# What are Neuro-Fuzzy Systems

AI and Robotics

Oct 20, 2013 (4 years and 8 months ago)

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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