Expert-Based Method of Integrated Waste Management Systems for Developing Fuzzy Cognitive Map - Complex System Modelling and Control Through Intelligent Soft Computations - page 118

components. These systems have nonlinear behaviour and cannot simply be derived
from summation of analyzed individual component behaviour (Stylos and
Groumpos 2004 ). Feedback mechanisms are important in the analysis of vulnera-
bility and resilience of social-ecological-technical systems. But how to evaluate
systems with direct feedbacks has been a great challenge. FCM was derived from
the fusion of fuzzy logic and theory of cognitive maps. Kosko ( 1986 ) developed the
fuzzy signed directed graphs with feedback in order to represent knowledge in a
comprehensive way. Since the FCM is formed for a selected system by determining
the concepts and their relationships, it is possible to quantitatively simulate the
system considering its parameters. It has to be noted however, that a FCM is
suitable for short term time series analysis and prediction. A FCM is a dynamic
modelling tool in which the resolution of the system representation can be increased
by applying a further mapping. The resulting fuzzy model can be used to analyze,
simulate, and test the in

uence of parameters and predict the behaviour of the
system (Papageorgiou and Kontogianni 2012 ).
According to Papageorgiou and Kontogianni ( 2012 ), the design of a FCM is a
process that heavily relies on the input from experts and/or stakeholders. This
methodology extracts the knowledge from the stakeholders and exploits their
experience on the system

fl

'

is model and behaviour. A FCM is fairly simple and easy
to understand for the participants. With the use of a participatory process it should
be ensured that different interests are used to build up synergies as well as part-
nerships and hence find sustainable solutions as a joint decision (Malena 2004 ).

Even though, the cognitive nature of a FCM makes it inevitably a subjective
representation of the system. The model is not arbitrary as it is built carefully and
re fl exively with stakeholders (Isak et al. 2009 ).

On the basis of a FCM

first step in the designing
process, the number and features of concepts are determined by a group of experts.
After the identi

' s development, during the

cation of the main factors affecting the topic under investigation,
each stakeholder is asked to describe the existence and type of the causal rela-
tionships among these factors and then assesses the strength of these causal rela-
tionships using a predetermined scale, capable to describe any kind of relationship
between two factors, positive and negative.
Starting from the primary elements of a FCM, the ith concept denotes a state, a
procedure, an event, a variable or an input of the system and is represented by Ci i
(i =1,2, , n). Another component of a FCM is the directed edge which connects

the concepts i and j. Each edge includes a weight w ij which represents the causality
between concepts C i and C j . The values of the concepts are within the range [0, 1],
while the values of the weights belong to the interval [

…

1, 1]. A positive value of
the weight w ij indicates that an increase (decrease) in the value of concept Ci i results
to an increment (decrement) of the concept

−

'

s value C j . Similarly, a negative weight
w ij indicates that an increase (decrease) in the value of concept Ci i results to a
decrement (increment) of the concept

'

s value C j , while a zero weight denotes the
absence of relationship between Ci i and C j (Fig. 1 ). Considering the interrelations
between the concepts of a FCM, the corresponding adjacency matrix can easily be
formed.