8 ijaems jan-2016-20-multi-attribute group decision making of internet public opinion emergency with interval intuitionistic fuzzy number

International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-2, Issue-1, Jan- 2016]
Infogain Publication (Infogainpublication.com) ISSN : 2454-1311
www.ijaems.com Page | 43
Multi-attribute Group Decision Making of
Internet Public Opinion Emergency with
Interval Intuitionistic Fuzzy Number
Yutong Feng , Qiansheng Zhang
School of Finance, Guangdong University of Foreign Studies, Guangzhou
Abstract—In this paper, an emergency group decision
method is presented to cope with internet public opinion
emergency with interval intuitionistic fuzzy linguistic
values. First, we adjust the initial weight of each
emergency expert by the deviation degree between each
expert’s decision matrix and group average decision
matrix with interval intuitionistic fuzzy numbers. Then we
can compute the weighted collective decision matrix of all
the emergencies based on the optimal weight of
emergency expert. By utilizing the interval intuitionistic
fuzzy weighted arithmetic average operator one can
obtain the comprehensive alarm value of each internet
public opinion emergency. According to the ranking of
score value and accuracy value of each emergency, the
most critical internet public emergency can be easily
determined to facilitate government taking related
emergency operations. Finally, a numerical example is
given to illustrate the effectiveness of the proposed
emergency group decision method.
Keywords— Internet Public Opinion Emergency,
Interval Intuitionistic Fuzzy Number, Group decision,
Weighted arithmetic average operator, Deviation degree.
I. INTRODUCTION
In recent years, with the enhancing enthusiasm of netizen
participating in discussing public events, the rapid spread
of internet public opinion which is made of complicated
social emotions, attitude and opinion has triggered many
unconventional emergencies. Obviously, the risk of this
type of internet public opinion are increasing rapidly,
severely impairing the harmony and stability of society.
Consequently, it is supposed to make some effective
policies and mechanisms to cope with Internet Public
Opinion Emergency (IPOE)
[ ]1
. Meanwhile, the
establishment of emergency decision-making attributes is
the key to evaluate the Internet Public Opinion
Emergency. In the light of causes and effects of Internet
Public Opinion Emergency, referring to studies
[ ]2 3−
, we
select five attributes, scale of spreading internet opinion,
sensitivity of internet opinion content, critical degree of
emergency, attention from publics and economic losses
respectively. Because the attributes are fuzzy and
qualitative, it is reasonable to utilize fuzzy linguistic value
to evaluate the Internet Public Opinion Emergency.
Nowadays, many scholars have utilized the fuzzy
linguistic value to solve decision making problem. Liu
[ ]4
presented an approach based on 2-tuple to solve Multiple
attribute decision making (MADM) problem. Xu
[ ]5
utilize
the interval intuitionistic fuzzy number developed by
Atanassov
[ ]6
in MADM problem. Among the decision-
making methods towards Internet Public Opinion
Emergency, MADM
[ ]7
is an important method. Not only
can it aggregate experts’ experience from various
departments, but also it can avoid the false decision from
individual due to the lack of knowledge. Nevertheless,
while aggregating the decisions from different experts, it
is significant to adjust the weights of experts after they
make decision so that the final decision will be more
easily adopted by each expert. In this paper, we will boost
group consensus by measuring the deviation degree
between individual decision and collective decision.
II. GROUP DECISION FOR INTERNET
PUBLIC OPINION EMERGENCY
1.1 Basic notations and operational laws
Definition 1
[ ]6
Let X be a nonempty set,
then ( ) ( ){ }~ ~ ~
, ,χ µ χ ν χ χΑ ΑΑ = 〈 〉 ∈Χ is call an
interval intuitionistic fuzzy set, verifying
( ) ( )
~ ~
sup sup 1, ,µ χ ν χ χΑ Α+ ≤ ∈Χ where
( ) [ ]
~
0,1µ χΑ ⊂ and ( ) [ ]
~
0,1 , .ν χ χΑ ⊂ ∈ Χ
Definition 2
[ ]8
The elements of
~
Α are called Interval
Intuitionistic Fuzzy Numbers (IIFNs), each of which
interval of membership degree and interval of non-
membership degree consist. Let the general form of IIFN
shortly denoted as [ ] [ ]( ), , , ,a b c d where
[ ] [ ] [ ] [ ], 0,1 , , 0,1a b c d⊂ ⊂ and 1b d+ ≤ . We will use

5 IIFNs to express 5 linguistic labels, showed as
follows:
( ) [ ] [ ]( )
( ) [ ] [ ]( )
( ) [ ] [ ]( )
( ) [ ] [ ]( )
( ) [ ] [ ]( )
: 0.00, 0.00 , 0.75, 0.95
: 0.00, 0.20 , 0.50, 0.70
: 0.25, 0.45 , 0.25, 0.45
: 0.50, 0.70 , 0.00, 0.20
: 0.75, 0.95 , 0.00, 0.00
Extremely Poor EP
Poor P
Fair F
Good G
Extremely Good EG
Definition 3
[ ]5
For any two linguistic interval
variables, [ ] [ ]( )1 1 1 1 1, , , ,a b c dα =
[ ] [ ]( )2 2 2 2 2, , ,a b c dα = , the operation law as follows:
( ) ( ) ( )( )1 2 1 2 1 2 1 2 1 2[min , ,min , ], max , ,max( , ) ;a a b b c c d dα α =   I
[ ] [ ]( )1 2 1 2 1 2 1 2 1 2 1 2 1 2, , , ;a a a a b b bb c c d dα α+ = + − + −
( ) ( )( )1 1 1 1 11 1 ,1 1 , , , 0.a b c d
λ λ λ λ
λα λ   = − − − − >  
Apply operation laws of IIFNs in Definition 3, we can
obtain the weighted arithmetic average operator of IIFNs.
Theorem 1
[ ]5
Let
( )( ), , , 1,2, ,j j j j ja b c d j nα    = =    L be a collection
of IIFNs. A weighted arithmetic average operator of IIFNs
is defined as:
( ) ( ) ( )1 2
1 1 1 1
, , , 1 1 ,1 1 , , .
j j j j
n n n n
n j j j j
j j j j
f a b c d
ω ω ω ωω
α α α
= = = =
    
= − − − −     
    
∏ ∏ ∏ ∏L
(1)
Where ( )1 2, , ,
T
nω ω ω ω= L is the weight vector
of ( )1,2, , ,j j nα = L [ ]
1
0,1 , 1.
n
j j
j
ω ω
=
∈ =∑
Xu
[ ]5
illustrated weighted arithmetic average operator
and weighted geometry average operator to aggregate
IIFNs. The weighted arithmetic average operator
emphasizes the effect of group while the weighted
geometry average operator emphasizes the effect of
individual. Therefore, we adopt the weighted arithmetic
average operator to aggregate IIFNs.
Definition 4
[ ]5
Let [ ] [ ]( )1 1 1 1 1, , ,a b c dα =
and [ ] [ ]( )2 2 2 2 2, , ,a b c dα = be two
IIFNs, ( ) ( )1 1 1 1 1
1
2
s a c b dα = − + − and
( ) ( )2 2 2 2 2
1
2
s a c b dα = − + − be the scores
of 1α and 2α , ( ) ( )1 1 1 1 1
1
2
h a c b dα = + + + and
( ) ( )2 2 2 2 2
1
2
h a c b dα = + + + be the accuracy degrees
of 1α and 2α , respectively, then
If ( ) ( )1 2 ,s sα α< then 1α is smaller than 2α , denoted
by 1 2 ;α α<
If ( ) ( )1 2 ,s sα α= then
(1) If ( ) ( )1 2 ,h hα α= then 1α is equivalent to 2α ,
denoted by 1 2 ;α α<
(2) If ( ) ( )1 2 ,h hα α< then 1α is smaller than 2α ,
denoted by 1 2.α α<
2.2 The MADM Problem
Let { }1 2, , , mΧ = Χ Χ ΧL be a finite set of Internet
Public Opinion Emergency (IPOE) proposed by
government. For comprehensiveness of the decision-
making, we invite experts ( )1,2, ,kE k q= L from
different departments to make decision and
suppose { }1 2, , , qλ λ λ λ= L be the initial weight vector
of decision experts, where kλ means the initial decision
weight of the expert kE about IPOE. In order to evaluate
IPOE better, we choose attributes ( )1,2, ,jA j n= L from
different aspects to evaluate IPOE and
suppose { }1 2, , , nω ω ω ω= L be the weight vector of
attributes. Assume that the making-decision matrix of
IPOEs ( )
( )k
k ij
m n
R r
×
= is constructed by the decision
expert kE , where
( )k
ijr is an interval intuitionistic fuzzy
number (IIFN), which indicates the value of attribute jA
of IPOE iΧ .
2.3 Adjust the weights of experts
While solving the MADM problem, the decision-making
weights is reliable to affect the weights of experts. For
increasing the accuracy of the final decision, we firstly
aggregate decision matrix ( )1,2, ,kR k q= L together by
initial weight vector of q experts to obtain collective
decision matrix m nR∗
× . Then compute the scores of
IPOE iΧ in decision matrix ( )1,2, ,kR k q= L , m nR∗
× and
define the scores as ( )( )k
is Χ ,

( ) ( )1,2, ,is i m
∗
Χ = L respectively. Finally adjust the
initial expert weight vector { }1 2, , , qλ λ λ λ= L by
evaluating the deviation degree between ( )k
s and s∗
.
In order to synthesize the decision from different experts,
we utilize initial expert weight
vector { }1 2, , , qλ λ λ λ= L to aggregate all decision
matrices ( )
( ) ( )1,2, ,k
k ij
m n
R r k q
×
= = L into a collective
decision matrix
( ) ( )1,2, , , 1,2, , .ij m n
R r i m j n∗ ∗
×
= = =L L As
( )k
ijr is
IIFN, let
( ) ( ) ( ) ( ) ( )
( )( ), , , 1,2, , , 1,2, , , 1,2, ,k k k k k
ij ij ij ij ijr a b c d i m j nk q   = = = =    L L L a
nd apply weighted arithmetic average operator (1) to
aggregate, obviously ijr∗
is
IIFN ( )( ), , ,ij ij ij ij ijr a b c d∗ ∗ ∗ ∗ ∗
   =     , so ijr∗
is defined as
( )
( ) ( )
( ) ( )
( ) ( )
( )1 1 1 1
1 1 ,1 1 , ,
k k k k
q q q q
k k k k
ij ij ij ij ij
k k k k
r a b c d
λ λ λ λ
∗
= = = =
    
= − − − −    
    
∏ ∏ ∏ ∏
(2)
Both
( )k
ijr in kR and ijr∗
in R∗ mean the evaluation value of
attribute jA of IPOE iΧ , but
( )k
ijr represents the value
from expert kE and ijr∗
represents the aggregated value
from all experts. So according weight vector of
attributes { }1 2, , , nω ω ω ω= L , we can aggregate the
attributes in kR and R∗
to obtain aggregated
value ( )( )k
iΧ and ( )i
∗
Χ of IPOE iΧ by applying weighted
arithmetic average operator ( 1), obviously ( )( )k
iΧ
and ( )i
∗
Χ are IIFNs.
So ( )( )
( )1,2, , , 1,2, ,
k
is i m k qΧ = =L L and ( )is
∗
Χ
are defined respectively as follows:
( )( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )1 1 1 1
1 1 ,1 1 , ,
j j j j
n n n n
k k k k k
i ij ij ij ij
j j j j
a b c d
ω ω ω ω
= = = =
    
Χ = − − − −     
    
∏ ∏ ∏ ∏
( ) ( ) ( ) ( ) ( )
1 1 1 1
1 1 ,1 1 , ,
j j j j
n n n n
i ij ij ij ij
j j j j
a b c d
ω ω ω ω∗ ∗ ∗ ∗ ∗
= = = =
    
Χ = − − − −     
    
∏ ∏ ∏ ∏
Apply definition 4, we can obtain scores of( )( )k
iΧ
and ( )i
∗
Χ as follows:
( )( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )1 1 1 1
1 1 1 1 2
j j j j
n n n n
k k k k k
i ij ij ij ij
j j j j
s a c b d
ω ω ω ω
= = = =
 
Χ = − − − + − − − ÷ 
 
∏ ∏ ∏ ∏
(3)
( )( ) ( ) ( ) ( ) ( )
1 1 1 1
1 1 1 1 2
j j j j
n n n n
i ij ij ij ij
j j j j
s a c b d
ω ω ω ω∗ ∗ ∗ ∗ ∗
= = = =
 
Χ = − − − + − − − ÷ 
 
∏ ∏ ∏ ∏
(4)
Definition 5 Let ( )
( )k
k ij
m n
R r
×
= and ( )ij m n
R r∗ ∗
×
= be
two making-decision matrix of IPOEs, the deviation
degree between kR and R∗
is defined as
( ) ( )( )
( )( )
2
1
,
m
k
k i i
i
d R R s s
∗∗
=
= Χ − Χ∑
(5)
( ),kd R R∗
showed in definition 5 reflects the reliability
of expert 'kE s decision, the bigger of
~
R∗
( ),kd R R∗
, the
wider of the opinion deviation between expert kE and
group E ,which can be reflected by weight.
[ ]9
Therefore,
adjust the weights of expert ( )1,2, ,kE k q= L as follows.
( )
( )
( )
1
1
,
1,2, ,
1
,
k
k
q
k
k
d R R
k q
d R R
λ
∗
∗
∗=
= =
∑
L
(6)
2.4 Determination of the most critical Internet Public
Opinion Emergency
After obtaining the adjusted expert weights, we can utilize
the weighted arithmetic average operator of IIFNs (1) to
aggregate all ( )1,2, ,kR k q= L into a collective making-
decision matrix
~ ~
ij
m n
R r∗ ∗
×
 
=  
 
, obviously
~
ijr∗
is
IIFN
~ ~ ~ ~ ~
, , ,ij ij ij ij ijr a b c d∗ ∗ ∗ ∗ ∗
     
=           
as
follows. ( )1,2, , ,i m= L ( )1,2, ,j n= L
( )
( ) ( )
( ) ( )
( ) ( )
( )
~
1 1 1 1
1 1 ,1 1 , ,
k k k k
q q q q
k k k k
ij ij ij ij ij
k k k k
r a b c d
λ λ λ λ∗ ∗ ∗ ∗
∗
= = = =
    
= − − − −    
    
∏ ∏ ∏ ∏
(7)
Then utilize the weighted arithmetic average operator of
IIFNs (1) to aggregate all attributes ( )1,2, ,jA j n= L into
aggregated value to evaluate the each IPOE and we

suppose the aggregated value as
~
i
∗
 
Χ 
 
~ ~ ~ ~~
1 1 1 1
1 1 ,1 1 , ,
j j j jn n n n
i ij ij ij ij
j j j j
a b c d
ω ω ω ω∗
∗ ∗ ∗ ∗
= = = =
              Χ = − − − −                             
∏ ∏ ∏ ∏
Apply definition 4, we can obtain scores
of ( )
~
1,2, ,i i m
∗
 
Χ = 
 
L as follows:
~ ~ ~ ~~
1 1 1 1
1 1 1 1 2
j j j jn n n n
i ij ij ij ij
j j j j
s a c b d
ω ω ω ω∗
∗ ∗ ∗ ∗
= = = =
           
 Χ = − − − + − − − ÷                         
∏ ∏ ∏ ∏
(8)
According to comparison laws in definition 4, we can list
the order of
~
is
∗
  
Χ     
. Therefore, we can determine the
most critical Internet Public Opinion Emergency.
III. ILLUSTRATIVE EXAMPLE
In the section our models and approaches are applied to a
group decision problem of Internet Public Opinion
Emergency (IPOE).
It is presumed that four Internet Public Opinion
Emergencies happened in a city. The emergency decision
department needs to find out the most critical Internet
Public Opinion Emergency. In order to evaluate the
IPOEs better, the emergency decision department
construct 5 attributes as follows. The first attribute 1A is
scale of spreading internet opinion. The second one 2A is
sensitivity of internet opinion content. The third one 3A is
critical degree of emergency. The fourth one 4A is
attention from publics. The fifth one 5A is economic
losses. The weight vector of attributes in IPOEs as The
decision-making section invited three
experts ( )1,2,3kE k = from different departments. In the
light of their academic experience and domain experience,
the emergency decision department determined the initial
weights of experts in group decision
as { } { }1 2 3, , 0.5,0.2,0.3 .λ λ λ λ= =
The experts’ decision matrices of IPOEs are listed as:
Expert 1 'E s decision matrix ( )
( )1
1
4 5
ijR r
×
=
1 2 3 4 5A A A A A
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
1
2
3
0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.00,0.20, 0.50,0.70 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45
0.75,0.95, 0.00,0.00 0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.00,0.20, 0.50,0.70
0.00
Χ
Χ
Χ [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(4
,0.20, 0.50,0.70 0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45
0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.00,0.20, 0.50,0.70 0.00,0.00, 0.75,0.95Χ
( )2
2
4 5
ijR r
×
=
1 2 3A A A
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
1
2
3
0.00,0.20,0.50,0.70 0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45 0.00,0.20, 0.50,0.70
0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.25,0.45,0.25,0.45 0.00,0.20,0.50,0.70 0.00,0.20, 0.50,0.70
0.00
Χ
Χ
Χ [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(4
,0.20,0.50,0.70 0.50,0.70, 0.00,0.20 0.00,0.20, 0.50,0.70 0.25,0.45, 0.25,0.45 0.25,0.45,0.25,0.45
0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.00,0.20, 0.50,0.70 0.00,0.20, 0.50,0.70Χ
( )3
3
4 5
ijR r
×
=
1 2 3A A A
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
1
2
3
0.25,0.45, 0.25,0.45 0.50,0.70,0.00,0.20 0.00,0.20,0.50,0.70 0.25,0.45, 0.25,0.45 0.00,0.20, 0.50,0.70
0.75,0.95, 0.00,0.00 0.25,0.45, 0.25,0.45 0.50,0.70,0.00,0.20 0.00,0.20,0.50,0.70 0.25,0.45, 0.25,0.45
0.00
Χ
Χ
Χ [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(4
,0.20, 0.50,0.70 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45
0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.25,0.45,0.25,0.45 0.00,0.20, 0.50,0.70Χ
Utilize the formula (2), aggregate three decision
matrices 1 2 3, ,R R R by applying initial weight vector of
experts and then obtain initial collective decision
matrix ( )4 5ijR r∗ ∗
×
= as:
1 2 3A A A
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( )
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( )
1
2
3
0.21,0.41,0.29,0.49 0.50,0.70,0.00,0.20 0.06,0.26,0.44,0.64 0.25,0.45,0.25,0.45 0.13,0.34,0.35,0.56
0.71,0.93,0.00,0.00 0.25,0.45,0.25,0.45 0.46,0.66,0.00,0.24 0.13,0.34,0.35,0.56 0.08,0.29,0.41,0.61
0.00
Χ
Χ
Χ [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( )
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( )4
,0.20,0.50,0.70 0.44,0.64,0.00,0.26 0.21,0.41,0.29,0.49 0.25,0.45,0.25,0.45 0.25,0.45,0.25,0.45
0.50,0.70,0.00,0.20 0.25,0.45,0.25,0.45 0.50,0.70,0.00,0.20 0.08,0.29,0.41,0.61 0.00,0.11,0.61,0.82Χ
Utilize weights of
attributes
{ } { }1 2 3 4 5, , , , 0.25,0.10,0.15,0.20,0.30ω ω ω ω ω ω= = ,
aggregate five attributes in decision
matrices 1 2 3, , ,R R R R∗
and
obtain ( )( )
( )( )
( )( )1 2 3
, , ,i i iΧ Χ Χ ( )i
∗
Χ . Then utilize
formula (3), (4) to calculate the scores of

them, ( )( )
( ) ( )( )
( ) ( )( )
( )1 2 3
, , ,i i is s sΧ Χ Χ ( )( )is
∗
Χ as:
while
1i =
( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )1 2 3
1 1 1 10.1285, 0.0044, 0.0307, 0.0744s s s s
∗
Χ = Χ =− Χ = Χ =
while
2i =
( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )1 2 3
2 2 2 20.5534, 0.0946, 0.5674, 0.5203s s s s
∗
Χ = Χ = Χ = Χ =
while
3i =
( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )1 2 3
3 3 3 30.0971, 0.0477, 0.1049, 0.0716s s s s
∗
Χ = Χ = Χ =− Χ =
while
4i =
( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )1 2 3
4 4 4 40.1312, 0.1687, 0.2252, 0.1682s s s s
∗
Χ = Χ = Χ = Χ =
Utilize the formula (5) to evaluate the deviation degree
between 1 2 3, ,R R R and R∗
respectively, denoted
as ( ) ( ) ( )1 2 3, , , , ,d R R d R R d R R∗ ∗ ∗
:
( ) ( ) ( )1 2 3, 0.0060, , 0.1881, , 0.0385,d R R d R R d R R∗ ∗ ∗
= = =
Adjust the weights of experts by formula (6) and
obtain { }1 2 3, ,λ λ λ λ∗ ∗ ∗ ∗
= as:
1 2 30.635, 0.114, 0.251,λ λ λ∗ ∗ ∗
= = =
Utilize the formula (7), aggregate three decision
matrices 1 2 3, ,R R R by applying adjusted weight vector of
expert { }0.635,0.114,0.251λ∗
= and then obtain
adjusted collective decision matrix
~ ~
4 5
ijR r∗ ∗
×
 
=  
 
as
1 2 3 4 5A A A A A
] [ ]) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
] [ ]) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
0.22,0.43, 0.27,0.47 0.50,0.70, 0.00,0.20 0.03,0.23, 0.46,0.67 0.25,0.45, 0.25,0.45 0.17,0.37, 0.32,0.53
0.73,0.94, 0.00,0.00 0.25,0.45, 0.25,0.45 0.48,0.68, 0.00,0.22 0.17,0.37, 0.32,0.53 0.07,0.27, 0.42,0.63
0.00 ] [ ]) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
] [ ]) [ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) [ ] [(
,0.20, 0.50,0.70 0.45,0.65, 0.00,0.25 0.22,0.43, 0.27,0.47 0.25,0.45, 0.25,0.45 0.25,0.45, 0.25,0.45
0.50,0.70, 0.00,0.20 0.25,0.45, 0.25,0.45 0.50,0.70, 0.00,0.20 0.07,0.27, 0.42,0.63 0.00,0.08, 0.65,0.85
Utilize formula (8), obtain the final scores of four Internet
Public Opinion Emergency as
~ ~ ~ ~
1 2 3 40.0904, 0.5361, 0.0784, 0.1603,s s s s
∗ ∗ ∗ ∗
              
Χ = Χ = Χ = Χ =                                   
Therefore, the order of Internet Public Opinion Emergency is
~ ~ ~ ~
3 1 4 2s s s s
∗ ∗ ∗ ∗
              
Χ < Χ < Χ < Χ                                   
, the
most critical emergency is 3Χ .
IV. CONCLUSION
In group decision making of Internet Public Opinion
Emergency, because of the lack of time and incomplete
information, decision experts is easier to evaluate the
emergency with interval intuitionistic fuzzy numbers. To
increase the accuracy of group decision making, a method
based on deviation degree is proposed to adjust initial
weights of experts from their individual decision matrices.
Finally, apply the weighted arithmetic average operator to
yield the collective decision matrix and determine the
most critical Internet Public Opinion Emergency to assist
the emergency decision department to make proper
response.
ACKNOWLEDGEMENTS
This work is supported by the National Social Science
Fund of China (13CGL130).
REFERENCES
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