statistical and geographical perspectives, a comparison is made to analyse differences in the ranking results of the two methods with the ranking issued by the WB. Entropy-TOPSIS-F performance evaluation of green suppliers "Management Commitment to GSCM", "Ecodesign" and "Environmental management system" are the first three criteria in the ranking of selection of sustainable suppliers.

Bai and
Sarkis (2018) Grey-based TOPSIS evaluating supplier performance The paper provides support for sustainable supplier selection.

TOPSIS classifiers bankruptcy prediction
Empirical results show an outstanding predictive performance both in-sample and out-of-sample and thus opens a new avenue for research and applications in risk modelling and analysis using TOPSIS as a non-parametric classifier and makes it a real contender in industry applications in banking and investment. The rest of the study is organized as follows: Section 1 introduces evaluation methods, involving traditional TOPSIS method and Mahalanobis distance-based TOPSIS; Section 2 empirically analyses the ranking of business environments of BRI countries and discusses the evaluation result from statistical and geographical perspectives; last Section concludes.

Evaluation methods
The traditional TOPSIS method inevitably shows the drawback of causing information loss (Wang & Wang, 2014;Wang et al., 2018) while Mahalanobis distance can favourably solve the problem of linear correlation between indicators (Ke et al., 2018;Hamill et al., 2016;González-Arteaga et al., 2016) and compensate for deficiencies in the traditional TOPSIS method. In the present study, the traditional TOPSIS method and Mahalanobis distancebased TOPSIS are introduced.

Traditional TOPSIS method
TOPSIS is a method for dealing with uncertain multi-attribute decision-making problem, which is applied to conduct ranking based on the distances of an evaluation object to positive and negative ideal solutions (Pelegrina et al., 2019;Zeng et al., 2020b;Yoon & Kim, 2017). A positive ideal solution consists of optimal values of all indicators while the negative ideal solution comprises the worst values of all indicators (Zeng et al., 2020a;Jiang et al., 2019;Zareie et al., 2018).
It is supposed that there are m countries , for decision making is established, in which x ij denotes the value of jth indicator of the ith country. The specific steps of TOPSIS method for evaluation are summarised as follows (Yoon, 1987;Hwang et al., 1993;Hwang & Yoon, 1981): Normalised decision matrix ( ) ij m n R r × = is constructed, that is, the decision matrix is normalised, where, (1) End of Table 1 Afterwards, positive and negative ideal solutions S + and S − are determined: , , , n S s s s Next, Euclidean distances ( i d + and i d − ) of indicators of various countries to positive and negative ideal solutions are separately calculated: Subsequently, the relative closeness c i of indicators of various countries to positive ideal solution is separately calculated: , 1,2,..., Finally, according to the level of c i , ranking is carried out: the larger c i is, the better the scheme.
Traditional TOPSIS evaluation objectively reflects the gap between various countries by introducing positive and negative ideal solutions; however, when there is a significant linear relationship between indicators, column vector consisting of n different attribute indicators fails to make up a group of bases for measuring the linear space. Therefore, in this case, calculating the distances of indicators of various countries to positive and negative ideal solutions according to Euclidean distance will lead to erroneous final rankings for various countries.

Mahalanobis distance-based TOPSIS
To tackle the problem of information overlapping caused by dependency between variables, Mahalanobis distance is introduced to improve the traditional TOPSIS method (Antuchevičienė et al., 2010;Chang et al., 2010). As a statistical distance, Mahalanobis distance is independent of measurement scale and is unaffected by dimension of coordinates. Moreover, it can eliminate interference caused by dependency between variables (that is, removing the influence induced by linear correlation between attribute indicators).
It is assumed that there are m countries , The decision matrix ( ) , 1,2,..., ; 1,2,..., ij m n X x i m j n × = = = for decision making is established, in which x ij denotes the value of jth indicator of the ith country. x i refers to the spatial coordinates of the corresponding attribute value of the ith country. The specific steps of the Mahalanobis distance-based TOPSIS for evaluation are described below. where, , 1,2,..., Finally, ranking is conducted according to the level of c i . The larger c i , the better the scheme.
When evaluation indicators are significantly correlated, Mahalanobis distance is unaffected by dimension of indicators and also eliminates the information overlapping caused by linear correlation of indicators. Therefore, Mahalanobis distance is more applicable for dealing with complex practical problems. Additionally, in practical application, the overall covariance matrix is generally unknown so can be replaced with a sample covariance matrix.

Empirical analysis of the business environments of BRI countries
Based on indicator data for business environments of various countries issued by the WB, 121 BRI countries are ranked by separately using a traditional TOPSIS method and Mahalanobis distance-based TOPSIS. Moreover, the list of 121 BRI countries was copied from the Belt and Road Portal (n.d.). The EDB rankings and indicator data for business environments of various BRI countries are all taken from Doing Business 2019: Training for Reform (The World Bank, 2018). The organisation of empirical analysis is described below.
At first, the indicator system for empirical analysis is explained and indicator data are subjected to descriptive statistical analysis. The mode and median of indicator data are separately calculated and Pearson correlation analysis is undertaken.
Afterwards, based on various indicator data, the WB's rankings are collected and recorded. By separately utilising the traditional TOPSIS method and Mahalanobis distance-based TOPSIS introduced in the last section, the EDB of various BRI countries is ranked.
Finally, statistical analysis is carried out on empirical results. The BRI countries are divided into nine regions including Northeast Asia and Southeast Asia according to their geographical locations. The results obtained through empirical analysis and statistical analysis are mapped.

Indicator system
The WB's Doing Business database has a set of mature and stable indicator system, which is used for measuring and evaluating EDB of various countries. Since 2003, the WB has issued Doing Business report every year. The report measures the supervision and regulations of each country (region) for their medium and small-sized enterprises based on ten indicator sets. The measurement indicators cover ten fields of life cycle of an enterprise, which can be partitioned into two aspects. The two aspects are respectively used to measure the effectiveness of government supervision on enterprises and completeness of the legal system of various countries. The former is applied to measure supervisory process and efficiency involved in starting a business, applying for construction permits, getting electricity, registering property, paying taxes and trading across borders; the latter is employed to evaluate the soundness of law and regulation framework in various aspects, including getting credit, protecting minority investors, enforcing contracts and resolving insolvency. These indicators are used to evaluate procedure, time and cost for completing a deal according to related regulations from the perspectives of enterprises, which are sound and perfect. Economic literature is used to validate the economic relevance and importance of the fields in which business environment is measured. By taking starting a business as an example, since 2003, 100 top-level academic journals have published more than 300 research papers describing how to evaluate how the regulation environment for market access influences extensive economic results such as production efficiency, growth, employment and informality (The World Bank, 2018). By taking the indicator system as reference standard, analysis is conducted (Table 2). Procedures, time, cost and minimum contributed capital required when a male or a female starts a limited liability company. Applying for construction permits (X 2 ) All procedures, time, cost of building warehouse and quality control and safety mechanism in construction permit system.

Getting electricity (X 3 )
Procedures, time and cost of connecting to the power grid, reliability of power supply, and transparency of electric charge. Registering property (X 4 ) Procedures, time and cost of dealing with land transfer and quality of land administration by a male or a female. Getting credit (X 5 ) law of chattel mortgage and credit information system. Protecting minority investors (X 6 ) Minority shareholders' rights in related transaction and corporate governance.
Paying taxes (X 7 ) The number and time of tax payments, total tax, total amount of levies, and post-filing process during the operation of a company complying with all tax laws and regulations. Trading across borders (X 8 ) Time and cost of exporting relatively superior products and importing auto parts. Enforcing contracts (X 9 ) Time and cost of solving commercial dispute and quality when a male or a female performs judicial process. Resolving insolvency (X 10 ) Time, cost, result and recovery rate of insolvency and intensity of insolvency legal framework.

Descriptive statistical analysis
Various characteristics (including high dependency) of various indicator data are likely to affect empirical result. To understand the characteristics (such as discrete degree, distribution condition and dependency) of various indicator data, all indicator data are subjected to descriptive statistical analysis before further empirical analysis. The specific descriptive statistical results are shown in Table 3: the maxima and minima of all indicators are all within reasonable ranges and the mean of various indicators is much greater than their standard deviation. This indicates that the discreteness of the data is low and the probability of having extreme outliers is low. The mean, median, and mode of starting a business (X 1 ) are relatively approximated to those of enforcing contracts (X 9 ), implying that the data of the two indicators are approximately symmetrically distributed. According to value of skewness, it can be seen that the 10 indicator data values all exhibit a right-skewed distribution.

Empirical results
The empirical results are organised as follows: at first, by looking up rankings of business environments of 190 countries across the world issued by the WB, rankings of business environments of 121 BRI countries are attained; then, using a traditional TOPSIS method, the rankings of business environments of BRI countries are calculated; Finally, the business environments of BRI countries are ranked by applying Mahalanobis distance-based TOPSIS.

Ranking method 1: collecting ranking results issued by the WB
Doing Business issued by the WB synthesised 10 indicators to list two criteria for measuring business environments of various countries (regions): EDB score and EDB ranking. The latter is sorted according to the level of the former: the country (region) with a higher EDB score ranks higher and vice versa. The EDB score is calculated by using simple additive weighting after assigning each indicator the same weight.
By looking up Doing Business 2019: Training for Reform issued by the WB, the EDB scores of 121 BRI countries are collected. According to scores, the BRI countries are ranked and the result is shown in Table 5.

Ranking method 2: traditional TOPSIS method
Based on the design of traditional TOPSIS method for business environments of BRI countries and construction and selection of the aforementioned evaluation indicators, the business environments of 121 BRI countries are ranked. The specific calculation steps are described below.
At first, by using all indicator data of 121 BRI countries, a 121×10 decision matrix for decision making is established. Where, x ij refers to the value of the jth indicator of the ith BRI country. The decision matrix for decision making is normalised based on (1).
Afterwards, the maximum of each column in the normalised decision matrix for decision making is collected to construct the positive ideal solutions S + of various indicators. Similarly, the minimum of each column is used to establish the negative ideal solutions Sof various indicators. The results are described below. Finally, according to Equation (6), the relative closeness c i of indicators of BRI countries to positive ideal solution is separately calculated using i d + and i d − . Where, the larger the closeness c i , the closer the indicators of a country to the positive ideal solution and the higher the EDB ranking of the country. The specific ranking result is displayed in Table 5.

Ranking method 3: Mahalanobis distance-based TOPSIS
According to the indicator system aforementioned and indicator data of the WB's Doing Business database, the business environments of BRI countries are evaluated by employing Mahalanobis distance-based TOPSIS. The specific steps for evaluation are as follows: At first, using all indicator data of 121 BRI countries, a 121×10 decision matrix is established in which, x ij denotes the value of the jth indicator of the ith BRI country.
Afterwards, the maximum of each column in the decision matrix is calculated to build the positive ideal solutions S + of various indicators. Here: Subsequently, the covariance matrix S of the decision matrix is calculated to attain its inverse matrix 1 − S through inverse calculation. Based on Eqs (7) and (8) Table 5.

Statistical analysis
It can be seen from Table 5 that the EDB rankings obtained according to EDB scores issued by the WB are different from those attained by using the traditional TOPSIS method and Mahalanobis distance-based TOPSIS. The better to judge the differentiation of the ranking results obtained through the three methods, the ranking results attained according to WB, traditional TOPSIS method, and Mahalanobis distance-based TOPSIS are shown in Figure 1 where the left and right-hand figures show scatter diagrams for the comparisons of the ranking results obtained through the traditional TOPSIS method and Mahalanobis distance-based TOPSIS with the ranking result issued by the WB, respectively. Furthermore, the Pearson correlation coefficients between the traditional TOPSIS method ranking and Mahalanobis distance-based TOPSIS and the WB's EDB ranking are 0.993 and 0.908, both of them are statistically significant at the 1% level. The WB attained the EDB scores of various countries based on simple additive weighting method by synthesising data pertaining to the aforementioned 10 indicators. The method used by the WB for calculating the EDB scores of various countries ignores the problem of information overlap between various indicators, which can cause certain common information to be overestimated in the evaluation. Additionally, the effect of negative ideal points is ignored, so the ranking result obtained according to the EDB scores will differ from those attained by using the other two methods to some extent. Moreover, the presence of correlation between indicators also results in a significant difference between ranking results acquired through traditional TOPSIS method and Mahalanobis distance-based TOPSIS. Due to having eliminated overlapping information, the Mahalanobis distance-based TOPSIS generally attains a higher level of relative closeness compared with the traditional methods.
As shown in Figure 2, the left-hand figure shows the scatter diagram of the EDB scores and ranking result issued by the WB; the right-hand figure presents the scatter diagram of closeness obtained through use of the traditional TOPSIS method and WB ranking result; furthermore, the Pearson correlation coefficients between EDB score and traditional closeness and WB's EDB ranking are -0.979 and -0.986, both of them are statistically significant at the 1% level.
It can be seen from the figure that a country with a lower ranking generally shows a lower EDB score and the relative closeness obtained through the traditional TOPSIS method. Moreover, the discreteness seen in the right-hand figure is higher than that in the left-hand figure. The reason for this is that the traditional TOPSIS method not only considers the distances of indicators of various countries to positive ideal solutions, but also takes into account those to the negative ideal solutions. Furthermore, Figure 3 shows the scatter diagrams of the distances of indicators of various countries to the positive and negative ideal solutions obtained according to the traditional TOPSIS method with the ranking result issued by the WB, respectively. The Pearson correlation coefficients between the positive distance and the negative distance of the traditional TOPSIS method and WB's EDB ranking are 0.318 and -0.344, both of them are statistically significant at the 1% level. The indicator of a country with a higher ranking issued by the WB is closer to the positive ideal point while further from the negative ideal point: however, the data in Figure 3 still show a certain discreteness. The reason for this is that the ranking provided by the WB only takes the positive ideal solution into account while apart from this, the TOPSIS method also considers the distances of an indicator of various countries to the lowest value of the indicator during ranking. In this way, a better evaluation and ranking result with comparability is attained. The TOPSIS method more sufficiently utilises the raw data and this better reflects the gaps among various countries.
In Figure 4, the left and right-hand figures show the scatter diagrams of the closeness obtained through the traditional TOPSIS method and Mahalanobis distance-based TOPSIS with the ranking result issued by the WB, respectively. The Pearson correlation coefficients between the closeness obtained through the traditional TOPSIS method and Mahalanobis distance-based TOPSIS with the ranking result issued by the WB are -0.986 and -0.897, both of them are statistically significant at the 1% level.
The discreteness of the data seen in the right-hand figure is much greater than that in the left-hand figure, which is because the correlation between indicators is taken into account in the right-hand figure. As shown in Table 3, the information overlap between various indicators is significant and correlation between indicators cannot be ignored, therefore, Mahalanobis distance-based TOPSIS can better evaluate the levels of EDB of different countries, the ranking result obtained through the Mahalanobis distance-based TOPSIS is taken as the actual ranking of BRI countries in the present research.
The better to compare differences between the ranking result issued by the WB and the actual ranking result, the ranking result issued by the WB and the actual ranking result are shown on the same scatter diagram ( Figure 5). The green scattered points refer to the ranking result issued by the WB while the blue points represent the actual ranking result. The business environments of countries corresponding to the blue scattered points below and above the green scattered point are underestimated and overestimated, respectively. The Pearson correlation coefficient between the EDB ranking results of Mahalanobis distance-based TOPSIS and the WB's EDB ranking is 0.908, which is statistically significant at the 1% level. As seen from Figure 5, the results of EDB ranking of most countries issued by the WB differ slightly from the actual results.
According to Table 5 and Figure 5, except for Georgia, Syria, Venezuela, and Somalia, the ranking results of business environments of the other countries are all likely to be either overestimated or underestimated. The rankings of New Zealand and South Korea are overestimated while those of Singapore, Macedonia, etc. are underestimated. There are 53 and 64 countries whose rankings are overestimated and underestimated, respectively: the number of countries whose ranking is underestimated is far larger than that whose ranking is overestimated. The specific conditions are summarised in Table 6 where the gap is obtained by subtracting the actual ranking from the WB's EDB ranking. End of Table 6 The traditional TOPSIS method or the equal weighted average method adopted by the World Bank repeatedly calculates the common information of the evaluation indicators, which means that the larger the value of the most relevant indicator, the larger the overestimated value of the evaluation result, resulting in a larger ranking gap.
If the absolute value of an overvalued gap in a country exceeds 30, it means that the country's business environment is seriously overvalued by the World Bank. According to Table 6, the business environments of the Czechia, India, Panama, Bosnia, Palestine, Cambodia, and another six countries are greatly overestimated. Table 4 shows that there is a significant correlation between the indicators. To explore why the business environments of these countries are so overestimated from the perspective of indicators, the average of 10 indicators for the countries that are greatly overrated and moderately estimated is calculated. From Table 7, the average of the indicators of moderately estimated countries is significantly smaller than the average of the countries of severely overrated countries.

Geographic analysis
In this study, 121 BRI countries are mapped (Figure 6): if a country is labelled in green, the country is a BRI member. If a country is marked in grey, it does not participate in BRI. It can be found from Figure 6 that BRI countries are mostly located in Asia, Africa, and Central and Eastern Europe and their distribution exhibits a significant regional characteristic. The areas of the BRI countries can be divided into nine regions including North East Asia, South East Asia, South Asia, West Asia, Africa, Central and Eastern Europe, Central Asia, South America and New Zealand. In this section, the ranking result of BRI countries based on EDB scores issued by the WB (hereinafter called the ranking result issued by the WB) is mapped: thereafter, the ranking result of BRI countries acquired by applying Mahalanobis distance-based TOPSIS is described in the map and analysed. Finally, the countries whose rankings are overestimated or underestimated in statistical analyses are presented.

(1) Geographic analysis of the ranking result issued by the WB
The ranking result issued by the WB obtained above is mapped (Figure 7). The country whose colour is closest to blue has a higher ranking while that closer to red has a lower ranking; grey denotes non-BRI countries. Figure 7 shows that among the BRI countries, New Zealand exhibits the optimal EDB; the EDB of countries in North East Asia, South East Asia, and Central Asia is generally favourable and there is an insignificant difference among various countries within these regions; the EDB of countries in South Asia is at a common level while that in West Asia is significantly different. Countries in Africa generally show a poor EDB and the EDB of countries in the south of Africa is superior to that in the north. There is a favourable EDB for countries in Central and Eastern Europe; the EDB of countries in the south of South America is better than that in the north; the country with the worst EDB is situated in the north of Africa; the EDB of China is dominant among all BRI countries; the countries bordering China exhibit different levels of EDB. On the whole, the EDB of neighbouring countries to the north of China is better than that of those to the south of China.

(2) Geographic analysis of actual ranking result
The actual ranking result attained above is mapped (Figure 8). The country whose colour is closest to blue has a higher ranking while that closer to red has a lower ranking; grey denotes non-BRI countries. As shown in Figure 8, among BRI countries, countries in North East Asia, South East Asia, Central Asia, and Central and Eastern Europe have a favourable EDB and insignificant differences exist within these regions. The business environments of countries in South Asia are unfavourable on the whole and their EDB values are significantly different; New Zealand exhibits a favourable EDB; countries in West Asia and Africa generally have a poor EDB, especially countries in North Africa, with insignificant internal differences therein; the EDB of countries in South America shows a great difference, and there are, separately, both high and low levels of EDB in the south and middle of the region. The country with the optimal business environment is located in South East Asia while that with the worst business environment is situated in Africa. The EDB of countries bordering China differs remarkably: the EDB of neighbouring countries to the South West of China is poor while that to the south of China is favourable. The EDB of China is dominant among BRI countries.
(3) Geographic analysis of countries whose EDB ranking is overestimated or underestimated According to Tables 5 and 6, a list is obtained, in which there are 53 and 64 countries with separately overestimated and underestimated EDB and four countries whose EDB values are moderately well estimated. According to the list, all countries are marked in a map to further conduct geographic analysis. The specific distribution of geographical locations of different countries is displayed in Figure 9 where, yellow, blue, and red denote countries whose EDB is underestimated, overestimated and moderately estimated, respectively, and grey represents non-BRI countries. As shown in Figure 9, there is significant regional distribution characteristics between the countries whose ranking is overestimated and underestimated: the EDB of countries in North East Asia and Central Asia is generally underestimated while that in South East Asia is commonly overestimated. In South Asia, the proportion of countries whose EDB is underestimated is larger than that of countries whose EDB is overestimated. In West Asia, the proportion of countries whose EDB is overestimated is equivalent to that of countries whose EDB is underestimated. The EDB of New Zealand is overestimated; in Central and Eastern Europe, the proportion of countries whose EDB is overestimated is greater than that whose EDB is underestimated; in Africa, far more countries have underestimated EDB than overestimated EDB. The EDB of countries in the west of Africa is generally underestimated while those in the south east of Africa are commonly overestimated; in South America, the proportion of countries whose EDB is overestimated is equivalent to that with underestimated EDB, in which the EDB of countries in the south is underestimated. According to Table 6, 50% of the countries that are greatly overvalued are in Asia, 33.33% in Europe, and 16.67% in North America: this shows that the countries with more repeated indicators have the characteristics of geographical distribution, which directly results in the countries with severe overestimation having regional characteristics.

Conclusions and future work
The ranking issued by the WB was collected and using the traditional TOPSIS method and Mahalanobis distance-based TOPSIS, the EDB of 121 BRI countries is ranked. Furthermore, the ranking results are analysed from statistical and geographic perspectives, thus drawing the following conclusions: (1) The ranking results of business environments of various countries obtained by the WB, traditional TOPSIS method, and Mahalanobis distance-based TOPSIS are compared. On this basis, when considering negative ideal points, the traditional TOPSIS method exhibits a ranking result superior to that issued by the WB. Mahalanobis distance-based TOPSIS not only takes negative ideal points into account but also considers the correlation between various indicators, thus yielding a better ranking result than that attained by using the traditional TOPSIS method. That is, among the three ranking results, the ranking result attained by employing Mahalanobis distancebased TOPSIS is closest to the actual situation. Accurate assessment of the business environment is conducive to better investment decisions and more effective government policies. Therefore, the WB is advised to modify their existing method for calculating EDB rankings and EDB scores.
(2) The ranking issued by the WB and actual ranking both exhibit significant regional characteristics. Among BRI countries, New Zealand and countries in North East Asia, Central Asia, South East Asia, and Central and Eastern Europe have a relatively favourable business environment; the business environments of countries in West Asia and Africa are generally unfavourable, having huge potential for improvement. By comparing the ranking result issued by the WB with the actual ranking result, it can be found that countries whose ranking is overestimated and underestimated also exhibit remarkable regional characteristics, that is, the business environments of countries in Central and Eastern Europe, New Zealand, etc. are generally overestimated while those in North East Asia, Central Asia, South East Asia, and the south of Africa are underestimated. If the EDB project had been undertaken using the Mahalonobis-TOPSIS method at an earlier juncture, it will enable companies to make better investment decisions and reduce the investment losses caused by erroneous assessment of the prevailing business environment. On the other hand, it will prompt government to formulate policies related to the business environment that are more suitable for the country.
(3) Evaluating EDB as an MCDM problem should maintain the convention of solving MCDM problems, which consists of measurement, weighting, and evaluation: this may be extended to forecasting and risk analysis, so future work should include building reasonable and reliable models to improve evaluation of EDB weighting, forecasting, and risk analysis. On the other hand, future work should introduce possible uncertainties such as the China-US trade dispute into the model.