International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 3, March 2013
ISSN 2319 - 4847
The Early Warning Evaluation and Urgent
Decision Mechanism for City Significant
Emergency in Uncertain Environment
Qiansheng Zhang1, Yirong Huang2
1
School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510420, P.R.China,
2
SunYat-sen Business School, Sun Yat-sen University, Guangzhou, 510275, P.R.China,
ABSTRACT
This paper presents the early warning evaluating method and decision mechanism for uncertain city emergency in which the
risk factors are easily assessed by intuitionistic fuzzy value. By using the proposed intuitionistic fuzzy entropy we calculate the
occurring probability of each risk factor. In the process of fuzzy risk analysis, the severity of loss and the grade of each risk
factor are evaluated by intuitionistic fuzzy numbers rather than the real numbers. By computing the similarity between the
fuzzy comprehensive risk value and the given risk grade, the early warning degree of the city significant emergency can be
determined for urgent emergency decision-making.
Keywords: city emergency, similarity measure, entropy, warning degree, decision making
1. INTRODUCTION
With the development and expansion of city, the frequency and strength of significant emergencies are increasing in
many cities. So city significant emergency index analysis and early warning become very important research issues in
emergency management. As is well known, many uncontrolled index factors easily incur the city emergency.
Simultaneously, the city emergency inevitably affects many aspects of city including city economy recession, safety of
environment and property, and casualties. In the past decades, Zhang [1] proposed the methods of index selecting and
weighting for emergency. The authors [2-6] have proposed some urgent decision making approaches for city significant
emergency. Also some early warning management methods for city incidents have been introduced [7-15]. However,
most of the existing early warning mechanisms and decision methods can only deal with the city emergency under
precise condition. In fact, due to the increasing complexity of the socio-economic environment and the lack of
knowledge about the problem domain, most of the real-world problems, such as city emergency decision analysis and
emergency warning degree evaluation, are involved variety of uncertainty like fuzzy value and intuitionistic fuzzy
value. Especially, in the warning degree evaluation process of city significant emergency it will inevitably involve some
uncertain factors including the serious economy depression, the wicked environment destroy, the improper emergency
broadcasting, the enormous casualties, and the critical traffic jam, as well as the inadequate emergency rescue facilities,
etc. Also, the values of above risk factors are easily expressed by intuitionistic fuzzy linguistic values. As is well known,
the unexpected and uncontrolled uncertain risks easily incur the city significant emergency. So, in order to decrease
the possibility of city significant emergency, there is much need to analyze and control the risk of City significant
emergency. And, it is a necessitous task for the city government department decision-maker to adopt the corresponding
strategy to avoid and reduce the occurrence of significant emergency in city zone according to the evaluated
intuitionistic fuzzy comprehensive risk value.
Recently, many researchers studied the risk analysis of emergency in [18-21], but the fuzzy risk factor was not
considered. Although Zhong [22] employed fuzzy entropy and comprehensive judgment method to calculate the
occurring probability of risk, it has some drawbacks since it is based on traditional Shannon entropy. And Li [23]
discussed the fuzzy comprehensive risk judgment of HR outsourcing, but the method is unable to determine the
accurate risk grade. In fact, most of the existing fuzzy risk computing methods can not effectively cope with the risk
evaluating and warning degree determining involved intuitionistic fuzzy risk factors. Thus, in this paper we aim to
propose an intuitioinstic fuzzy risk evaluation approach for city emergency in the uncertain environment.
Volume 2, Issue 3, March 2013
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 3, March 2013
ISSN 2319 - 4847
2. PRELIMINARIES
Intuitionistic fuzzy set(IFS) introduced by Atanassov [24] is a useful generalization of the ordinary fuzzy set, which has
been proved to be more suitable way for dealing with uncertainty. Particularly, the information entropy [25], similarity
measure and distance measure of IFSs play very important roles in the application areas like pattern recognition,
medical diagnosis, and decision-making [26].
Definition 1[24].
An intuitionistic fuzzy set A in the universe X  {x1 , x 2 ,  , x n } is defined as
A  {( xi ,  t A ( x i ), f A ( xi ) ) / xi  X } , i.e., A( x i )  [t A ( x i ),1  f A ( x i )] and the condition 0  t A ( xi ) + f A ( x i )  1 must
hold for any xi  X , where t A ( xi ) , f A ( xi ) are called the membership degree and non-membership degree of element xi
to the intuitionistic fuzzy set A , respectively;
 A ( xi )  1  t A ( x i )  f A ( x i ) is called the hesitation degree of xi to the IFS A .
We denote by IF (X ) the family of all the intuitionistic fuzzy sets in universe X .
Definition 2. A mapping E from IF (X ) to interval [0,1] is named as intuitionistic fuzzy entropy, if it satisfies the
following extension of DeLuca-Termini axioms:
(p1) E (A) =0, if A is a crisp set, i.e., A( xi )  0,1  or  1,0  , for all xi  X ;
(p2) E (A) =1, iff t A ( xi )  f A ( xi ) for all xi  X ;
(p3) E ( A * )  E (A) , if A*  A , i.e., A* is a sharpened version of A defined as
t A* ( xi )  t A ( xi ) and


t A* ( xi )  t A ( xi ) and

f A* ( xi )  f A ( xi ),
for t A ( xi )  f A ( xi );
f A* ( xi )  f A ( xi ),
for t A ( xi )  f A ( xi ).
(p4) E (A)  E ( A c ) , where A c is the complement set of IFS A .
One can easily see that the formula
E (A) =
1
n
n
t A ( x i )  f A ( x i )  0.5 A ( x i )
,
A ( x i )  f A ( x i )  0.5 A ( x i )
t
i 1
(1)
is an information entropy measure of intuitionistic fuzzy set A .
Definition 3. The function S : IF ( X )  IF ( X )  [0,1] is defined as the similarity between IFSs if the following
conditions hold.
(1) S ( A, B)  0 , for all A, B  IF ( X ) ;
(2) S ( A, B )  1 , iff A  B .
(3) if A  B  C , then S ( A, C )  S ( A, B ) and S ( A, C )  S ( B, C ) .
Definition 4. For any two intuitionistic fuzzy sets
A  {( xi ,  t A ( xi ), f A ( xi ) ) / xi  X } ,
B  {( xi ,  t B ( x i ), f B ( x i ) ) / x i  X } , a similarity measure between them is defined as
n
1
2n
S ( A, B )  1 

2
2
2
[ t A ( xi )  t B ( x i )  f A ( xi )  f B ( xi )   A ( xi )   B ( xi ) ] ,
and
(2)
i 1
For convenience, according to the work of Xu [27], we call a~  a , b  an intuitionistic fuzzy number (IFN), if
0  a  b 1.
Definition 5. Let a~1  a1 , b1  and a~2  a 2 , b2  be two IFNs, two intuitionistic fuzzy aggregation operators are
defined as
a~1  a~2  a1  a 2  a1 a 2 , b1b2 
(3)
w
w
~
wa  1  (1  a ) , b  , w  0 .
1
1
1
3. EARLY WARNING EVALUATION METHOD
EMERGENCY
AND
DECISION MECHANISM
FOR
CITY
As we know, the city significant emergency will possibly face to many kinds of risk factors with different probabilities.
Especially in the uncertain emergency environment, the accurate value of risk factor is difficult to measure. However, it
can be easily evaluated by intuitionistic fuzzy linguistic term in the real-life world. By intuitionistic fuzzy linguistic
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 2, Issue 3, March 2013
ISSN 2319 - 4847
term, we can conveniently represent the possibility and the severity of loss of each risk factor. Through the fuzzy risk
analysis method, we can correctly estimate the risk grade of city significant emergency.
Generally, by questionnaire survey and statistical analysis from some field experts and emergency managers we can
easily get some important risk factors of city significant emergency. As we know, the risk factors that incur the city
significant emergency mainly include the economy risk, the environment risk, the humanity risk, and the traffic jam
risk, public health risk, as well as the emergency facility risk, etc. Suppose the set of all risk factors of city significant
emergency is denoted by U  {u1 , u 2 , , u m } . Generally, the risk factor is intuitionistic fuzzy concept, for example,
serious economic recession, severe environment pollution, wicked emergency broadcasting, bad public health,
incomplete emergency facility, and so on. As we are aware, the accurate values of the severity of loss and the occurring
probability of each risk factor are difficult to measure in uncertain setting. On the contrary, government managers and
related field experts tend to evaluate the possibility and the severity of loss of the above uncertain risk factors in city
significant emergency by using intuitionistic fuzzy language terms like P = {Very Low, Low, Medium, High, Very
High} and R = {Critical, Serious, Medium, Weak, Neglectful} rather than by using accurate real numbers.
In order to simplify the treatment of judgment expression, a unified set of linguistic variables is predetermined in
this paper, which can be adapted to every risk factor of city significant emergency from the satisfaction perspective as
shown in Table 1.
Table 1: Linguistic terms for rating the severity of loss of the risk factors in city significant emergency
Linguistic terms
Critical (C)
Serious (S)
Medium (M)
Weak (W)
Neglectful (N)
IFNs
<0.9, 0.1>
<0.7, 0.2>
<0.5, 0.4>
<0.3, 0.6>
<0.1, 0.9>
where each linguistic term is assigned as an intuitionistic fuzzy number, for example, W=<0.3, 0.6> represents the
membership is 0.3 and non-membership is 0.6, indicating the degree of strength lies in interval [0.3, 0.4], That is to
say, the severity of the loss of the risk factor is weak.
In order to determine the risk grade of city significant emergency and provide early warning in time, we should set the
different risk grades firstly. For convenience, the five risk grades of city significant emergency are pre-established and
characterized by the following intuitionistic fuzzy linguistic terms as listed in Table 2.
Table 2: Linguistic terms for rating the warning grade of city significant emergency
Linguistic terms
Extremely high (EH)
Very high (VH)
Fair high
(FH)
Medium
(M)
Low
(L)
IFNs
<0. 9, 0. 1 >
<0. 8, 0. 2>
<0. 6, 0..3>
<0. 4, 0. 5>
<0. 2, 0. 7>
Here, we denote all the five risk grades by the set G  { G1 (EH), G 2 (VH), G3 (FH), G 4 (M), G5 (L)}. Based on the
above risk analysis and the previous formulae, here we give the intuitionistic fuzzy comprehensive risk evaluation
process for the city significant emergency involved intuitionistic fuzzy risk evaluation value under uncertain
environment.
Step 1. Let U be the set of all fuzzy risk factors {u1 , u 2 , , u m } of city significant emergency, and given the
judgment set V  {v1 , v 2 ,  , v n } for risk occurring probability, v j ( j  1,2, , n) denotes the different probability grade
~
of the occurrence of each risk factor. Assume the fuzzy judgment matrix is D  (~
r )
, ~
r is the intuitionistic fuzzy
ij mn
ij
membership value of risk factor u i with respect to the judgment criteria v j , which can be given by the knowledge and
experience of field experts.
Step 2. By using entropy formula (1), we can compute the entropy of each intuitionistic fuzzy value in the
intuitionistic fuzzy judgment matrix and get the entropy matrix of this judgment matrix as D  (hij ) mn , where
h = E (~
r ).
ij
ij
Step 3. Normalize the entropy values in the above decision matrix by using the following equation
hij 
hij
max j hij
Volume 2, Issue 3, March 2013
,
j  1,2,  , n , i  1,2,  , m .
(4)
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ISSN 2319 - 4847
And the normalized entropy matrix is expressed as D  (hij ) mn .
Step 4. Calculate the occurring probability of each risk factor u i by applying formula
n
1

hij
j 1
wi 
m
m
,
n

i 1
i  1,2,  , m .
(5)
hij
j 1
Step 5. Calculate the fuzzy comprehensive risk value according to the above probability and the severity of loss of
each risk factor in city significant emergency by the following formula
m
R   wi R i
(6)
i 1
where Ri is the severity of loss of the risk factor u i .
Step 6. Calculate the similarity measure S ( R , G j ) between the intuitionistic fuzzy comprehensive risk value R and
each pre-established risk grade G j , where G j is the jth risk grade in the pre-established risk grade set
G  { G1 (EH), G 2 (VH), G3 (FH), G 4 (M), G5 (L) }.
Step 7. Determine the risk grade of the unexpected city significant emergency.
By means of the similarity degree calculated, we can determine the risk grade of the uncertain city significant
emergency. If k  arg max j {S ( R, G j ) / 1  j  5} , then the unexpected city significant emergency should belong to the
given risk grade G k .
Step 8. According to the estimated early warning grade, we can design the decision mechanism and adopt the
corresponding emergency response or strategy to avoid the occurrence of city emergency or decrease the losses of city
significant emergency as following Table 3.
Table 3: Decision mechanism for the corresponding early warning grade of city significant emergency
Early warning grade
G1 (Extremely High marked by Red alarm)
G 2 (Very High marked by Orange alarm)
G3
(Fairly High marked by Yellow alarm)
G4
(Medium marked by Blue alarm)
G5
(Low marked by Green alarm)
Emergency decision mechanism
Mobilize ambulance and transport urgent needs
Coordinate emergency management among different
municipal zones and districts
Monitor the safety hazard in some important city areas
and estimate the public interest losses of intimidate
Examine the procedures and facilities for coping with
emergency and notify citizens to take some necessary
safety measures
Keep education and training in safety and get ready for
dealing with possible emergency
4. NUMERICAL EXAMPLE
Recently, emergency managers and field experts usually tend to employ intuitionistic fuzzy values to evaluate the
uncertain city emergency with respect to various earning indexes. In this section, we give a numeric example to
illustrate the application of the proposed intuitionistic fuzzy information entropy measure and similarity measure in
early warning degree evaluation and decision making for uncertain city significant emergency.
Example 1. Now suppose the city government try to design an emergency decision mechanism and carry out some
emergency rescue measures, it requires the emergency management monitor all the uncertain index information of
possible city emergency and evaluate the comprehensive risk value of city emergency. Assume the set of risk factors
U ={ u1 (serious environment disruption and bad public health condition), u 2 (disloyal disaster report), u3 (incomplete
emergency facility), u 4 (severe traffic jam)} must be taken into account for the city significant emergency. And the
occurring probability of each risk factor is unknown, but may be evaluated by the intuitionistic fuzzy judgment criteria
in V  { v1 (Very Low), v 2 (Low), v 3 (Medium)， v 4 ( High), v 5 ( Very High)}. The evaluating results are expressed by
an intuitionistic fuzzy comprehensive judgment matrix, where v j ( 1  j  5 ) denotes the different occurring possibility
of each risk factor of city significant emergency as in Table 4. And the severity of loss of each risk factor is given by
intuitionistic fuzzy linguistic term from the related emergency management experts. Assume we know that the severity
of loss of the above four risk factors of city significant emergency are serious, medium, weak and critical, respectively.
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Volume 2, Issue 3, March 2013
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Table 4: Intuitionistic fuzzy judgment of the occurring probability of risk factors in city significant emergency
Risk factor
v1
v2
v3
v4
v5
u1
<0.1, 0.8>
<0.3, 0.5>
<0.5, 0.4>
<0.8, 0.1>
<0.6, 0.3>
u2
<0.7, 0.2>
<0.6, 0.2>
<0.8, 0.1>
<0.5, 0.3>
<0.9, 0.1>
u3
<0.5, 0.4>
<0.8, 0.1>
<0.1, 0.5>
<0.25, 0.65>
<0.2, 0.5>
u4
<0.6, 0.3>
<0.4, 0.6>
<0.3, 0.7>
<0.2, 0.6>
<0.3, 0.4>
Our main task is to determine the early warning grade of the city significant emergency involved intuitionistic
fuzzy value. That is to decide which risk grade, out of the five grades G1 , G 2 ,  , G5 , the unexpected city emergency
belongs to. In what follows we employ the intuitionistic fuzzy entropy measure to calculate the occurring probability of
each fuzzy risk factor and the total risk value of city significant emergency, and then help the related city emergency
management department adopt the corresponding decision mechanism to control and decrease the comprehensive risk
of city emergency.
~
First, we regard Table 4 as the intuitionistic fuzzy comprehensive judgment matrix D  (~
rij ) 45 of risk factors
~
with respect to all the judgment criteria, where r represents the intuitionistic membership value of risk factor u with
ij
i
respect to probability grade v j , for example, ~
r21  0.8,0.1  represents the true membership and the false membership
of risk factor u 2 belong to the occurring probability grade v1 are 0.8 and 0.1, respectively.
By using the entropy formula (1), we can compute the information entropy of each intuitionistic fuzzy value in the
above judgment matrix and get the following entropy matrix
D  (hij ) 45
 0.1765


 0.3333

 0.8182


 0.5385

0.6667 0.8182 0.1765 0.5385 


0.4286 0.1765 0.6667 0.1579 
.
0.1765 0.4286 0.4286 0.5385 


0.6667, 0.4286 0.4286 0.8182 

With formula (4), we transform the above entropy matrix to the normalized entropy matrix below.
 0.2157 0.8148 1.000 0.2157 0.6582 




 0.4999 0.6429 0.2647 1.000 0.2368 
.
D  (hij ) 45  
 1.0000 0.2157 0.5238 0.5238 0.6582 




 0.6582 0.8148 0.5238 0.5238 1.0000 


Then, by the formula (5) we can compute the occurring probability of each risk factor of the city emergency by the
5
1

hij
j 1
formula wi 
4
4
i 1
, i  1,2,  ,4 .
5

hij
j 1
Thus, the probability vector of all the risk factors of city significant emergency are obtained as W =( 0.238, 0.206,
0.241, 0.315).
Next, according to the given severity of loss of each risk factor, we get
( R1 , R 2 , R3 , R 4 )  { Serious, Medium, Weak, Critical, }
={<0.7, 0.2>, <0.5, 0.4>, <0.3,0.6>, <0.9,0.1>} .
Volume 2, Issue 3, March 2013
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Volume 2, Issue 3, March 2013
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From the previous formulae (3), (6), we calculate the intuitionistic fuzzy comprehensive risk value as
4
R   wi Ri = 0.238R1  0.206R 2  0.241R3  0.315R 4
i 1
=  0.7108,0.2417  .
Then, according to the similarity formula (2) between intuitionistic fuzzy values, we calculate the similarity measures
between the calculated fuzzy comprehensive risk value and each given risk grade in
G  { G1 (EH), G 2 (VH), G3 (FH), G 4 (M), G5 (L) } as follows.
S ( R, G1 ) =0.8295,
S ( R , G 4 ) =0.7118,
S ( R , G 2 ) =0.9227,
S ( R, G 5 ) =0.5133.
S ( R , G 3 ) =0.904,
Since S ( R , G 2 ) > S ( R , G 3 ) > S ( R, G1 ) > S ( R , G 4 ) > S ( R , G 5 ) ,
i.e., 2  arg max j {S ( R , G j ) / G j  G} ,
then the comprehensive risk of city significant emergency should belong to G 2 grade (the second serious grade), and
the risk of this city significant emergency may be “Very High” and marked by orange alarm. That is to say, the
unexpected city significant emergency will undertake some risk of grade G 2 . The related city emergency management
department will raise the corresponding warning and take emergency mechanism and strategy to coordinate all kinds of
urgent management facilities among different municipal zones and districts to decrease the “very high” occurrence of
the unexpected city emergency before implementing some emergency response.
5. CONCLUSION
In this paper, we propose an intuitionistic fuzzy entropy measure to calculate the occurring probability of each risk
factor, it is then used to compute the fuzzy comprehensive risk value of city significant emergency. Finally, according
to the similarity measure between the evaluated intuitionistic fuzzy comprehensive risk value and each given risk grade,
we can assign the city significant emergency to the proper warning grade, which can help the related city emergency
management department make the correct decision mechanism in accord with the early warning evaluation result.
ACKNOWLEDGEMENT
This work is supported by the Humanities and Social Sciences Research Youth Foundation of Ministry of Education of
China (No. 12YJCZH281), the Guangzhou Social Science Planning Project “The study of early warning index selection
and urgent decision mechanism for city significant emergency in uncertain environment” (No. 2012GJ31), the National
Statistical Science Research Planning Project (No. 2012LY159), the National Natural Science Foundation (Nos.
61202271, 60974019, 61273118, 61070061, 60964005), the Guangdong Province Natural Science Foundation (No.
S2012040007184, S2012010010570, 9451009001002686 ), the Youth Project of Humanities and Social Sciences
Research of Ministry of Education of China (No. 10YJC790104 ), the Fundamental Research Funds for the Central
Universities in China, and the Guangdong Province High-level Talents Project.
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Volume 2, Issue 3, March 2013
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AUTHOR
Qiansheng Zhang born in Jiangxi province on July 31, 1975, received his Ph D in Mathematics in 2004 from School
of Mathematics and Computation Sciences, Zhongshan University, Guangzhou, Guangdong province, China. His
major field of study is fuzzy control and decision making. His research interests include intelligent information
processing, statistical inference and decision. He is now working at Guangdong University of Foreign Studies, and he is
a professor in school of Informatics, Guangdong University of Foreign Studies, Guangzhou, China. He has published
more than twenty journal papers in the related area. The current research field is fuzzy reasoning , risk management
and decision making, as well as intelligent computing.
Yirong Huang born in1976, received his Ph D in Statistics in 2004 from School of Statistics, Xiamen University,
Xiamen, Fujian Province, China. His major field of study is fuzzy statistical analysis and decision making. His research
interests include risk management, statistical inference and decision. He is now working at Sun Yat-sen University ,
and he is an associate professor in school of Business, Zhongshan University, Guangzhou, China. He has published
ten journal papers in the related area. The current research field is fuzzy risk analysis and decision making.
Volume 2, Issue 3, March 2013
Page 264