Expert-Based Method of Integrated Waste Management Systems for Developing Fuzzy Cognitive Map - Complex System Modelling and Control Through Intelligent Soft Computations - page 128

The other input data set was the range of historical data consisting of sequences
of the state vectors. According to Demirbas ( 2011 , den Boer and Lager 2007 ,
Graymore et al. 2008 , Langa et al. 2006 , Morrissey and Browne 2004 , Wilson et al.
2001 , van de Klundert and Anschutz 1999 , Thorneloe et al. 1999 ), the trend of the
studied factors was assessed by values between 0 and 1 from the 1980s to the
2010s. The sequences of the state vector were designed on the basis of the literature
and therefore it may be assumed that they specify soundly the role of the factors
according to changes in the legislation, the available techniques, the social attitude,
the state of the environment and the economic and institutional context as a time
series (see Table 3 , columns t 0 -

t 4 ).
During the simulation, we selected various values for in order to see how the

λ

parameter in uenced the results of the simulation. The simulation was always

started with the input of the above data. The simulation resulted in somewhat
different iterations according to the value of

fl

. We scaled the initial state of the
system in the [0, 1] interval and we used this model and ran the simulation for 10
iteration cycles. The results are presented below.
From Fig. 7 it can be observed that the system converges to an equilibrium state
which is robust to the initial state variation however, the values of

λ

λ are different in

each simulation. The estimated optimal value of may be determined by comparing

the obtained results with the expert system database.
It may be observed that in the FCM model all factors converge rather fast to a
steady state. After the

λ

five iterations the transient behaviour seems to end and
the FCM approaches an obviously stable state where each concept assumes a
constant value (a

rst

, between 0.5 and 0.9). While the
qualitative behaviour of the simulation result is virtually independent from the
steepness, the actual constant values to which the concept in

' plateau ' , depending on

λ

uence state converges
are more or less similar, thus after normalization, the results are very consistent.
The initial states of the factors are known from Table 2 . The

fl

final states of the

concepts computed for each are shown in Table 4 .

The average results of the simulation with different

λ

values are presented in the
last column of Table 3 . As IWMS are sophisticated and complex systems, priorities
and targets need to be set up at the early stage of planning and implementation. The
technical, environmental, economic, legal, social and institutional factors need to be
balanced to attain sustainable waste management (Kurian 2006 ). Assuming, that the

λ

Table 3 The sequences of the state vectors
t 0 t 1 t 2 t 3 t 4 FCM averages

Technical 0.20 0.35 0.60 0.75 0.80 0.80

Environmental 0.15 0.20 0.40 0.60 0.80 0.71

Economic 0.10 0.15 0.30 0.50 0.70 0.62

Social 0.10 0.15 0.20 0.40 0.60 0.56

Legal 0.10 0.30 0.50 0.70 0.80 0.71

Institutional 0.10 0.20 0.30 0.50 0.60 0.58