Information Technology Reference
In-Depth Information
The concepts of the Fuzzy Cognitive Model stand for the main characteristics
comprising an abstract model of any system; each concept of the FCM represents a
granular entity such as state, variable, input, output, event, action, goal, trend of the
system that is modeled as an FCM. The value of every concept
C
i
is
A
i
and it results
from the transformation of the real fuzzy value of the system's variable, for which
this concept stands for, in the interval
. Thus, when the initial concept value
is produced, then this value is updated as it is computed through the interaction of
the interconnected concepts with the corresponding weights. Generally, between
two concepts there are three possible types of causal relationships that express the
type of influence from one concept to the other.
[
0
,
1
]
The weight of the arc between
concept
C
i
and concept
C
j
could be positive
which means that an increase
in the value of concept
C
i
leads to the increase of the value of concept
C
j
,anda
decrease in the value of concept
C
i
leads to the decrease of the value of concept
C
j
.
Or there is negative causality
(
W
ij
>
0
)
which means that an increase in the value of
concept
C
i
leads to the decrease of the value of concept
C
j
and vice versa. The value
A
i
of concept
C
i
expresses the degree of its corresponding physical value. Fuzzy
Cognitive Map is used to model the behavior of a system; during the simulation
step, the value
A
i
of a concept
C
i
is calculated by computing the influence of the
interconnected concepts
C
j
's on the specific concept
C
i
following the calculation
rule:
(
W
ij
<
0
)
N
∑
A
(
k
+
1
)
i
A
(
k
)
i
A
(
k
)
j
=
f
(
)+
·
w
ji
(27.1)
j
=
1
,
j
=
i
1,
A
(
k
i
is the value of
concept
C
i
at simulation step
k
,
w
ij
is the weight of the interconnection from concept
C
i
to concept
C
j
and
f
is the sigmoid threshold function:
where
A
(
k
+
1
)
i
is the value of concept
C
i
at simulation step
k
+
1
f
=
(27.2)
+
e
−
λ
x
1
where
λ
is a parameter that determines its steepness. In this approach, the value
λ
=
1 has been used. This sigmoid function is selected since the values
A
i
of the
concepts lie in the interval
[
,
]
0
1
.
27.2.1
Fuzzy Cognitive Maps and Decision Support Systems
Fuzzy Cognitive Maps have been successfully used to develop Decision Support
Systems (FCM-DSS) for control engineering applications [20, 45]; urban design
[55] in banking Business [54]; IT projects risks scenarios [35]; qualitative dynamic
systems in humanities, social sciences and economics [6, 7]. Especially in the med-
ical decision support systems, FCMs have been used for differential diagnosis [13],
to determine the success of the radiation therapy process estimating the final dose
delivered to the target volume [30]; for decision making in obstetrics [43] and many
other applications. FCMs are particularly well suited for such applications, since
