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for an agent
a
, compared to other agents in
A
. If the possibility weights of two agents
are equal, say 0.2 and 0.8 for trust ratings
τ
and
τ
, and the number of interactions with
the first agent is much higher than the second agent, we should give more credit to the
first agent's reported distribution of
Π
a→a
D
(
τ
)
,
T
. However, the current model
is unable of doing so. Therefore, we propose to use a Trust Event Coefficient for each
trust value
τ
, denoted by
TEC
(
τ
)
, in order to consider the number of interactions, which
satisfies:
∀
τ
∈
1)
If
m
τ
=0
,
TEC
(
τ
)=0
2)
If
Π
a
S
a
(
τ
)=0
,
TEC
(
τ
)=0
3)
If
m
τ
≥
→
TEC
(
τ
)
m
τ
,
TEC
(
τ
)
≥
Π
a
S
→a
(
τ
)
,
4)
If
m
τ
=
m
τ
and
Π
a
S
→a
(
τ
)
≥
TEC
(
τ
)
,
TEC
(
τ
)
≥
where
τ
T
P
O
a
,
m
τ
is the frequency of the trust rating
τ
in the interactions between
agents
a
S
and
a
. Considering conditions 1) and 2), if the number of occurrences of trust
rating
τ
or its corresponding possibility is 0, then
TEC
(
τ
)
is also zero. Condition 3)
increases the value of
TEC
by increasing the number of occurrences of trust rating
τ
.As
observed in Condition 4), if the number of observances of two trust ratings,
τ
and
τ
are
equal, then the trust rating with higher possibility is given the priority. When comparing
the number of interactions and the possibility value of
Π
a
S
∈
→a
(
τ
)
, the priority is given
first to number of the interactions, and then, to the the possibility value of
Π
a
S
→a
(
τ
)
in order to avoid giving preference to the possibility values driven out of few interac-
tions. The following formula is an example of a
TEC
function which satisfies the above
conditions.
TEC
(
τ
)=
0
,
m
τ
=0
or
Π
a
S
→a
(
τ
)=0
(8)
m
τ
)]
(1
/m
τ
)
+
Π
a
S
→a
(
τ
)
χ
[1
/
(
γ
×
,otherwise
where
γ>
1
is the discount factor and
χ
1
. Higher values of
γ
impede the
convergence of
TEC
(
τ
)
to one and vice-versa.
χ
which is a very large value insures that
the influence of
Π
a
S
→a
(
τ
)
on
TEC
(
τ
)
remains trivial and is noticeable only when the
number of interactions are equal. In this formula, as
m
τ
grows,
TEC
(
τ
)
converges to
one.
TEC
(
τ
)
can be utilized as a coefficient for trust rating
τ
when comparing different
agents. Note that the General Case mentioned above gives the guidelines for merging
successive possibility distributions and
TEC
feature is only used as an attribute when
the number of interactions should be considered and can be ignored otherwise.
Possibility Distribution of Agent
a
S
's Trust in Agent
a
D
6
We
propose
two
approaches for
estimating
the
final
possibility
distribution
of
Π
a
S
→a
D
(
τ
)
,
T
considering different available possible choices. The first ap-
proach is to consider all
K
possibility distributions of
Π
a
S
→a
D
(
τ
)
,
∀
τ
∈
∀
τ
∈
T
and take the
weighted mean of them by giving each distribution
Π
a
S
→a
D
(
τ
)
,
∀
τ
∈
T
a weight equal
