Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 221

forward computation to determine the linear consequents of the Takagi-Sugeno
rules, while for the optimal tuning of an antecedent membership function
backpropagation is used (Kim and Kim, 1997).
The neuro-fuzzy model of Chak et al. (1998) can locate the fuzzy rules and
optimize their membership functions by competitive learning and a Kalman filter
algorithm. The key feature is that a high-dimensional fuzzy system can be
implemented with fewer rules than that required by a conventional Sugeno-type
model. This is because the input space partitions are unevenly distributed, thus
enabling a real-time network implementation.
The approach of Nie (1997) concerns the development of a multivariable fuzzy
model from numerical data using a self-organizing counterpropagation network.
Both supervised and unsupervised learning algorithms are used for network
training. Knowledge can be extracted from the data in the form of a set of rules.
This rule base is then utilized by a fuzzy reasoning model. The rule base of the
system, which is supposed to be relatively simple, is updated on-line in an adaptive
way (in terms of connection weights) in response to the incoming data.
Cho and Wang (1996) developed an adaptive fuzzy system to extract the IF-
THEN rules from sampled data through learning using a radial basis functions
network. Different types of consequent, such as constants, first-order linear
functions, and fuzzy variables are modelled, thereby enabling the network to
handle arbitrary fuzzy inference schemes. There is not an initial rule base, and
neither does one need to specify in advance the number of rules required to be
identified by the system. Fuzzy rules are generated (when needed) by employing
basis function units.
Wang and Mendel (1992a) described a fuzzy system by series of basis
functions, which are algebraic superpositions of membership functions. Each such
basis function corresponds to one fuzzy logic rule. An orthogonal least squares
training algorithm is utilized to determine the significant fuzzy logic rules
(structure learning) and associated parameters (parameter learning) from input-
output training pairs. Owing to the possibility of acquiring and interpreting the
linguistic IF-THEN rules by human experts, the fuzzy basis function network
provides a framework for combining both numerical and linguistic information in a
uniform manner.
Zhang and Morris (1999) used a recurrent neuro-fuzzy network to build long-
term prediction models for nonlinear processes. Process knowledge is initially used
to partition the process operation into several local fuzzy operating regions and
also to set up the initial fuzzification layer weights. Membership functions of fuzzy
operating regions are refined through training, enabling the local models to learn.
The global model output is obtained by centre-of-gravity defuzzification involving
the local models.
6.2.1 Fuzzy Neurons
The perceptron or processing unit described in Chapter 3, which employs
multiplication, addition, and the sigmoid activation function to produce the
nonlinear output from the applied input, is generally known as a simple neural
network . However, if their architectures are extended by adding other mathematical