Intelligent Tuning of Fuzzy Controllers by Learning and Optimization - Fuzzy Modeling and Control: Theory and Applications - page 134

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Fuzzy partitions (IFP-FCM), is the generalization by adding a parameter that allows

to switch on, according to its value, between the IFP-FCM algorithm and the FCM
(Zhu et al. 2009 ).
Another interesting technique is the Evolving Clustering Method (ECM), applied
to set membership functions and fuzzy rules (Kasabov and Song 2002 ). It basically
consists of a single-iteration algorithm for the dynamic on-line clustering of a data set
and begins with an initial set for the first datum. On the basis of Euclidean distances
and the clustering threshold value ( D thr ), the algorithm either adds each datum to an
existing set (updating the center and the radius of the set) or creates a new set for all
subsequent data. The resulting clusters are circular and are used to create Gaussian
membership functions. For that purpose, the center of the set is taken as the center
of the Gaussian function, and the radius is taken as the width.

7.3.2 Neuro-fuzzy Strategies

The main advantage of a fuzzy controller is that it is not necessary an exact mathe-
matical model of the system to be controlled. Moreover, this controller can emulate
the behaviour of expert operators due to knowledge base, using the human expe-
rience, and if-then rules. However, there are some basic aspects in the rule-based
systems that require special attention. One important issue is that nowadays there is
not generalizable method for transforming human knowledge or know-how into the
rule base and database of a fuzzy system. Additionally, tuning of membership func-
tions (MF), rule base and other parameters of the fuzzy systems is done basically by
ad-hoc methods, whereas many open control problems are still waiting for automatic
and effective methods.
One the main advantages of the simplified fuzzy models is that they provide ana-
lytical description of the relationship between the system's input and output; this
property allow us to represent fuzzy models as neural networks and to apply learn-
ing techniques to carry out identification from data. Neuro-Fuzzy Systems (NFS)
appeared in this context merging Artificial Neural Networks (ANN) and Fuzzy Infer-
ence System (FIS). Neuro-Fuzzy systems combine the semantic transparency of rule-
based fuzzy systems with the learning capability of neural networks. Therefore, NFS
are capable of representing systems by means of if-then rules represented in a net-
work structure, which learning algorithms from the area of artificial neural networks
can be applied.
Nowadays, several approaches use neuro-fuzzy systems to control nonlinear sys-
tems or to adjust controllers. Most of them use the pioneering neuro-fuzzy system,
Adaptive Neuro Fuzzy Inference System (ANFIS) (Jang 1993 ) because of its sim-
plicity and its computationally efficient procedure. Several works have been reported
in the last decade using neuro-fuzzy techniques to adjust off-line the structure of the
fuzzy controller. However, the complexity and nonlinear dynamics of real-world
problems require new paradigms to go beyond the current state of the art in neuro-
fuzzy techniques for control purposes. The last generations of computerized systems