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Title: Fuzzy Systems and Control G

1
Fuzzy Systems and ControlGünay Karli, Ph.D.
2
Before we begin some clever people have said in
the past
3
Precision is not truth. Henri Matisse
4
So far as the laws of mathematics refer to
reality, they are not certain. And so far as they
are certain, they do not refer to
reality. Albert Einstein
5
As complexity rises, precise statements lose
meaning and meaningful statements lose precision.
6
(No Transcript)
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What is Fuzzy Logic
Fuzzy logic is a convenient way to map an input
space to an output space.
8
What is Fuzzy Logic
Fuzzy logic is a convenient way to map an input
space to an output space. With
restaurant, a fuzzy logic system can tell you
what the tip should be. With your
specification of how hot you want the water, a
fuzzy logic system can adjust the faucet valve to
the right setting. With information about
how far away the subject of your photograph is, a
fuzzy logic system can focus the lens for you.
With information about how fast the car is
going and how hard the motor is working, a fuzzy
logic system can shift gears for you.
9
What is Fuzzy Logic
A graphical example of an input-output map
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What is Fuzzy Logic
The black box can contain any number of things
fuzzy systems, linear systems, neural networks,
differential equations, interpolated
multidimensional lookup tables, .
11
Why use Fuzzy Logic
"In almost every case you can build the same
product without fuzzy logic, but fuzzy is faster
12
Why use Fuzzy Logic
• Here is a list of general observations about
fuzzy logic
• Fuzzy logic is conceptually easy to understand.
• Fuzzy logic is flexible
• Fuzzy logic is tolerant of imprecise data.
• Fuzzy logic can model nonlinear functions of
arbitrary complexity.
• Fuzzy logic can be blended with conventional
control techniques.
• Fuzzy logic is based on natural language.

13
When NOT to Use Fuzzy Logic
If you find Fuzzy Logic is not convenient, try
something else. If a simpler solution already
exists, use it.
14
An Intoductory ExampleFuzzy vs. Non-Fuzzy
What is the right amount to tip your
waitperson? The Basic Tipping Problem. Given a
number between 0 and 10 that represents the
quality of service at a restaurant (where 10 is
excellent), what should the tip be?
15
An Intoductory Example Tipping Problem The
Non-Fuzzy Approach
The tip always equals 15 of the total bill Tip?
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An Intoductory Example Tipping Problem The
Non-Fuzzy Approach
Because service is rated on a scale of 0 to 10,
you might have the tip go linearly from 5 if the
service is bad to 25 if the service is
excellent. Tip?
17
An Intoductory Example Tipping Problem The
Non-Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant, what should the tip be?
18
An Intoductory Example Tipping Problem The
Non-Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant, Suppose you want the service to be a
more important factor than the food quality.
Specify that service accounts for 80 of the
overall tipping grade and the food makes up the
other 20. what should the tip be?
19
An Intoductory Example Tipping Problem The
Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant,
• capture the essentials of this problem
• leave aside all the factors that could be
arbitrary
• what really matters in this problem

20
An Intoductory Example Tipping Problem The
Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant,
Tipping Problem Rules Service Factor If
service is poor, then tip is cheap If service is
good, then tip is average If service is
excellent, then tip is generous
21
An Intoductory Example Tipping Problem The
Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant,
Tipping Problem Rules Service Factor If service
is poor, then tip is cheap If service is good,
then tip is average If service is excellent, then
tip is generous
Tipping Problem Rules Food Factor If food is
rancid, then tip is cheap If food is delicious,
then tip is generous
22
An Intoductory Example Tipping Problem The
Fuzzy Approach
The Extended Tipping Problem Given two sets of
numbers between 0 and 10 (where 10 is excellent)
that respectively represent the quality of the
service and the quality of the food at a
restaurant,
Tipping Problem Rules Service Factor If service
is poor, then tip is cheap If service is good,
then tip is average If service is excellent, then
tip is generous
Tipping Problem Rules Food Factor If food is
rancid, then tip is cheap If food is delicious,
then tip is generous
Tipping Problem Both Service and Food
Factors If service is poor OR the food is
rancid, then tip is cheap If service is good,
then tip is average If service is excellent OR
food is delicious, then tip is generous
23
An Intoductory Example Tipping Problem The
Fuzzy Approach
Tipping Problem Both Service and Food
Factors If service is poor or the food is
rancid, then tip is cheap If service is good,
then tip is average If service is excellent or
food is delicious, then tip is generous
24
An Intoductory Example Tipping Problem The
Fuzzy Approach
Tipping Problem Both Service and Food
Factors If service is poor or the food is
rancid, then tip is cheap If service is good,
then tip is average If service is excellent or
food is delicious, then tip is generous
How are the rules all combined? How do
I define mathematically what an average tip is?
25
Fuzzy Logic System
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Fuzzy Logic SystemFuzzy Inference Diagram
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Fuzzy Logic SystemA 2 input 1 output FLS
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Implementation of FLS
tip 16.7
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Building System with the MATLAB Fuzzy Logic
Toolbox