Transcript Chapter 2: Introduction to Microprocessor

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Definition
Bit of History
Why Fuzzy Logic?
Applications
Fuzzy Logic Operators
Operations
Fuzzy Controllers
Controller Structure
Fuzzification
Inference Engine
Defuzzification
Rule Base
Fuzzy Air Conditioner
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Experts rely on common sense when they solve problems.
Fuzzy logic is not logic that is fuzzy, but logic that is used to describe
fuzziness. Fuzzy logic is the theory of fuzzy sets, sets that calibrate
vagueness.
Fuzzy logic is based on the idea that all things admit of degrees.
Temperature, height, speed, distance, beauty – all come on a sliding
scale.
◦ The motor is running really hot.
◦ Tom is a very tall guy.
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Many decision-making and problem-solving tasks are too complex to be
understood quantitatively, however, people succeed by using knowledge
that is imprecise rather than precise.
Fuzzy set theory resembles human reasoning in its use of approximate
information and uncertainty to generate decisions.
It was specifically designed to mathematically represent uncertainty
and vagueness and provide formalized tools for dealing with the
imprecision intrinsic to many engineering and decision problems in a
more natural way.
Boolean logic uses sharp distinctions. It forces us to draw lines
between members of a class and non-members.
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Fuzzy, or multi-valued logic, was introduced in the 1930s by Jan
Lukasiewicz, a Polish philosopher. While classical logic operates with
only two values 1 (true) and 0 (false), Lukasiewicz introduced logic
that extended the range of truth values to all real numbers in the
interval between 0 and 1.
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In 1965 Lofti Zadeh, published his famous paper “Fuzzy sets”. Zadeh
extended the work on possibility theory into a formal system of
mathematical logic, and introduced a new concept for applying natural
language terms. This new logic for representing and manipulating fuzzy
terms was called fuzzy logic.
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Why fuzzy?
As Zadeh said, the term is concrete, immediate and descriptive; we all know what it
means. However, many people in the West were repelled by the word fuzzy, because it is
usually used in a negative sense.
Why logic?
Fuzziness rests on fuzzy set theory, and fuzzy logic is just a small part of that theory.
The term fuzzy logic is used in two senses:
◦ Narrow sense: Fuzzy logic is a branch of fuzzy set theory, which deals (as logical
systems do) with the representation and inference from knowledge. Fuzzy logic, unlike
other logical systems, deals with imprecise or uncertain knowledge. In this narrow, and
perhaps correct sense, fuzzy logic is just one of the branches of fuzzy set theory.
◦ Broad Sense: fuzzy logic synonymously with fuzzy set theory
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ABS Brakes
Expert Systems
Control Units
Bullet train between Tokyo and Osaka
Video Cameras
Automatic Transmissions
Washing Machines
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Fuzzy Logic:
◦ NOT (A) = 1 - A
◦ A AND B = min( A, B)
◦ A OR B = max( A, B)
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A
AB
B
AB
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A
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Used to control a physical system
input
system
controller
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output
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Fuzzification
◦ Scales and maps input variables to fuzzy sets
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Inference Mechanism
◦ Approximate reasoning
◦ Deduces the control action
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Defuzzification
◦ Convert fuzzy output values to control signals
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Conversion of real input to fuzzy set values
e.g. Medium ( x ) = {
◦ 0 if x >= 1.90 or x < 1.70,
◦ (1.90 - x)/0.1 if x >= 1.80 and x < 1.90,
◦ (x- 1.70)/0.1 if x >= 1.70 and x < 1.80 }
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Fuzzy rules
◦ based on fuzzy premises and fuzzy consequences
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e.g.
◦ If height is Short and weight is Light then feet are Small
◦ Short( height) AND Light(weight) => Small(feet)
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Rule base has many rules
◦ so some of the output fuzzy sets will have membership value > 0
◦ Defuzzify to get a real value from the fuzzy outputs
 One approach is to use a centre of gravity method
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Air Temperature
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Set cold {50, 0, 0}
Set cool {65, 55, 45}
Set just right {70, 65, 60}
Set warm {85, 75, 65}
Set hot {, 90, 80}
Fan Speed
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Set stop {0, 0, 0}
Set slow {50, 30, 10}
Set medium {60, 50, 40}
Set fast {90, 70, 50}
Set blast {, 100, 80}
Air Conditioning Controller Example:
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IF Cold then Stop
If Cool then Slow
If OK then Medium
If Warm then Fast
IF Hot then Blast
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0
100
90
80
If Hot
then
Blast
st
Bla
Fa
st
If Warm
then
Fast
70
60
Med
50
40
If Just Right
then
Medium
ium
IF Cool
then
Slow
Slo
w
30
if Cold
then Stop
20
op
St
10
0
Ho
t
W
ar
m
Jus
Rig t
ht
ld
Co
Co
o
l
1
0
45
50
55
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60
65
70
75
80
85
90