An Approach on Merging Agents’ Trust Distributions in a Possibilitic Domain - Agents and Artificial Intelligence - page 282

probability of occurrence. This means that while the predominant behavior of the agent
is driven by τ PEA a and the trust ratings next to it, there is a small probability that the
agent does not follow its dominant behavior. Figure 1(a) demonstrates an example of
the internal trust distribution of an agent. The closer τ PEAK
a

is to τ , the more trustworthy

the agent is and vice-versa.

3.3 Interaction between Agents

When a customer rates a provider's service, its rating depends not only on the provider's
quality of service but also on the customer's personal point of view. In this paper, we
just model the provider's quality of service. In each interaction a trustor agent, say α ,
requests a service from a trustee agent, say β . Agent β should provide a service in
correspondence with its degree of trustworthiness which is implied in its internal trust
distribution. On this purpose, it generates a random value from the domain of T by using
its internal probability distribution of trust. The peak of the internal trust distribution,
τ PEA a , has the highest probability of selection while other trust ratings in T have a
relatively smaller probability to be chosen. This will produce a mostly specific and yet
not deterministic value. Agent β reports the generated value to α which represents the
quality of service of β in that interaction.

3.4 Building Possibility Distribution of Trust

Possibility theory is one of the current theories for addressing uncertainty arising from
variability and ignorance. Variability is due to the fluxing behaviour the system under
study while ignorance is due to lack of sufficient information about the system under
study. Probability distributions are too normative to address all sorts of uncertainty [6].
It can address variability [16], [17], but not ignorance. Ignorance can be represented by
interval analysis or possibility theory [6]. We use possibility theory as it is capable of
addressing both types of uncertainty. Moreover, as mentioned in [16], it is the simplest
theory for addressing incomplete information (ignorance). These are the main factors
guiding us to use the possibility theory for addressing uncertainty in this research.
Once a number of interactions between a trustor agent, α , and a trustee agent, β ,
agent α is completed, we can model the trust distribution of β , by usage of the val-
ues received from β during their interactions. If the number of interactions between
the agents is high enough, the frequencies of each trust rating can almost represent the
internal trust distribution of β . Otherwise, if few interactions are made, the randomly
generated values may not represent the underlying distribution of β 's trust [18]. In order
to model an agent α 's trust with respect to the uncertainty associated with the occur-
rence of each trust rating in the domain, we use possibility distributions which can
present the degree of possibility of each trust rating in T . A possibility distribution is
defined as: Π : T

T Π ( τ )=1 .
We apply the approach of [18] to build a possibility distribution from empirical data
given the desired confidence level. In this approach, first simultaneous confidence in-
tervals for all trust ratings in the domain are measured by usage of the empirical data
(which in our model are derived from interaction among agents). The measured con-
fidence intervals are based on the research presented in [19]. Then, an algorithm is

→ [0 , 1] with max

τ ∈