Information Technology Reference
In-Depth Information
where the coefficients
v
i
are defined in (21.2) and the average preference
x
i
is given
by
x
i
=
∑
i
=
j
v
ij
x
j
∑
.
(21.13)
j
v
ij
i
=
Then, the iterative step of the non-linear diffusion mechanism corresponds to a con-
vex combination
x
i
=(
1
−
ε
v
i
)
x
i
+
ε
v
i
x
i
.
(21.14)
The opinion changing aversion mechanism is based on the gradient term
∂
U
x
i
=
u
i
(
x
i
−
s
i
)
.
(21.15)
∂
The non-linearity of the opinion changing aversion mechanism is encoded in the
inertial coefficient
u
i
which modulates the convex combination between the opinion
value
x
i
and the original opinion value
s
i
x
i
=(
1
−
ε
u
i
)
x
i
+
ε
u
i
s
i
.
(21.16)
The full dynamics associated with the cost function
W
acts iteratively on each expert
e
i
through convex combinations of the opinion value
x
i
, the average opinion value
x
i
, and the original opinion value
s
i
x
i
=(
1
−
ε
(
v
i
+
u
i
))
x
i
+
ε
v
i
x
i
+
ε
u
i
s
i
.
(21.17)
The expert
e
i
is in dynamical equilibrium, in the sense that
x
i
=
x
i
, if the following
stability equation holds
x
i
=(
v
i
x
i
+
u
i
s
i
)
/
(
v
i
+
u
i
)
(21.18)
that is, if the present opinion
x
i
coincides with an appropriate weighted average of
the original opinion
s
i
and the average opinion
x
i
.
21.5
Conclusions
In the first part of this paper we introduced a GDSS architecture based on the
Sadegh-Zadeh's diagnostic framework as a spatio-temporal network of collective
actions. Then we discussed some basic issues related to the representation of group
decision making processes, summarizing key concepts stemming from the semi-
nal work of Kenneth Arrow and mostly focused on the modeling of consensual
dynamics. By referring to the fuzzy representation of individual binary fuzzy rela-
tions, an approach to consensus modeling in group based-diagnosis was introduced
combining a soft measure of collective disagreement with an inertial mechanism of
opinion changing aversion. For the future, we would like to extend the analysis of
consensual dynamics considering linguistic preference relations defined on sets of
linguistic summaries coming out from different knowledge sources.
