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Constructing road safety performance indicators using Fuzzy Delphi Method

and Grey Delphi Method

Zhuanglin Ma a, Chunfu Shao b,⇑, Sheqiang Ma c, Zeng Ye d

a School of Automobile, Chang’an University, Xi’an 710064, Chinab MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, Chinac Traffic Management Engineering Department, Chinese People’s Public Security University, Beijing 102623, Chinad Beijing Transportation Research Center, Beijing 100055, China

a r t i c l e i n f o

Keywords:

Safety performance indicator

Fuzzy Delphi Method

Grey Delphi Method

Regional road safety

Urban road safety

Highway safety

a b s t r a c t

The main goal of this paper is to construct three sets of road safety performance indicators, which are

regional road safety performance indicators, urban road safety performance indicators and highway

safety performance indicators, respectively. Fuzzy Delphi Method and Grey Delphi Method are applied

to quantify experts’ attitudes to regional road safety, urban road safety and highway safety. Comparing

the results of two methods, the different results of two methods are analyzed, and then the final safety

performance indicators are obtained by taking the intersection of results of two methods. Finally, three

sets of performance indicators are constructed, which can be described and evaluated the safety level of

region, urban road and highway, respectively. The research findings show that the method used in this

paper is feasible and practical and can be provided as a reference for the administrative authority of road

safety.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Road safety management is an important means for forecasting

and preventing traffic accidents, and its core is the evaluation, fore-

cast and decision-making technique of road safety. Especially, road

safety evaluation is the foundation of safety management. In gen-

eral, the process of evaluation is made up of evaluation object,

evaluation indicator, weighting and evaluation model. In practice,

the process of weighting and evaluation model is always paid

much attention, but the selection of evaluation indicator is ignored.

In fact, it is very important to choose scientific and rational evalu-

ation indicators, which is the first step to conduct evaluation and

the key problemconcerning the success or failure of the whole pro-

cess of evaluation. Therefore, how to establish a set of scientific and

rational road safety performance indicators is the key problem forroad safety management.

Many researchers have dedicated to the research of the macro

road safety model over 50 years, and these research results were

remarkable, such as Smeed’s law (Smeed, 1949), Rumar descriptive

model (Rumar, 1987), Koornstra’s function (Koornstra, 1996), Na-

vin Model (Navin, Bergan, & Zhang, 1996) and Trinca model

(Trinca, 1988). These models were used to compare countries’ road

safety level by means of risk indicators, such as fatalities per vehi-

cles, fatalities per population, fatalities per vehicle kilometers or

the number of passenger miles. But some indirect influence factors,

such as Socio-economic factor level and social medical condition,

have not been considered.

Some researchers established a comprehensive performance

indicators taking into account the impact of direct and indirect

influence factors from the view of systems engineering. Al-haji

(2003) proposed a road safety development index (RSDI) allowing

comparison among nations and adopted a framework used to de-

velop a human development index (HDI), which included nine ba-

sic dimensions with 14 indicators and averaged them to produce

the RSDI. Fu and Fang (2006) proposed highway network safety

performance indicators, which included five basic dimensions with

13 relative indicators. Wu, Liu, and Xiao (2006) proposed freeway

safety performance indicators, which included three basic dimen-

sions with 11 indicators. Ma, Sun, and Han (2008) proposed urbanroad safety performance indicators, which included three basic

dimensions with 11 indicators. Above all, these safety performance

indicators have overcome the deficiency of indicators which were

considered from the aspect of accidents, and have made great pro-

gress. But the present researches do not specify the detailed pro-

cess of constructing road performance indicators and why those

indicators are selected.

Delphi Method was widely applied to select performance indi-

cators in many fields, but it requires multiple investigations to

achieve the consistency of expert opinions and experts are

required and forced to modify their opinions so as to meet the

mean value of all the expert opinions. However, Fuzzy Delphi

0957-4174/$ - see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.eswa.2010.07.062

⇑ Corresponding author.

E-mail addresses: [email protected] (Z. Ma), [email protected] (C. Shao).

Expert Systems with Applications 38 (2011) 1509–1514

Contents lists available at ScienceDirect

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http://dx.doi.org/10.1016/j.eswa.2010.07.062

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Method requires only a small number of samples and the derived

results are objective and reasonable. Not only it saves time and

cost required for collecting expert opinions but also experts’ opin-

ions will also be sufficiently expressed without being distorted

(Hsu & Yang, 2000; Ishikawaet al., 1993; Kuo & Chen, 2008; Murry,

Pipino, & Gigch, 1985). Furthermore, grey system theory also can

deal with uncertain, hazy and incomplete data (Liu, Dang, & Fang,

2004). Grey whitening weight function can be described evaluation

objects belonging to the degree of a certain grey class, and it has

been widely used (Li, Wang, & An, 2008; Shao, Tang, & Bai, 2003;

Xie & Pan, 2007). Therefore, two kinds of methods are used to filter

road safety performance indicators, which are Fuzzy Delphi Meth-

od and Grey Delphi Method, respectively.

The main goal of this paper is to construct three sets of road

safety performance indicators, which are regional road safety per-

formance indicators, urban road safety performance indicators and

highway safety performance indicators, respectively. Through Fuz-

zy Delphi Method and Grey Delphi Method, the importance of indi-

cators can be derived. The comparative analysis on the results of

two methods was carried out, and then three sets of road safety

performance indicators could be constructed. The research results

can be provided as a reference for the administrative authority of

road safety.

2. Methodology

In order to simplify the process of survey, three primary road

safety performance indicators from the region, the urban road and

the highway were proposed with reference to the related litera-

tures. They are summarized in Appendices A, B and C, respectively.

Based on three primary road safety performance indicators, the

questionnaire was designed. A panel of 15 members from universi-

ties and research institutions was formed. The importance of road

safety performance indicators was divided into five grades, and

five-point Likert scales, ranging from five, ‘‘very important” to one,

‘‘not very important” were used forscoringof each indicator. At last,a total of 15 questionnaires (one for each expert) were distributed,

and 13 returned were valid. The valid response rate was 86.7%.

2.1. Fuzzy Delphi Method

The Delphi Method was first developed by Dalkey and Helmer

(1963) in corporation and has been widely applied in many man-

agement areas, e.g. forecasting, public policy analysis and project

planning. However, the traditional Delphi Method also has some

disadvantages, such as low convergence expert opinions, high exe-

cution cost, the possibility of filtering out particular expert opin-

ions, and so on. Therefore, Murry et al. (1985) proposed the

concept of integrating the traditional Delphi Method and the fuzzy

theory to improve the vagueness of the Delphi Method. Member-ship degree is used to establish the membership function of each

participant. Ishikawa et al. (1993) further introduced the fuzzy the-

ory into the Delphi Method and developed max–min and fuzzy

integration algorithms to predict the prevalence of computers in

the future. But the limitation of this method is only applicable to

predict time series data. Hsu and Yang (2000) applied triangular

fuzzy number to encompass expert opinions and establish the Fuz-

zy Delphi Method. The max and min value of expert opinions are

taken as the two terminal points of triangular fuzzy numbers,

and the geometric mean is taken as the membership degree of tri-

angular fuzzy numbers to derive the statistical unbiased effect and

avoid the impact of extreme values. The advantage of this method

is simplicity that all the expert opinions can be encompassed in

one investigation. As a result, this method may create a better ef-fect of criteria selection. Kuo and Chen (2008) summarized advan-

tages of the Fuzzy Delphi Method, and applied it to construct key

performance appraisal indicators for mobility of the service

industries.

In this paper, the Fuzzy Delphi Method proposed by Hsu and

Yang (2000) was adopted in the process of the selection of road

safety performance indicators. Geometric means are used to de-

note experts consensus in this paper, and the process is demon-

strated as follows:

(1) Experts’ opinions were collected from questionnaires, and

questionnaires were dealt with. At the same time, the trian-

gular fuzzy numbers eai were created, which were shown as

follows:eai ¼ ðai; di; ciÞ;

ai ¼ minðBijÞ;

di ¼Ynk¼1

Bij

!1=n

;

ci ¼ maxðBijÞ;

where i is the number of indicators; j is the number of ex-

perts; ai is the bottom of all the experts’ evaluation valuefor indicator i; di is the geometric mean of all the experts’

evaluation value for indicator i; ci is the ceiling of all the ex-

perts’ evaluation value for indicator i; Bij is the evaluation va-

lue of the jth expert for indicator i.

(2) Selection of performance indicators.

In this paper, the geometric mean di of each indicator’s triangu-

lar fuzzy number was used to denote the consensus of the expert

group on the indicator’s evaluation value, so that the impact of ex-

treme values could be avoided. The threshold value r was deter-

mined. If di is no less than r , indicator i is accepted, and vice versa.

2.2. Grey Delphi Method

Grey Delphi Method is the integration of grey system theory

and Delphi Method, which uses grey whitening weight function

based on Delphi questionnaires to select evaluation indicators.

The process of Grey Delphi Method was as follows.

Step 1. According to the evaluation requirement, s grey classes

were developed and the selection range of value of indicator j

½a1 j ; b

s j was divided into k grey classes.

Step 2. For k = 1 and s, half trapezoidal whitening weight func-

tion was used. The formations were as follows.

f 1 j ð xÞ ¼

1; x 6 a1 j ;

b1 j x

b1

j a1

j

; a1 j < x 6 b1

j ;

x > b1

j ;

8>>><>>>: ð1Þ

f s j ð xÞ ¼

0; x < as j ;

xas j

bs j as

j

; as j 6 x < b

s j ;

1; xP bs j :

8>>><>>>: ð2Þ

For k = m (m = 2, 3, . . . , s 1), triangular whitening weight func-

tion was used. The formation was as follows:

f k j ð xÞ ¼

0; x R ½ak j ;b

k j ;

xak j

kk j

ak j

; x 2 ½ak j ; k

k j ;

bk j x

bk j kk

j; x 2 ½k

k j ; b

k

j ;

8>>>>><>>>>>:

ð3Þ

1510 Z. Ma et al. / Expert Systems with Applications 38 (2011) 1509–1514



where kk j ¼ ðak

j þ bk

j Þ=2. The starting point ak j is the lower bound-

aries of the kth grey class; the end point bk

j is the upper bound-

aries of the kth grey class.

Step 3. The synthetic clustering coefficient rk j was calculated,

and the formation was as follows.

rk j ¼ Xml¼1

f k j ð xÞ gl j;

where f k j ð xÞ is the whitening weight function of k grey class indica-

tor j; m is the number of categories of experts’ opinions; g l j is the

weight of indicator j in the synthetic cluster, namely, the number

of experts’ opinions in category l.

Step 4. The decision vectors of evaluation indicators were iden-

tified. The criterion of max16k6sfrk j g ¼ rk

j was used to judge

whether indicator j belongs to class k*.

3. Results and discussion

3.1. Results of Fuzzy Delphi Method

In this paper, the threshold value r is set as 2.5. Then the selec-

tion criteria are as follows:

(1) If d iP 2.5, this performance indicator is accepted.

(2) If d iP 2.5, this performance indicator is rejected.

It can be seen from Appendix A that 16 indicators were retained

and 14 indicators were deleted. The retained indicators are mainly

attributed to regional road safety, which focus on four dimensions:

road user behaviour, vehicle safety, traffic risk and Socio-economic

factor. Road user behaviour includes driving license less than

3 years, drunken driving rate, overspeed rate and fatigue driving

rate. Vehicle safety includes the level of motorization, the growth

rate of vehicles and percentage of motorcycle. Traffic risk includesaccidents per 10,000 vehicles, fatalities per 10,000 vehicles, acci-

dents per 100,000 people, fatalities per 100,000 people, accidents

per 100 km, fatalities per 100 km and casualty rate. Socio-eco-

nomic factor includes GDP per capita and popularizing rate of traf-

fic laws and traffic safety common sense.

It can be seen from Appendix B that 21 indicators were retained


attributed to urban road safety, which focus on five dimensions:

road user behaviour, vehicle safety, road situation, traffic risk and

Socio-economic factor. Road user behaviour includes driving li-

cense less than 3 years, drunken driving rate, overspeed rate, fati-

gue driving rate and laws broken by pedestrian at intersection.

Vehicle safety includes the level of motorization and percentage

of motorcycle. Road situation includes proportion of not lightingsection at night, proportion of channelized intersections, propor-

tion of signalized intersections, percentage of undivided roads

and number of days of adverse weather. Traffic risk includes acci-

dents per 10,000 vehicles, fatalities per 10,000 vehicles, accidents

per 100,000 people, fatalities per 100,000 people, accidents per

100 km, fatalities per 100 km and casualty rate. Socio-economic

factor includes percentage of floating population and popularizing

rate of traffic laws and traffic safety common sense.

It can be seen from Appendix C that 18 indicators were retained

and two indicators were deleted. The retained indicators are

mainly attributed to highway safety, which focus on four dimen-

sions: road user behaviour, road situation, traffic environment

and traffic facility. Road user behavior includes driving license less

than 3 years, drunken driving rate, overspeed rate, fatigue drivingrate and helmet wearing rate. Road situation includes proportion

of the radius of circular curve under ordinary value, percentage

of longitudinal grade above the maximum, proportion of shoulder

width under ordinary value, percentage of tunnel and bridge sec-

tions and percentage of sections at heavy hill area. Traffic environ-

ment includes degree of saturation, percentage of large vehicles,

stopping sight distance, over loading rate of heavy truck and num-

ber of days of adverse weather. Traffic facility includes perfect rate

of traffic sign, serviceability rate of traffic marking and traffic acci-

dent emergency rescue.

3.2. Results of Grey Delphi Method

In this paper, five grey classes were selected, namely, s = 1, 2, 3,

4 and 5, which stands for not very important, no important, unde-

cided, important and very important, respectively. The range of

each grey class are [1, 2.5], [0.5, 3.5], [1.5, 4.5], [2.5, 5.5] and

[3.5, 5], respectively. Then the synthetic clustering coefficient rk j

could be calculated and the decision vectors of evaluation indica-

tors are obtained, which are shown in Appendices A, B and C,

respectively. The selection criteria are as follows:

(1) If class k* belong to class 4 and 5, namely, the value of clas-ses of important or very important is the maximum in the

vector decision, this performance indicator is accepted.

(2) If the ratio of class k* attached to class 4 and 5 to class k*

attached to class 1 and 2 is more than 1, namely, classes of

important and very important account for an over 50%

degree except for class of undecided, this performance indi-

cator is accepted.

It can be seen from Appendix A that 13 indicators were retained


attributed to regional road safety, which focus on four dimensions:

road user behaviour, vehicle safety, traffic risk and Socio-economic

factor. Road behavior includes driving license less than 3 years,

drunken driving rate, overspeed rate and fatigue driving rate. Vehi-

Table 1

Regional road safety performance indicators.

Fuzzy Delphi Method Grey Delphi Method The final results

Road user behaviour

Driving license less than

3 years

Driving license less

than 3 years


than 3 years

Drunken driving rate Drunken driving rate Drunken driving rate

Overspeed rate Overspeed rate Overspeed rate

Fatigue driving rate Fatigue driving rate Fatigue driving rate

Vehicle safety

The level of motorization The level of

motorization

The level of

motorization

The growth rate of vehicles

Percentage of motorcycle

Traffic risk

Accidents per 10,000

vehicles


vehicles


vehicles

Fatalities per 10,000

vehicles


vehicles


vehicles


people

Accidents per

100,000 people

Accidents per

100,000 people


people


people


people

Accidents per 100 km Accidents per 100 km Accidents per 100 km

Fatalities per 100 km Fatalities per 100 km Fatalities per 100 km

Casualty rate Casualty rate Casualty rate

Socio-economic factor

Popularizing rate of traffic

laws and traffic safety

common sense

Popularizing rate of

traffic laws and traffic

safety common sense



safety common sense

GDP per capita

Z. Ma et al. / Expert Systems with Applications 38 (2011) 1509–1514 1511



cle safety includes the level of motorization. Traffic risk includes

accidents per 10,000 vehicles, fatalities per 10,000 vehicles, acci-

dents per 100,000 people, fatalities per 100,000 people, accidents

per 100 km, fatalities per 100 km and casualty rate. Socio-eco-

nomic factor includes popularizing rate of traffic laws and traffic

safety common sense.

It can be seen from Appendix B that 17 indicators were retained


attributed to urban road safety, which focus on five dimensions:

road user behaviour, traffic risk and Socio-economic factor. Road

user behaviour includes drunken driving rate, overspeed rate, fati-

gue driving rate and laws broken by pedestrian at intersection.

Vehicle safety includes percentage of motorcycle. Road situation

includes proportion of not lighting section at night, proportion of

channelized intersections, proportion of signalized intersections,

percentage of undivided roads and proportion of uncontrolled

intersections. Traffic risk includes accidents per 10,000 vehicles,

fatalities per 10,000 vehicles, accidents per 100,000 people, fatali-

ties per 100,000 people, fatalities per 100 km and casualty rate. So-

cio-economic factor includes popularizing rate of traffic laws and

traffic safety common sense.

It can be seen from Appendix C that 16 indicators were retained

and four indicators were deleted. The retained indicators are

mainly attributed to highway safety, which focus on four dimen-

sions: road user behaviour, road situation, traffic environment

and traffic facility. Road user behaviour includes driving license

less than 3 years, drunken driving rate, overspeed rate, fatigue

driving rate and helmet wearing rate. Road situation includes

proportion of the radius of circular curve under ordinary value,

percentage of longitudinal grade above the maximum and percent-

age of sections at heavy hill area. Traffic environment includes de-

gree of saturation, percentage of large vehicles, stopping sight

distance, over loading rate of heavy truck and number of days of

adverse weather. Traffic facility includes perfect rate of traffic sign,

serviceability rate of traffic marking and traffic accident emergency

rescue.

3.3. Comparison analysis

It is obvious that results of Fuzzy Delphi Method and Grey Del-

phi Method are different.For regional road safety performance indicators, the number of

selected indicators using Fuzzy Delphi Method is more than Grey

Delphi Method. Three indicators, which are the growth rate of

vehicles, percentage of motorcycle and GDP per capita, are selected

by Fuzzy Delphi Method, but are not selected by Grey Delphi Meth-

od. Therefore, the final regional road safety performance indicators

Table 2

Urban road safety performance indicators.

Fuzzy Delphi Method Grey Delphi Method The final results

Road user behaviour


3 years

Drunken driving rate Drunken driving rate

Drunken driving rate Overspeed rate Overspeed rate

Overspeed rate Fatigue driving rate Fatigue driving rate

Fatigue driving rate Laws broken by

pedestrian at

intersection

Laws broken by

pedestrian at

intersection

Laws broken by pedestrian

at intersection

Vehicle safety

The level of motorization Percentage of

motorcycle

Percentage of

motorcycle

Percentage of motorcycleRoad situation

Proportion of not lighting

section at night

Proportion of not

lighting section at

night

Proportion of not

lighting section at

night

Proportion of channelized

intersection

Proportion of

channelized

intersection

Proportion of

channelized

intersection

Proportion of signalized

intersection

Proportion of

signalized

intersection

Proportion of

signalized

intersection

Percentage of undivided

roads

Percentage of

undivided roads

Percentage of

undivided roads

Number of days of adverse

weather

Proportion of

uncontrolled

intersection

Traffic risk


vehicles


vehicles


vehicles


vehicles


vehicles


vehicles


people

Accidents per

100,000 people

Accidents per

100,000 people


people


people


people

Accidents per 100 km Fatalities per 100 km Accidents per 100 km

Fatalities per 100 k m Casualty r ate Fatalities per 100 km

Casualty rate Casualty rate


Percentage of floating

population



safety common sense



safety common sense

Popularizing rate of traffic

laws and traffic safety

common sense

Table 3

Highway safety performance indicators.

Fuzzy Delphi Method Grey Delphi method The final results

Road user behaviour


than 3 years


than 3 years


than 3 yearsDrunken driving rate Drunken driving rate Drunken driving rate

Over speed rate Over speed rate Over speed rate

Fatigue driving rate Fatigue driving rate Fatigue driving rate

Helmet wearing rate Helmet wearing rate Helmet wearing rate

Road situation

Proportion of the radius

of circular curve

under ordinary value


of circular curve under

ordinary value


of circular curve under

ordinary value

Percentage of

longitudinal grade

above the maximum

Percentage of

longitudinal grade

above the maximum

Percentage of

longitudinal grade

above the maximum

Proportion of shoulder

width under

ordinary value

Proportion of sections

at heavy hill area

Percentage of sections

at heavy hill area

percentage of tunnel

and bridge sections

Proportion of sectionsat heavy hill area

Traffic environment

Degree of saturation Degree of saturation Degree of saturation

Percentage of large

vehicles

Percentage of large

vehicles

Percentage of large

vehicles

Stopping sight distance Stopping sight distance Stopping sight distance

Over loading rate of

heavy truck


heavy truck


heavy truck

Number of days of

adverse weather

Number of days of

adverse weather

Number of days of

adverse weather

Traffic facility

Perfect rate of traffic

sign


sign


sign

Service ability rate of

traffic marking


traffic marking


traffic marking

Traffic accident

emergency rescue

Traffic accident

emergency rescue

Traffic accident

emergency rescue




should be obtained by taking the intersection of results of two

methods, and the results are shown in Table 1.

It is very interesting that indicators related road situation are no

considered. This is probably because road situation is closely re-

lated to regional GDP. On the one hand, the increase of regional

GDP means that the investment on transport infrastructure will in-

crease, and then the length and grade of highway will increase cor-

respondingly. On the other hand, the increase of the length and

grade of highway will promote the development of regional trans-

port activity in turn, and then the development of regional

transport activity will provide a substantial foundation for the in-

crease of regional GDP. This conclusion is consistent with that of

a Chinese study (Xu, Li, & Yang, 2007).

For urban road safety performance indicators, the number of se-

lected indicators using Fuzzy Delphi Method is more than Grey

Delphi Method. Five indicators, which are driving license less than

3 years, the level of motorization, number of days of adverse

weather, accidents per 100 km and percentage of floating popula-

tion, are selected by Fuzzy Delphi Method, but are not selected

by Grey Delphi Method. At the same time, one indicator, which is

proportion of uncontrolled intersections, is selected by grey Delphi

Method, but is not selected by Fuzzy Delphi Method. Therefore, the

final urban road safety performance indicators should be obtained

by taking the intersection of results of two methods, and the re-

sults are shown in Table 2.

For highway safety performance indicators, the number of se-

lected indicators using Fuzzy Delphi Method is more than Grey

Delphi Method. Two indicators, which are proportion of shoulder

width under ordinary value and percentage of tunnel and bridge

sections, are selected by Fuzzy Delphi Method, but are not selected

by Grey Delphi Method. Therefore, the final highway safety perfor-

mance indicators should be obtained by taking the intersection of

results of two methods, and the results are shown in Table 3.

Table A1

Regional road safety performance indicators.

Indicators Triangular

fuzzy

number

Grey decision vector

Road user behaviour


3 years

(3, 3.26, 5) (0, 3.33, 10.67, 5.67, 1.67)

Drunken driving rate (2,3.97, 5) (0.33, 1.333,3.67, 8.67, 6.33)

Overspeed rate (2, 3.77, 5) (0.33, 1.33, 4.67, 10.67, 4 .33)

Fatigue driving rate (3, 4.24, 5) (0, 0.67, 3.67, 7.67, 7.67)

Seat belt wearing rates for

drivers and front passengers

(1, 1.87, 5) (5.67, 7.33, 5.2, 0.33)

Helmet wearing rate (1,2.29, 4) (3.67, 5.7,33.4, 0.67)

Vehicle safety

The level of motorization (1, 2.83, 4) (1.67, 4.33, 8.6,1.33)

The growth rate of vehicles (1, 2.54, 5) (3.33, 5.33, 4.67, 5,2.33)

Coaches per 1000 people (1, 1.97, 4) (5.8, 5.33, 2,0.33)Heavy truck per 1000 people (1, 2.18, 4) (4.67, 6.33, 4, 4.33, 1.33)

Percentage of motorcycle (1,2.6,4) (2.33, 6,7.33, 4.67, 1)

Road situation

The length of freeway per

capita

(1, 1.85, 4) (6, 7.67, 3.67, 2.33, 0.67)

Percentage of high and sub-

high class pavement

(1, 2.3,5) (3.67, 7,6, 2.67, 1.33)

Percentage of freeways, first

class roads and second class

roads

(1, 2.36, 5) (3.33, 8.33, 5.67, 2.33, 1.33)

Highway density (1, 2.27, 4) (3.33, 8.67, 6.67, 2.33, 0.33)

Congestion degree of freeway (1, 2.41, 4) (2.67, 7.33, 8, 3, 0.33)

Congestion degree of provincial

highway

(1, 2.49, 4) (2.33, 6.67, 8.67, 3.33, 0.33)

Traffic risk

Accidents per 10,000 vehicles (1, 3.33, 5) (1, 2, 6.67, 7.33, 3.67)

Fatalities per 10,000 vehicles (1, 3.16, 5) (1.33, 3, 6.67, 6.33, 3.3)

Accidents per 100,000 vehicles (1, 2.93, 5) (1.67, 4.33, 7.33, 4.67, 2.67)

Fatalities per 100,000 vehicles (1, 2.99, 5) (1.67, 4, 6.67, 5.33, 3)

Accidents per 100 km (1,3.24, 5) (1.33, 2.33, 5.67, 8.33, 3.3)

Fatalities per 100 km (1,3.38, 5) (1.33, 2.33, 4.67, 8.33, 3.33)

Casualty rate (1, 3 .69, 5 ) (0, 2, 7 .33, 7, 4.33)


GDP per capita (1, 2 .54, 5 ) (3.33, 5.33, 4 .67, 5 , 2.33)

Percentage of urban population (1, 2.08, 4) (4.33, 8.67, 5.67, 2, 0.33)

Highway turnover of passenger

traffic

(1, 2.17, 4) (4.6, 7.33, 3,0.33)

Highway turnover of freight

traffic

(1, 2.34, 4) (3.67, 4.67, 6.67, 4.67, 1)

Popularizing rate of traffic laws

and traffic safety common

sense

(1, 3.77, 5) (1, 0.67, 3.33, 8.67, 6.33)

The number of beds in health

care per 1000 people

(1, 1.67, 4) (7.33, 6.33, 3, 2.33, 0.67)

Table A2

Urban road safety performance indicators.


fuzzy

number


Road user behaviour

Driving license less than 3 years (1, 2.75, 5) (1.67, 5, 9, 4, 1.33)

Drunken driving rate (2, 3.67, 5) (0.33, 2,5.67, 8.67, 4.33)

Overspeed rate (2, 3 .47, 4) (0.33, 2 .33, 7, 9 .33, 6 7)

Fatigue driving rate (2, 3.45, 5) (1, 3.33, 4.33, 8, 4.33)



(1, 2.04, 4) (4.67, 7.33, 6,2.33,0.33)

Helmet wearing rate (1, 2.22, 4) (4,5.67, 6.67, 3.67, 0.67)

Laws broken by pedestrian at

intersection

(1, 3.45, 5) (1, 2, 6, 6, 5)

Vehicle safety

The level of motorization (1, 2.54, 4) (2.33, 6.33, 8,4, 0.67)

The growth rate of vehicles (1, 2.38, 5) (3.33, 6.33, 6.67, 3,1.33)

Qualification rate of vehicles

periodic survey

(1, 2.38, 5) (3.33, 6.33, 6.67, 3, 1.33)

Percentage of motorcycle (1, 2.87, 4) (2,4.33, 6,7,2)

Road situation

Proportion of not lightingsection at night

(2, 3.04,5) (1.5,8,5.33,2)

Proportion of channelized

intersections

(1, 2.98, 5) (2, 4, 5, 7, 3)

Proportion of signalized

intersections

(1, 3.1,5) (1.33, 3,7,7, 2.67)

Percentage of undivided roads (1, 2.97, 5) (2, 4.33, 5.33, 5.67, 3.33)

Percentage of expressways (1, 1.76, 4) (6.67, 7, 3.33, 2.33, 0.67)

Proportion of uncontrolled

intersection

(1, 2.47, 4) (3.33, 3.67, 6.67, 5.67, 1.33)

Percentage of speed limits roads (1, 2.17, 4) (4, 6, 7.3333, 3, 0.33)

Degree of saturation of

expressway

(1, 2.34, 4) (3.33, 6.33, 7,3, 0.67)

Degree of saturation of arterial

roads

(1, 2.49, 5) (3.33, 5.67, 5.33, 4.33, 2)

Density of road network (1, 1.93, 4) (5.33, 6.67, 5.67, 2.33, 0.33)


weather

(1, 2.63, 4) (2.67, 6, 5.33, 5.67, 1.67)

Traffic risk

Accidents per 10,000 vehicles (1, 3.39, 5) (1, 2, 6.33, 6.67, 4.33)

Fatalities per 10,000 vehicles (1, 2.9, 5) (2.33, 3, 5.67, 6, 3.33)

Accidents per 100,000 people (1, 2.73, 5) (2.33, 3.67, 7.33, 5.33, 2)

Fatalities per 100,000 people (1, 2.97, 5) (2.33, 2.67, 5, 6.67, 3.67)

Accidents per 100 km (1, 2.73, 5) (2,5.33, 7.67, 4.33, 1.67)

Fatalities per 100km (1, 2.81, 5) (2.67, 3.67, 5,5.67, 3.33)

Casualty rate (2, 3 .75, 5) (0.33, 1 .67, 5, 9 .33, 4 .67)

Socio-ecomic factor

GDP per capita (1, 1 .89, 5) (6.33, 1.67, 5 , 9.33, 4 .67)

Percentage of floating

population

(1, 2.52, 4) (3, 5,6.33,5.33, 1.33)

Popularizing rate of traffic laws

and traffic safety common

sense

(1, 2.94, 5) (3, 1.33, 3.33, 8,4.33)

The number of beds in health

care per 1000 people

(1, 1.7,5) (7.33, 6.33, 2.67, 1.67, 1.33)

Z. Ma et al. / Expert Systems with Applications 38 (2011) 1509–1514 1513



4. Conclusions

This paper explored the application of Fuzzy Delphi Method and

Grey Delphi Method to quantify experts’ attitudes to regional road

safety, urban road safety and highway safety. Possible factors im-

pacted regional road safety, urban road safety and highway safety

are considered. Then, safety performance indicators are selected

using Fuzzy Delphi Method and Grey Delphi Method, respectively.

Comparing the results of two methods, the different results of two

methods are analyzed, and then the final safety performance indi-

cators are obtained by taking the intersection of results of two

methods. Finally, three sets of performance indicators are con-

structed, which can be described and evaluated the safety levelof region, urban road and highway, respectively.

It can be discovered that some indicators were deleted. The

main reason is that investigated experts had different focuses on

the safety evaluation. This paper proposed three sets of primary

performance indicators based on literature reviews in advance,

which cover influencing factors on safety as much as possible. Be-

sides, due to insufficient human resource and other objective fac-

tors, some biases of the survey results could still exist. However,

these biases impacted on the results are too insignificant to men-

tion and can be ignored. Therefore, the results in this paper are fea-

sible and practical and can be provided as a reference for the

administrative authority of road safety.

Acknowledgment

This study was supported by the research projects sponsored by

National Key Technology R&D Program of the People’s Republic of

China (No. 2007BAK35B06) and Natural Science Foundation of China (No. 50878026).

Appendix A

See Table A1.

Appendix B

See Table A2.

Appendix C

See Table A3.

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Table A3

Highway safety performance indicators.


fuzzy

number


Road user behaviour

Driving license less than 3

years

(2, 3.13, 5) (0.67, 4.33, 8.67, 5.67, 2)

Drunken driving rate (2, 3.91,5) (0.33, 1.33, 4,9.33, 5.67)Overspeed rate (2, 3.77, 5) (0.33, 1.33, 4.67, 10.67, 4.33)

Fatigue driving rate (1, 3.53,5) (1.33, 1.33, 3.33, 9.67, 5)



(1, 2.22, 4) (4, 5.67, 6.67, 3.67, 0.67)

Helmet wearing rate (1, 2.8, 4) (2.33, 3, 6.33, 7.33, 2)

Road situation

Proportion of the radius of

circular curve under

ordinary value

(2, 3.12, 4) (1, 4.33, 7,7.33,2)

Percentage of longitudinal

grade above the maximum

(2, 3.01, 5) (1.33, 5.33, 6.67, 5.67, 2.33)

Proportion of shoulder width

under ordinary value

(2, 2.74, 4) (1.67, 6.67, 7.67, 4.67, 1)

Percentage of tunnel and

bridge sections

(1, 2.45, 5) (3, 5.67, 7.33, 3.33, 1.33)

Percentage of sections at heavy

hill area

(1, 2.79, 5) (3, 4,3.67, 6,3.67)

Traffic environment

Degree of s aturation (2, 3.15, 4) (0.67, 4, 8.33, 7, 1.67)

Percentage of large vehicles (1, 3.01, 5) (1.67, 3.67, 6.33, 6.67, 2.67)

Design speed (1, 2 .34, 4 ) (3, 8, 7.33, 2.67, 0.33)

Stopping sight distance (1, 2.77, 5) (2.33, 5.33, 5.67, 5.33, 2.33)

Overloading rate of heavy

truck

(3, 4.24, 5) (0, 0.67, 3.67, 7.67, 7.67)


weather

(2, 3.08, 5) (1.33, 5,6, 6.33, 2.67)

Traffic facility

Perfect rate of traffic sign (1, 2.94, 5) (1.67, 4,7, 6,2.33)

Serviceability rate of traffic

marking

(1, 3.13, 5) (6.67, 4.33, 8.67, 8.67, 2)

Traffic accident emergency

rescue

(1, 3.24, 5) (1.33, 2.33, 5.67, 8.33, 3.33)


1-road safety management

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