What are Neuro

Fuzzy Systems
A neuro

fuzzy system is a fuzzy system that uses a
learning algorithm derived from or inspired by
neural network theory to determine its parameters
(fuzzy sets and fuzzy rules) by processing data
samples.
A neuro

fuzzy system can be viewed as a 3

layer
feedforward neural network. The first layer
represents input variables, the middle (hidden) layer
represents fuzzy rules and the third layer represents
output variables.
Nuero fuzzy models
Mamdani Fuzzy Model
The
Mamdani fuzzy model
was proposed as the very first attempt to
control a steam engine and boiler combination by a set of linguistic
control rules obtained from experienced human operators.
two fuzzy inference systems
were used as two controllers to generate the heat input
to the boiler and throttle opening of the engine cylinder,
respectively, in order to regulate the steam pressure in the
boiler and the speed of the engine. Since the plant takes
only crisp values as inputs, we have to use a defuzzifier
to convert a fuzzy set to a crisp value.
Defuzzification
refers to the way a crisp value is extracted from a fuzzy
set as a representative value. The most frequently used
defuzzification strategy is the centroid of area.
Sugeno Fuzzy Model
The
Sugeno fuzzy model (also
known as the
TSK fuzzy
model) was proposed by Takagi,
Sugeno, and Kang in
an effort to develop a
systematic approach to generating fuzzy rules from a given
input

output data set.
A typical fuzzy rule in a Sugeno
fuzzy
model has the form
if z is
A and y is B then z = f ( z ,y )
where
A and
B are fuzzy sets in the antecedent, while
z = f(z,y ) is a crisp function in the consequent. Usually
f ( z , y) is a polynomial in the input variables z and y.
When
f(z,y ) is a first

order
polynomial, the resulting fuzzy
inference system is called a
first

order Sugeno fuzzy model,
which was originally
proposed in
[89], [96]. When f is a
constant, we then have a zero

order
Sugeno fuzzy model,
NEURO

FUZZY CONTROL
Once a fuzzy controller is transformed into an adaptive
network, the resulting ANFIS can take advantage
of all the
NN controller design techniques proposed in
the literature.
u(t)
x(t)
the block diagram of a typical
feedback control system consists of a plant block and a
controller block. The plant block is usually represented by
a set of differential equations that describe the
phy$ical
system
to be controlled. These equations govern the behavior
of the plant state
x ( t )
x(t) =
f(x(t),
u ( t ) ) (plant dynamics),
u(t) = g(x(t)) (controller).
Controller
Plant Dynamics
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