what-when-how
In Depth Tutorials and Information
In Reference 25 the opinion expressed by node j about given predicate p and the
opinion of node i about j are denoted as O p j and O i , respectively. hus, the opin-
ion of node i about p is calculated by the recommendation operator denoted by
[25]:
ij
j
j
j
j
O
=
O O
i
⊗ =
b b b d
i
,
i
,
d
i
+
u
i
+
b u
i
(11.23)
p
p
p
p
p
From the equation we can see that the result of recommendation is based on the
order of the opinions. he joint opinion of node i and node j about the given predi-
cate is calculated by the consensus operator denoted by [25]:
ij
j
j
j
j
j
j
k u u k
=
⊕ =
+
+
(11.24)
O
O O
i
(
b u
i
b u
i
)
k d u
,(
i
d u
i
)
,
i
p
p
p
p
p
p
p
p
p
p
p
p
p
j
j
k
=
u
i
+
u
u u
i
(11.25)
p
p
Based on the small world and scale free theory the trust model in [25] only consid-
ers two parameters in STNs: clustering coefficient and centrality. Centrality deter-
mines the relative importance of a node in the STN. Many centrality measures can
be used to compute this parameter. he clustering coeicient of a node in STN
is used to represent the closeness of the node and neighbors as a clique. It can be
computed as follows:
{ }
e
k k
ik
=
C
)
v v
,
N e
,
E
(11.26)
i
i
k
i
ik
(
1
i
i
where: v i is node i , N i is the neighborhood of the node i , e ik is the link between node
i and node k , and k i is the degree of the node i .
In [25] it also introduces a trust evaluation algorithm to establish and update
the trust relationship as follows: Assume that node i is a newcomer of a network.
We can use the algorithm shown below to compute node i 's trust of node j in the
network (
O i :
Get all opinions about node j . k
)
= {
}
k k
,
,...,
k n
is a set of all the nodes that have
1
2
opinion about node j .
O
net
= (
b
,
d
,
u
)
11.27)
net k
,
net k
,
net k
,
k
i
i
i
i
represents the position of node k i in the whole network.
O k net
i
b
net k i , =
CENTRALITY
(11.28)
d
= −
1
b
u
(11,29)
net k
,
k j
,
k j
,
i
i
i
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