Expert-Based Method of Integrated Waste Management Systems for Developing Fuzzy Cognitive Map - Complex System Modelling and Control Through Intelligent Soft Computations - page 120

hypothetical FCM could be established. The 75 individual maps were however
merged into a representative, collective map. In this phase we were primarily
interested in investigating how the stakeholders perceive the future prospects of the
IWMS.

3.1 Fuzzy Cognitive Map

In the next two chapters the applied Computational Intelligence Tool Kit will be
brie y described.

As mentioned above, the FCM is a very convenient and simple tool for
modelling complex systems. It is rather popular due to its simplicity and user
friendliness. According to Stach et al. ( 2005 ), human experts are generally rather
subjective and can handle only relatively simple networks therefore there is an
urgent need to develop methods for automated generation of FCM models. The
present research deploys the FCM and applies the BEA for parameter optimization.
An FCM is a fuzzy graph structure representing causal reasoning. Causality is
represented here as a fuzzy relation of causal concepts. The FCM may be used for
dynamic modelling of systems. The FCM approach uses nodes corresponding to the
factors and edges for their interactions, to model different aspects in the behaviour
of the system. These factors interact with each other in the FCM simulation, pre-
senting the dynamics of the original system (Stylos and Groumpos 2004 ). The FCM
has been described as the combination of neural networks and fuzzy logic. Thus,
learning techniques and algorithms can be borrowed and utilized in order to train
the FCM and adjust the weights of its interconnections (Stylos et al. 1997 ).
We have to mention here, that optimization algorithms (e.g. BEA) can be
considered as machine learning algorithms in the sense that the optimized FCM
parameters (the

fl

parameter of the threshold function and the weights of the con-
nection matrix) result in the most realistic description of the examined system
(IWMS in this case). This chapter does not deal with the learning of a huge amount
of data. The goal of this study is to optimize the parameters of FCM

λ

rst, then to
compare the time series generated by this FCM with the time series given in the
literature. Thus the words are used as synonyms in

this paper. If optimization is considered as a kind of learning, the performance
index, learning set and test set can also be identi

' learning ' and ' optimization '

ed.

The performance index corresponds to the objective function (the difference
between the time series generated by FCM using the optimized parameter values
and the time series given in the literature).

￿

￿ The time series given in literature can be considered as the training set.

The information collected from the above mentioned survey generates the
test set.