Two Classes of Stability — Strong Core and Weak Core - Belief-based Stability in Coalition Formation with Uncertainty - page 46

dences

E = { (Director = Spielberg) ∧ (Type = S.F.) } ,

and Example 3.6, where the experience I 3 of agent A 3 are represented
by the rules R1 to R6, we see that rule R1 and rule R2 are fired, and
the corresponding opinion of the agent A 3 is therefore

B 3 = { Good , Averge } .

Note that this does not intend to mean A 3 believes the probability of
any other state value other than 'Average' or 'Good' must be zero.
This does not imply that the probability that the quality of the cur-
rent movie is average, and that is good, are both

1

2 ,either.Inmost
applications including the current scenario, the obtained samples (i.e.,
the agents' experience rules) are far too sparse to provide any mean-
ingful assessment to the probabilistic distribution of the state values.
Rather, the opinion

B 3 = { Good , Averge }

should be understood as the following statement from agent A 3 :'From
my (i.e., agent A 3 's) limited (self-conflicting) experience so far, I have
reason to believe the quality of the current movie (i.e., state) may be
either average or good.'

The situation for agent A 1 is simpler. As evidences

Example 3.8

are

E = { (Director = Spielberg) ∧ (Type = S.F.) }

in Example 3.5, there are totally 3 rules in agent A 1 's experience rules
that are fired, which correspond to the previous cases when agent
A 1 watched E.T. the Extra-Terrestrial , The Lost World ,and Jurassic
Park . Hence the corresponding opinion of agent A 1 is

B 1 = { Good , Good , Good } ,

or simply { Good } . It is important to note that, again, this does not in-
tend to mean that agent A 1 believes the probability that the quality of