Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 242

the RBF networks. The fuzzy logic systems are justified from the human
reasoning point of view and, therefore, the membership functions can have
any suitable form within the range [0, 1], appropriate to representing the
knowledge of a human expert through IF-THEN rules. On the other hand,
RBF networks are based on biological motivations. Therefore, it is difficult
to justify the use of many different kinds of non-homogeneous basis
functions in a single RBF network.

One of the fundamental differences between a neuro-fuzzy network and an RBF
network is that the former takes the linguistic information explicitly into
consideration and makes use of it in a systematic manner, whereas the latter does
not. Furthermore, while using the neuro-fuzzy network, besides the generated
model accuracy we are also concerned about the transparency of the model,
whereas for the RBF network, and also for other types of neural network, we are
only concerned about the model accuracy (black-box modelling).

6.6 Comparison of Neural Network and Neuro-fuzzy Network
Training

We would now like to compare the back-propagation training algorithms for the
multi-layer perceptron networks and neuro-fuzzy networks described in this
chapter. The training algorithms are similar in the following sense:

x Their basic operation, i.e. forward computation and backward training, is

the same, and in order to minimize the sum squared error between the
actual output and the desired output of the network, both of them use either
the same gradient method or the second-derivative-based recursive
algorithm, i.e. the approximate Hessian matrix.

x Both of them are universal approximators and, therefore, well qualified to

solve any nonlinear mapping to any degree of accuracy within the universe
of discourse.

However, they differ distinctly in the following:

x The parameters (weights and biases) of the neural networks have no clear

physical meaning or interpretation (black-box modelling), which makes the
selection of their initial values difficult; thus, they are chosen rather
randomly. On the other hand, the parameters of the neuro-fuzzy networks
have clear physical meaning (membership functions), so that if the
sufficient knowledge about the system to be modelled by the neuro-fuzzy
networks is available, then a good initial parameter setting procedure can
be developed.

x Besides numerical information, linguistic information can also be

incorporated into neuro-fuzzy systems.