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

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.

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 Go back

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 B

A B A B AGo

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Used to control a physical system

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inputsystem

output

controller

Fuzzification◦ Scales and maps input variables to fuzzy sets

Inference Mechanism◦ Approximate reasoning◦ Deduces the control action

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

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

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

• Set stop {0, 0, 0}• Set slow {50, 30,

10}• Set medium {60, 50,

40}• Set fast {90, 70, 50}• Set blast {, 100,

80}Go back

Air Conditioning Controller Example:

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

10

20

30

40

50

60

70

80

90

100

0

1

45 50 55 60 65 70 75 80

0

85 90

if Coldthen Stop

IF CoolthenSlow

If Just Rightthen

Medium

If WarmthenFast

If HotthenBlast

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