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quantitative analysis, but allows the comparison between nodes, which are attached
by fuzzy activity degrees (de
ned as
'
active
'
:1,
'
inactive
'
:0or
'
active to a certain
degree
: values between 0 and 1), see Stach et al. (
2005
).
During the optimisation of our FCM with BEA, forced mutation (Hatw
'
á
gner and
Horv
th
2012a
) was used to increase the otherwise very low value of genetic
diversity, to speed up computations in this manner. Forced mutation is a simple and
easily implementable operator that slightly modi
á
es some bacteria in the population
if they seem very similar (typically in the
final generations of the optimization).
Forced mutation was applied in all subsequent generations after gene transfer.
The value of
rst
gene of the bacteria. The following 30 genes corresponded to the elements of the
6
used by the transformation function was represented by the
λ
6 connection matrix (without the elements of the main diagonal, which were not
stored).
The FCM determined the values of the factors in the subsequent iterations using
the connection matrix. The goal of using the BEA was to
×
find a connection matrix
that minimizes a difference between the state values obtained from the literature
(see Table
3
) and the generated values of the factors. This difference d is expressed
in Eq.
3
.
X
6
2
d
¼
c½
t
^
c½
t
ð
3
Þ
t
¼
1
where c½
t
denotes the real and
c½
t
the calculated values of factors.
The results of the optimization are contained in the connection matrix presented
in Table
5
. Here
^
= 1, which resulted in d = 0.727 between the obtained and the
experts suggested state vectors. It is rather surprising how far the interrelation
coef
λ
cients obtained by automatic learning (based on the more or less objective
data of the time series observed) are from the coef
cients calculated from the
median of the experts
questionnaires! We have no doubt that the matrix obtained
by learning is rather independent from subjective elements, especially as it resulted
from data obtained throughout a relatively long observation period. The fact that
expert opinions differ so much from the objective reality de
'
nitely poses a question
how deep the insight of waste management experts may be wherever the system on
hand is constituted from a set of complex technical and social subsystems con-
sisting of several mutually in
fl
uencing (and rather
fl
fluctuating) factors.
Table 5 The resulting
optimized connection matrix
C1
C2
C3
C4
C5
C6
C1
0.00
0.39
1.00
1.00
1.00
0.75
−
−
C2
0.21
0.00
1.00
−
1.00
1.00
−
1.00
C3
0.72
1.00
0.00
1.00
1.00
1.00
−
−
−
C4
1.00
0.38
1.00
0.00
1.00
1.00
−
−
−
C5
1.00
1.00
0.75
−
1.00
0.00
−
1.00
C6
1.00
0.82
1.00
1.00
1.00
0.00
−
−
−
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