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What are Neuro-Fuzzy SystemsPowerPoint Presentation

What are Neuro-Fuzzy Systems

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What are Neuro-Fuzzy Systems

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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.

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.

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,

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