Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 219

connection weights of the network correspond to the parameters of fuzzy reasoning
(Nauck et al ., 1997).
Gupta (1994) has presented two additional models for fuzzy neural systems.
The first model (Figure 6.1(a)) consists of a fuzzy inference block, followed by a
neural network block, consisting of a multilayer feedforward neural network, the
input of which is fed by the inference block (Fuller, 1995). The neural network
used can be adapted and adequately trained with training samples to yield the
desired outputs.
In the second model (Figure 6.1(b)), the neural network block drives the fuzzy
inference system to generate the corresponding decisions. Hence, the first model
takes linguistic inputs and generates the numerical outputs, whereas the second
model takes numerical inputs and generates the linguistic outputs.

Knowledge
Base

Neural
Inputs

Neural
output

Output /
Decisions

Neural
Network

Fuzzy
Inference

NN-Learning
Algorithm

Figure 6.1. (b) Fuzzy-neural system (second model)

Alternatively, the second approach is to use fuzzy membership functions to pre-
process or post-process signals with neural networks as shown in Figure 6.2. A
fuzzy inference system can encode an expert's knowledge directly and easily using
rules with linguistic labels (Kulkarni, 2001).

L 2

L 3

L 1

f ( x 1 ; c 11 , sig 11 )
f ( x 1 ; c 12 , sig 12 )
f ( x 1 ; c 13 , sig 13 )

x 1

o 1

:
:

:
:

:
:

o 2

f ( x n ; c n1 , sig n1 )
f ( x n ; c n2 , sig n2 )
f ( x n ; c n3 , sig n3 )

x n

o 3

Figure 6.2. Fuzzy-neural model with tuneable membership function

In practice, for optimal tuning of membership functions of the fuzzy logic part
of a neuro-fuzzy system, a reliable skill is required. The incorporated neural
network part of the same system can, using its learning capability, perform on-line