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model from binary to multi-valued event in the probabilistic domain is quite challeng-
ing due to its technical complexity. We use possibility theory which is a flexible and
strong tool to address uncertainty and at the same time it is applicable to multi-valued
domains. BLADE [14] is another recent trust model which considers subjectivity, de-
ception and change. While we address the latter two features, the first one is missing in
our model. The subjectivity reflects the personal point of view of each agent regarding
the quality of a service, which can differ from an agent to another. BLADE considers
the uncertainty arising from variability, however, it does not model the uncertainty due
to ignorance. This is a shortcoming of the probabilistic models which are too normative
to consider all sorts of uncertainty [6] and cannot demonstrate the uncertainty arising
from ignorance .
3
Multi-agent Platform
In this section, we present the components that build the multi-agent environment and
the motivation behind each choice. We first discuss the set of trust values (Section 3.1),
the agent's internal trust distribution (Section 3.2) and the interactions among the agents
(Section 3.3). Later, we describe the formation of the possibility distribution on an
agent's trust (Section 3.4) and the possible agent information manipulations (Section
3.5). Finally, the game scenario in this paper is discussed (Section 3.6).
3.1
Trust Values
Service providers ask customers to provide their feedbacks on the received services
commonly in form of a rating selected from a multi-valued set. The selected rating in-
dicates a customer's degree of satisfaction or, in other words, its degree of trust in the
provider's service. This motivates us to consider a multi-valued trust domain. We de-
fine a discrete multi-valued set of trust ratings denoted by
T
, with
τ
being the lowest,
τ
being the highest and
representing the number of trust ratings. All trust ratings
are within
[0
,
1]
and they can take any value in this range. However, if the trust rat-
ings are distributed in equal intervals, the
i
th trust rating equals to:
(
i
|
T
|
−
1)
/
(
|
T
|−
1)
for
i
=1
,
2
,...,
|
T
|
. For example, if
|
T
|
=5
, then the set of trust ratings is
{
0
,
0
.
25
,
0
.
5
,
0
.
75
,
1
}
.
3.2
Internal Probability Distribution of an Agent's Trust
In our multi-agent platform, each agent is associated with an internal probability dis-
tribution of trust, which is only known to the agent. This allows modelling a specific
degree of trustworthiness in that agent where each trust rating
τ
is given a probability
of occurrence. In order to model a distribution, given its minimum, maximum, peak,
degree of skewness and peakness, we use a form of beta distribution called modified
pert distribution [15]. It can be replaced by any distribution that provides the above
mentioned parameters. Well known distributions, e.g., normal distribution, are not em-
ployed as they do not allow positive or negative skewness of the distribution. In modified
pert distribution, the peak of the distribution, which is denoted by
τ
PEAK
a
, has the highest
