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referred to as an adaptive neuro-fuzzy approach and the related fuzzy logic system
as an adaptive fuzzy logic system (Wang, 1994).
6.4 Takagi-Sugeno-type Neuro-fuzzy Network
In the recent years much attention has been paid to deriving an effective data-
driven neuro-fuzzy model because of its numerous advantages. For example,
ANFIS-based (neuro-fuzzy) modelling was initially developed by Jang (1993) and
Jang and Sun (1995), and later on widely applied in engineering. Similarly,
singleton-rule-based and data-driven multi-input single output neuro-fuzzy
modelling was initially developed by Wang and Mendel (1992b) and used for
solving a variety of systems identification and control problems. A similar neuro-
fuzzy network, with an improved training algorithm, was later developed and
applied by Palit and Popovic (1999, 2000a, 2002b) and Palit and Babuška (2001)
for time series forecasting. Because of its advantages compared with ANFIS, at
least as far as model accuracy and the training time are concerned, this similar
model, but with multi-input and multi-output structure, will be used in this chapter
as a neuro-fuzzy forecaster. The advantages of this approach, where an explicitly
Takagi-Sugeno-type multi-input multi-output fuzzy model is used, will be
demonstrated on simulation examples of benchmark problems. Furthermore, the
type of network selected can be regarded as a generalization or upgraded version of
both a singleton-consequent-type multi-input single-output neuro-fuzzy network
and the Takagi-Sugeno-type multiple input single output neuro-fuzzy network of
Palit and Babuška (2001).
To avoid the fine tuning difficulties of initially chosen random membership
functions, an efficient training algorithm for modelling of various nonlinear
dynamics of multi-input multi-output systems is proposed that relies on a Takagi-
Sugeno-type neuro-fuzzy network. The algorithm is further used for training the
neuro-fuzzy network with the available data of a nonlinear electrical load time
series. Thereafter, the trained network is used as a neuro-fuzzy model to predict the
future value of electrical load data. In order to verify its prediction capability with
other standard methods, some benchmark problems, such as Mackey-Glass chaotic
time series and second-order nonlinear plant modelling, are considered.
Furthermore, the neuro-fuzzy approach described here attempts to exploit the
merits of both neural-network and fuzzy-logic-based modelling techniques. For
example, the fuzzy models are based on fuzzy IF-THEN rules and are, to a certain
degree, transparent to interpretation and analysis, whereas the neural-networks-
based black-box model has a unique learning ability.
In the following, the Takagi-Sugeno-type multiple-input multiple-output neuro-
fuzzy system is constructed by multilayer feedforward network representation of
the fuzzy logic system, as described in Section 6.4.1, and its training algorithm is
described in Section 6.4.2. Thereafter, some comparisons between the radial basis
function network and the proposed neuro-fuzzy network are made, followed by
similar comparisons of the training algorithm for neural networks and neuro-fuzzy
networks. Neuro-fuzzy modelling and time series forecasting are subsequently
described and then, finally, some engineering examples are presented.
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