Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 220

tuning of membership functions and gradually improve the performance of the
entire hybrid system. This concept, which became very popular in engineering
applications, was originally proposed and extended to multidimensional
membership functions by Takagi and Hayashi (1991).
Lin and Lee (1991) proposed a neural-network-based model for fuzzy logic
control consisting of a feedforward neural network, the input nodes of which are
fed by input signals and its output nodes delivering the output and decision signals.
Nodes in the hidden layers of the system implement the membership functions and
the fuzzy rules, making up a fuzzy inference system with distributed representation
and learning algorithms of the neural network. Parameters representing
membership functions are determined using any suitable network training
algorithm. Pal and Mitra (1992) proposed a similar model in which inputs are fed
to a preprocessor block, which performs the same functions as that in the above
fuzzy inference system. The output of the preprocessor delivers the fuzzy
membership function values. For each input variable term, linguistic labels such as
low , medium , and high are used. If input consists of n variables, then the
preprocessor block yields m × n outputs, where m represents the number of term
values used in the model. The output of the preprocessor block is then fed to a
multilayer perceptron model that implements the inference engine. The model was
successfully used for classifying vowels in English alphabets. Kulkarni (1998),
again, developed a similar model and successfully used it for multi-spectral image
analysis. Some authors have designed neuro-fuzzy systems incorporating some
processing stages implemented with neural networks and some with a fuzzy
inference system. In another design, a neural-network-based tree classifier was
used. Finally, Kosko (1992) suggested some remarkable neuro-fuzzy models for
fuzzy associative memory (FAM).

x 1 x 2

Layer 1

Layer 2 Layer 3 Layer 5

A 1

E J

x 1

J

3 N

y 1 TS

A 2

y

¦

B 1

E

J output

J

x 2

y 2 TS

3 N

B 2

R1: If X 1 is A 1 and X 2 is B 1 Then y 1 Ts = w 1 0 + w 1 1 X 1 + w 1 2 X 2
R2: If X 1 is A 2 and X 2 is B 2 Then y 2 Ts = w 2 0 + w 2 1 X 1 + w 2 2 X 2

x 1 x 2

Figure 6.3. ANFIS architecture with Takagi-Sugeno-type fuzzy model with two rules

The neuro-fuzzy model ANFIS (adaptive-network-based fuzzy inference system)
of Jang (1993), presented in Figure 6.3, incorporates a five-layer network to
implement a Takagi-Sugeno-type fuzzy system. The proposed model has a
relatively complex architecture for a large number of inputs, and it can process a
large number of fuzzy rules. It uses the least mean square training algorithm in the