The assessment of traffic accident risk based on grey relational analysis and fuzzy comprehensive evaluation method

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1 Nat Hazards (2017) 88: DOI /s ORIGINAL PAPER The assessment of traffic accident risk based on grey relational analysis and fuzzy comprehensive evaluation method Yaolong Liu 1 Xiaoli Huang 1 Jin Duan 2 Huaming Zhang 3 Received: 15 October 2016 / Accepted: 11 May 2017 / Published online: 19 May 2017 Ó Springer Science+Business Media Dordrecht 2017 Abstract The traffic accident risk includes three aspects, traffic accident probability, traffic accident severity, and traffic accident trend respectively. In this paper, nine indicators are selected to evaluate the traffic accident risk. The grey relational analysis method was used to determine the weights, and the fuzzy comprehensive evaluation method was used to calculate the risk. These methods were applied to assess the comprehensive risk of traffic accident in 31 provinces in China. The results show that the average value of traffic accident risk is Nine provinces which are located in the northwest area and southeast area belong to the high-risk level. The medium-risk areas are widely distributed in the central, northeast, and southwest regions. The low-risk areas are Jilin, Neimenggu, Guizhou, and Being. The results have great significance for the measurement and management of regional traffic accident risk. Keywords Grey relational degree Fuzzy comprehensive evaluation Traffic accident risk Safety 1 Introduction Road traffic safety is a health and safety issue that global public concerned. According to statistics of WHO, there are about 1 million 200 thousand people died, and 20 million to 50 million people suffered non-fatal injuries from road traffic accidents every year (WHO 2009). With the rapid development of economy, the road traffic safety situation in China is & Yaolong Liu liuyaolong@tyut.edu.cn College of Economics and Management, Taiyuan University of Technology, Jinzhong , China Institute of Politics and Law, Taiyuan University of Technology, Jinzhong , China Meteorological Disaster Prevention Technology Center of Shanxi Province, Taiyuan , China

2 1410 Nat Hazards (2017) 88: also becoming more and more serious. Specifically, the number of road traffic accidents increased from 55,400 (1970) to 198,400 (2013), with an average annual growth of over 3%. The number of deaths rose from 9,654 to 58,539, with an average annual growth of 4.38%. In 2012, the death rate per million cars is 2.5. It is 5 times that of the UK, 2 times of the USA. Meanwhile,traffic accident death rate is up to 29.38%. Therefore, it is very urgent and important to assess the risk of road traffic accidents in China. Road traffic system is a complex system which contains the comprehensive factors such as human, vehicle, road and natural environment. At present, scholars pay more attention to traffic safety evaluation (Shahdah 2014; Mohan et al. 2016) and accident risk assessment (Don et al. 2015; Fitzgerald and Landfeldt 2015; Tortum and Atalay 2015; Costescu et al. 2016). The former analyzes the safety characteristics from the historical data. The latter focuses on the dynamic change of the accident risk and the general law of the vulnerability of bearing receptor. In addition, it is also discussed the relationship between driver s behavior (such as sleep quality, driving habits, etc.) and traffic accidents (Ebrahimi et al. 2015; Niezgoda et al. 2015; Machado-León et al. 2016). Other scholars concern the influence factors of road traffic safety (Wang 2011; Men et al. 2012; Ren and Peng 2013; Chen 2014), the type of traffic accident risk (Zhao and Tan 2013; Zhao 2014) and evaluation of road system safety. Artificial neural network method (Huang 2009), factor analysis method (Liu and Lu 2009), principal component analysis (Fan and Cao 2010), matter element analysis (Zhu et al. 2010), data envelopment analysis (Zhou and Li 2012), fuzzy comprehensive evaluation method (Wang 2012), and grey prediction theory (Du et al. 2016) are involved in these studies. At present, there are three key steps in the research of road traffic accident risk: the selection of evaluation indicator, the determination of indicator weight and the selection of evaluation method. Reference to previous research, nine indicators that reflect the incidence of traffic accidents, traffic accidents and the trend of traffic accidents are put forward in this paper. The grey incidence analysis method was used to determine the indicator weight. The fuzzy comprehensive evaluation method was used to calculate the risk value. These methods were applied to assess the comprehensive risk of road traffic safety in 31 provinces in China in This study evaluated the characteristics and spatial distribution of traffic accident risk in various provinces. The results can be used for traffic accident risk identification, quantification, partition and control. 2 Indicators selection and methods 2.1 Indicators selection Guo et al. (2006) stated that index selection should adhere to three essential elements: measurability, representative and comparability. Based on this principle, nine indicators were selected: ten thousand vehicles accident rate, one hundred thousand population accident rate, 100 million yuan gross domestic product accident rate, ten thousand kilometers accident rate, traffic accident death rate, equivalent death toll, standard highway rate, rate of decline in traffic accidents, rate of decline in death toll of traffic accidents (Table 1). At the same time, these indicators can also measure the two elements of risk (severity and possibility). Indicators of traffic severity reflect the severity of the risk. The indicators of traffic accidents trend reflect the possibility of the risk. And the indicators of

3 Nat Hazards (2017) 88: Table 1 Evaluation indicators of traffic accident risk Aspects Id Indicators Computing method Traffic accidents frequency Traffic accidents severity Traffic accidents trend I1 I2 I3 I4 Ten thousand vehicles accident rate One hundred thousand population accident rate 100 million yuan gross domestic product accident rate Ten thousand kilometers accident rate Accidents (numbers)/motor vehicles ownship (ten thousand) Accidents (numbers)/permanent resident population (one hundred thousand) Accidents (numbers)/gdp (100 million yuan) Accidents (numbers)/highway mileage (ten thousand kilometers) I5 Traffic accident death rate Deaths toll(numbers)/accidents (numbers) I6 Equivalent death toll Death toll (numbers)? number of injuries (numbers) ? direct property loss (ten thousand yuan) I7 Standard highway rate Standard highway mileage (km)/highway mileage (km) I8 I9 Rate of decline in traffic accidents Rate of decline in death toll of traffic accidents Reduction in traffic accident (numbers)/traffic accidents in the last year Reduction in death toll of traffic accidents/death toll in traffic accidents in the last year traffic accidents reflect both. The method for calculating weights of each indicator is shown in part. Among them, there are four indicators: ten thousand vehicles accident rate (I1), one hundred thousand population accident rate (I2), 100 million yuan gross domestic product accident rate (I3), ten thousand kilometers accident rate (I4) represent the frequency of traffic accidents. Traffic accident death rate (I5) and equivalent death toll (I6) represent the severity of the traffic accidents. Standard highway rate (I7), rate of decline in traffic accidents (I8), and rate of decline in death toll of traffic accidents (I9) represent the trend of traffic accidents. 2.2 Data collection Raw data which are used to calculate the first four indicators contain the main impact of road traffic accidents (Ren and Peng 2013): motor vehicle ownership, population, GDP, and highway mileage. The number of accidents, the number of deaths in accidents, the number of injuries in accidents, direct property losses (yuan), and the level of road mileage are used to calculate the traffic accident death rate, equivalent death toll, and standard highway rate. The calculation method of equivalent death toll refers to the literature (Cao 2013). Population and GDP data of 31 provinces was obtained in the People s Republic of China National Bureau of Statistics ( Motor vehicle ownership, highway mileage, number of accidents, number of deaths in accidents, the number of injuries in accidents, direct property loss, rate of traffic accidents decrease, and rate of death toll from traffic accidents decline in 2013 were derived from Statistical annual

4 1412 Nat Hazards (2017) 88: report of road traffic accidents in the people s Republic of China (2013) (Traffic management bureau of the public security ministry 2014). 2.3 Methods Grey relational analysis The grey relational analysis refers to the quantitative description and comparison of the developing tendency of a system. This method can usually be used to analyze the influence of each factor on the results. In this paper, grey relational analysis was used to calculate the weights. The calculation procedure is as follows: Step 1 Determining the reference sequence and comparative sequence. Nine indicators values of 31 provinces were selected as the comparison sequence: X i ¼fx j i ¼ 1; 2;...; n; j ¼ 1; 2;...; m ð1þ In the formula, X i stand for comparative sequence, x is the value of j indicator in sample i; m is the number of indicators, n is the number of sample. Optimal values of each indicator in 31 provinces were selected as the reference sequence X 0 : X 0 ¼fx oj j j ¼ 1; 2;...; mg ð2þ In the formula, x 0j is optimal value (the optimal value is its maximum if the indicator is positive) of the first j indicator in the sample. Step 2 Raw processing. The first six indicators selected in this paper are the contrary indicators, so handling the indicators positively was necessary. Furthermore, it was necessary to standardize the original data because of the different parameters of the original data dimension. There are some data normalization methods: the initial value method, the mean method, the standard method, and the range method. The use of standard method is more realistic (Zhou et al. 2005). x 0 ¼ max 1 i n fx g x ð3þ x 0 0j ¼½x 0j x j Š=s j ð4þ x 00 ¼½x0 x jš=s j ð5þ In the formula, x 0 is the result of the positive indicator; x 0 0j and x 00 0j are the results of the standardization of the original data; x j and s j are the mean and the standard deviation of the indicator j, respectively. Step 3 The calculation of correlation coefficient. The formula for calculating the correlation coefficient of dimensionless data is as follows: n ¼ D min þ gd max D þ gd max In the formula, n is the correlation coefficient, D min ¼ min i min j ð6þ D, D max ¼ max max i j D, D = x 00 - x 0 0j ; g is the resolution ratio, g 2½0; 1Š, g generally is 0.5. Grey incidence degree judgment matrix can be obtained from the formula (6):

5 Nat Hazards (2017) 88: n 11 n 12 n 1m n 21 n 22 n 2m F ¼ B A n n1 n n2 n nm In the formula, F is grey incidence degree judgment matrix. ð7þ Step 4 Weights calculation. n is the grey correlation degree of the sample i to the indicator j. It takes the X 0j as the mother factor, and the X is the sub-factor. It represents the degree of correlation between the factor j value and the ideal value of each sample, so its average value represents the proportion of the indicator j in the whole indicator space: c j ¼ 1 n X n n i¼1 In the formula, c j is the proportion of the indicator j in the whole indicator space. The weight of each indicator can be obtained by normalizing the weight of each indicator: ð8þ k j ¼ c j, X m In the formula, k j is the weight of indicator j. c j j¼1 ð9þ Fuzzy comprehensive evaluation The fuzzy comprehensive evaluation method is widely used in fuzzy mathematics. It is an effective means to address some problems with uncertain and fuzzy boundary. The idea of the method is that the contributions of multiple related actors are comprehensively considered according to weight factors, and the fuzziness is decreased using membership functions. The basic procedure of the fuzzy comprehensive evaluation method is that: establishing the evaluation factor (viz. index) set and grading level set of the evaluated object first; and then the fuzzy evaluation matrix being calculated after determining weight factor and membership vector of each evaluation factor; finally, the object class being achieved based on the fuzzy arithmetic on the fuzzy evaluation matrix and weight vector of factors. The steps of risk assessment for the traffic accidents are as follows: Step 1 Determining the set of evaluation factors and the discourse domain. In this paper, nine indicators were selected to form a set of fuzzy comprehensive evaluation factors. It is X ¼ f x 1 ; x 2 ;...; x 9 g. The evaluation set is the evaluation results of the factors. The road traffic accident risk is divided into four levels according to the current situation of road traffic accidents. And the comment set is V = {highest, high, average, small}. Step 2 Determining the fuzzy relation matrix and the degree of membership. Because the different dimension of each indicator, it is necessary to standardize the evaluation indicators. In this paper, the range method was used to deal with it, and the formula is as follows:

6 1414 Nat Hazards (2017) 88: x min x x i n ¼ max x min x 1 i n 1 i n In the formula, x 000 is the result of the standardization of the original data, x is the value of j indicator in sample i. The fuzzy evaluation matrix is composed of the membership degree of the each indicator. The membership degree of each indicator is the fuzzy relation from the indicator set to the evaluation set, which is the possibility of indicator X j is comment V t. Generally, the fuzzy evaluation matrix from the set of indicator to the evaluation matrix is: 0 1 r ði1þ1 r ði1þ2 r ði1þl r ði2þ1 r ði2þ2 r ði2þl R i ¼ B C A r ðimþ1 r ðimþ2 r ðimþl In the formula, R i is the fuzzy evaluation matrix of simple i, r ()t (i = 1, 2,, n; j = 1, 2,, m; t = 1, 2,, l) is the membership that indicator j of simple i belong to the comment V t, n is the number of sample, m is the number of indicators, l is the number of levels in comment set. The membership of indicator (r ()t ) can be obtained by membership function. Road traffic accident risk level is divided into highest, high, average, and small. The membership function of each grade is as follows: 8 1; x 000 \a 1 >< a 2 x 000 r ðþ1 ¼ ; a 1 x 000 a 2 a a 2 ð12þ 1 >: 0; x 000 [ a 2 8 0; x 000 \a 1 x 000 a 1 >< ; a 1 x 000 a r ðþ2 ¼ 2 a a 2 1 a 3 x 000 ; a 2 x 000 a 3 a a 3 2 >: 0; a 3 \x ; x 000 \a 2 x 000 a 2 >< ; a 2 x 000 a r ðþ3 ¼ 3 a a 3 2 a 4 x 000 ; a 3 x 000 a 4 a a 4 3 >: 0; a 4 \x 000 ð10þ ð13þ ð14þ

7 Nat Hazards (2017) 88: >< r ðþ4 ¼ >: 0; x 000 \a 3 x 000 a 3 a 4 a 3 ; a 3 x 000 a 4 1; a 4 \x 000 In the formula, x 000 is the result of the standardization of the original data; a 1, a 2, a 3, and a 4 is the threshold value of each evaluation level, respectively. In this paper, the cumulative percentile method was used to determine the threshold. This method works as follow: sorting j indicator in 31 provinces according to ascending order (x 000 (1)j B x 000 (2)j B B x 000 (31)j); finding k (positive integer) that satisfies the condition: k n ð15þ \p kþ1 n ; calculating the quantile of order p: b p = (np - k)(x 000 (k?1)j - x 000 (k)j)? x 000 (k)j (n is the number of sample), a 1 = b 20%, a 2 = b 40%, a 3 = b 60%, a 4 = b 80%. The comprehensive membership value is the overall membership of the 9 indicators for each level, which is used to approximately evaluate the level of individual or thing that is affected by many factors in the research area. The calculation of the comprehensive membership value is as follows B i ¼ k R i ¼ðb i1 ; b i2 ; ; b il Þ ð16þ In the formula, B i is the Comprehensive membership matrix of simple i; k(k = (k 1,- k 2,, k m ))is the matrix of all indicator weight values; R i is fuzzy evaluation matrix of simple i; b il is the comprehensive membership degree of the sample i belong to the comment v t. Step 3 Comprehensive evaluation. Assigning values to each level of the comment set V = {highest, high, average, small}. And the coefficients are from Wang et al. (2013). The comprehensive risk of the urban traffic accident can be obtained as follows: h i ¼ b i1 90 þ b i2 70 þ b i3 50 þ b i4 20 ð17þ h i is the risk value of fuzzy comprehensive evaluation; b i1, b i2, b i3, and b i4 represent the comprehensive membership degree of the sample belong to the comment: highest, high, average and small. 3 Results 3.1 Weights of indicators The weights of 9 indicators were calculated by formula (1) (9). The results are shown in Table Evaluation results The cumulative percentile method is used to determine the threshold values of each level of different indicators. The results are shown in Table 3. The comprehensive membership value (B) and risk value of 31 provinces in China are shown in Table 4. The risk value can be divided into five levels referring to Likert scale. When h \ 20, the risk level is very low;

8 1416 Nat Hazards (2017) 88: Table 2 Weights of road traffic accident evaluation index Id Evaluating indicator Weights I4 Ten thousand kilometers accident rate I3 100 million yuan gross domestic product accident rate I6 Equivalent death toll I7 Standard highway rate I1 Ten thousand vehicles accident rate I8 Rate of decline in traffic accidents I5 Traffic accident death rate I2 One hundred thousand population accident rate I9 Rate of decline in death toll of traffic accidents Table 3 Threshold for each level of nine indicators Id Indicators Highest High Average Low Quantile of Quantile of Quantile of Quantile of order 20% order 40% order 60% order 80% I1 Ten thousand vehicles accident rate I2 One hundred thousand population accident rate I3 100 million yuan gross domestic product accident rate I4 Ten thousand kilometers accident rate I5 Traffic accident death rate I6 Equivalent death toll I7 Standard highway rate I8 Rate of decline in traffic accidents I9 Rate of decline in death toll of traffic accidents when 20 B h \ 40, the risk level is low; when 40 B h \ 60, the risk level is medium; when 60 B h \ 80, the risk level is high; when 80 B h, the risk level is very high. The comprehensive risk value of road traffic safety in 31 provinces of China is between and (Table 4), the mean value is Specifically, the value of traffic accident risk is in the Xinjiang. Guangdong follows, and the risk value is The value of road traffic safety comprehensive risk is between 60 and 70 in Anhui, Chongqing, Zhejiang, Qinghai, Gansu, Shanxi, Xizang Autonomous Region, Fujian, Hainan, Jiangsu, Tianjin, and Ningxia. All of them belong to high-risk area. The risk value is between 50 and 60 in Hunan, Sichuan, Guangxi, Liaoning, and Hebei. The value risk is between 40 and 50 in Shandong, Shanxi, Yunnan, Heilongjiang, Hubei, Jiangxi, Henan and Shanghai. The risk value is between 30 and 40 in Being, Guizhou, and Ningxia, which

9 Nat Hazards (2017) 88: Table 4 Comprehensive membership value and risk value of 31 provinces in China Provinces Comprehensive membership value Risk Highest High Average Low h value Level Xinjiang High Guangdong High Anhui High Chongqing High Zhejiang High Qinghai High Gansu High Shanxi High Xizang High Fujian High Hainan High Jiangsu High Tianjin High Ningxia High Hunan Medium Sichuan Medium Guangxi Medium Liaoning Medium Hebei Medium Shandong Medium Shanxi Medium Yunnan Medium Heilongjiang Medium Hubei Medium Jiangxi Medium Henan Medium Shanghai Medium Being Low Guizhou Low Neimenggu Low Jilin Low also belongs to the low-risk areas. The value of risk is in Jilin, which is the lowest in all provinces. In order to analyze the causes of road traffic accident risk in each province, Table 5 lists the memberships of each indicator corresponding to the high and highest calculated by the formula (11). Because the frequency of traffic accidents is high, and the standard highway rate (I7) is low, the traffic accident risk in Xinjiang, Qinghai, Xizang, Gansu, and Chongqing is high. In addition, the development of regional economy in these areas is slow. The education level is generally low, and the proportion of high grade highway is relatively small. Besides, the risk is high in Guangdong, Zhejiang, Shanxi, Hainan, Tianjin,

10 1418 Nat Hazards (2017) 88: Table 5 Membership values of indexes for two levels of 31 provinces and cities Provinces Frequency of traffic accidents Severity of the traffic accidents Trend of traffic accidents High Highest High Highest High Highest High Highest High Highest High Highest High Highest High Highest High Highest Xinjiang Qinghai Xizang Gansu Ningxia Shanxi Chongqing Anhui Jiangsu Zhejiang Fujian Guangdong Hainan Tianjin Heilongjiang Liaoning Hubei Shandong Shanxi Henan Hubei Hunan Guangxi

11 Nat Hazards (2017) 88: Table 5 continued Provinces Frequency of traffic accidents Severity of the traffic accidents Trend of traffic accidents High Highest High Highest High Highest High Highest High Highest High Highest High Highest High Highest High Highest Jiangxi Sichuan Yunnan Shanghai Being Guizhou Jilin Neimenggu Blank cells in the table represent a value of 0.00

12 1420 Nat Hazards (2017) 88: Jiangsu and Ningxia because of high occurrence rate and tendency of traffic accidents. These provinces are developed areas, and there are more vehicles. The reason of high risk in Anhui, Fujian is that the traffic accident rate and severity indicators are high. It s because that more serious traffic accidents occurred in this area in In all medium-risk areas, the number of traffic accidents and the equivalent death toll (I6) are high. Among them, rate of decline in traffic accidents (I8) is low in Hunan. The standard highway rate (I7) and rate of decline in death toll of traffic accidents (I9) are low in Liaoning. The traffic accident death rate (I5) is high in Sichuan, Shandong, Hubei, and Shanxi. That is, the serious traffic accident occurred in these regions. The traffic accident death rate (I5) is high, and rate of decline in death toll of traffic accidents (I9) is low in Guangxi, Hebei, and Shanghai. This can be attributed to a serious traffic accident occurred in these areas. The spatial distribution of traffic accident risk in China is shown in Fig. 1. The traffic accident risk shows a spatial situation that southeast northwest is high, the middle is low. That is the risk in Jiangsu, Anhui, Zhejiang, Fujian, Guangdong, and Hainan which located in southeast coastal area, Shanxi, Chongqing, Gansu, Xinjiang, and Xizang in the western region is high. The risk in Shanxi, Hebei, Henan, Hubei, Hunan, and Jiangxi in middle areas is medium. This spatial distribution can be attributed to the population distribution and economic level. That is, dense population with developed economy and sparse population with developing economy lead to higher traffic accident risk. The former is mainly due to huge traffic accident bearing body large number of population. And the incidence and severity of traffic accidents are higher. The latter lies in the insufficient ability to cope with the traffic accident risk, because of the underdevelopment of the economy. Fig. 1 Spatial distribution of traffic accident risk in China

13 Nat Hazards (2017) 88: Conclusion and discussion Selection of indicators is the key of traffic accident risk assessment. In this paper, nine indicators are selected from three aspects, which are traffic accident rate, traffic accident severity and traffic accident occurrence trend. They are ten thousand vehicles accident rate, one hundred thousand population accident rate, 100 million yuan gross domestic product accident rate, ten thousand kilometers accident rate, traffic accident death rate, equivalent death toll, standard highway rate, rate of decline in traffic accidents, and rate of decline in death toll of traffic accidents. These indicators reflect the traffic accident risk from different angles. They have been proved to be feasible. Grey relational analysis and fuzzy comprehensive evaluation method can be used to assess the traffic accident risk. In this study, the Grey relational analysis method was used to determine the weights. The fuzzy comprehensive evaluation method was used to calculate the risk value. The results show that the traffic accident risk is between and in 31 provinces of China. The risk is highest in Xinjiang and Guangdong. It is relatively low in Guizhou, Neimenggu, Jilin, and Being. High-risk areas are distributed in the southeast coastal areas and the northwest regions. The low-risk areas are scattered in the northern and southwestern regions. The membership value of each grade of different indicators is helpful for reason identification and risk response. As far as the research area is concerned, low standard highway rate, coupled with the slow economic development and low education level is the main reason for high traffic accident risk in the northwest areas. The reason for the high risk of the eastern coastal areas is that the developed transportation industry, dense population, and huge motor vehicle ownership. Relatively speaking, all the indicators in the central areas are at a moderate level. The main causes of the risks lie in the severity and occurrence trend of traffic accidents. In addition, the comprehensive risk can be compared in different regions for further analysis. The method proposed in this paper is helpful to the risk assessment of road traffic and the reason analysis, and the results can be used by the relevant policy makers and researchers. But it still has some flaws inevitably. First, the risk value is relative. It is only applicable to discovering differences within a country or region. Second, the indicators are the annual data, which led to the risk is not real time. Finally, taking into account the difficulty of data acquisition, the regional data is used in this paper, which led to the application of results is limited. For the future, more efforts needed to focus on real-time risk assessment, and it is best to establish a set of global evaluation criteria. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (NSFC) (Nos , ), Youth Foundation of Taiyuan University of Technology (2015QN086), the Qualified Personnel Foundation of Taiyuan University of Technology (No. TYUT- RC201110A). We gratefully acknowledge the thoughtful comments of the editor and reviewers. References Cao JJ (2013) Calculation model research on equivalent death toll in traffic accidents. J Chongqing Jiaotong University (Natural Sciences) 1(32):91 95 (in Chinese) Chen C (2014) Research on influencing factors of road traffic accidents empirical study based on structural equation model. J Saf Sci Technol 5: (in Chinese) Costescu D, Raicu S, Rosca M et al (2016) Using intersection conflict index in urban traffic risk evaluation. Procedia Technol 22:

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