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F
X
0,7
0,3
Ability
Y
0,25
0,80
Figure 3.3
Probabilities for two different values of
Y
's ability to perform the task
τ
(as output of the
function
F
)
and
τ
) of the different strengths of the belief sources (in X's point of view: Str
1
,Str
2
,
...
,Str
n
)
that weigh the different contents (Qual-i
s1Y
(
))
.
F
X,Y,
τ
is a
selective and normalizing function
that associates couples
quality-values
/
strengths-of-beliefs
with a probability curve (with all the constraints the probability model
introduces).
In clearer terms,
F
X,Y,
τ
should produce a matrix with
n
rows and two columns, where
the number of rows corresponds with the
number
of
quality-values
that have to be taken
into consideration by the selective process (not necessarily all the values reported by the
belief sources
7
) while the two columns represent the
contents
of the
quality-values
and their
normalized probabilities
respectively (the sum of the probabilities in the second column must
be equal to
1
).
As an example we can show how, starting from Figure 3.2,
F
X,Y,
τ
by selection (for example
the values
0.2
and
0.4
are collapsed in
0.25
) and by normalization (producing
0.7
and
0.3
as
probabilities values) gives the output of the matrix:
0
τ
), Qual-i
s2Y
(
τ
),
...
, Qual-i
snY
(
τ
.
25
0
.
7
0
.
80
0
.
3
or, to see this in a clear visual form see the graph in Figure 3.3
In the following, for the sake of simplicity,
DoC
X
(Qual-i
(s1,
...
sn),Y
(
))
will give as a result the
more probable value of that quality weighted on the basis of its strength and of the probability
of the other results and strengths. In other words,
we reduce the function F to a single number
averaging the complexity of the different values, sources and strengths
.
Given that we postulate that the degree of trust basically is a function of the 'strength' of
the trusting beliefs, i.e. of their
credibility
(expressing both the subjective probability of the
fact and trust in the belief): the stronger
X
's belief in
Y
's competence and performance, the
stronger
X
's trust in
Y
.
τ
7
In some cases maybe there is an integration of some of these values.
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