Fuzzy Logic Seminar

8/2/2019 Fuzzy Logic Seminar

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Fuzzy Logic andFuzzy Logic and

Fuzzy SetsFuzzy Sets

SUBMITTED BY: JATINBUDHIRAJAROLL NO. 9


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Sub-topics:

Motivation

History

Fuzzy logicrepresentation

Crisp set Vs Fuzzy set

Membership functions How Fuzzy logic is

applied?

Applications


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Motivation

The termfuzzy logic

refers to a

logic of approximation.

Boolean logic assumes that everyfact is either entirely true or false.

Fuzzy logic allows for varyingdegrees of truth.

Computers can apply this logic torepresent vague and impreciseideas.


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History

Lotfi Zadeh, at the University ofCalifornia at Berkeley, firstpresented fuzzy logic in the mid-1960's.

Zadeh developed fuzzy logic as away of processing data. Insteadof requiring a data element to beeither a member or non-memberof a set, he introduced the idea

of partial set membership.

In 1974 Mamdani and Assilianused fuzzy logic to regulate asteam engine.


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WHAT IS FUZZY LOGIC?

Definition of fuzzy Fuzzy not clear, distinct, or

precise; blurred

Definition of fuzzy logic A form of knowledge representation

suitable for notions that cannot be

defined precisely, but whichdepend upon their contexts.


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FUZZY LOGICREPRESENTATION

For everyproblem mustrepresent in

terms of fuzzysets.

Fastest

Slow

Fast

[ 0.0 0.25 ]

[ 0.25 0.50 ]

[ 0.50 0.75 ]

[ 0.75 1.00 ]

Slowest


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Misconceptions andControversies

Fuzzy logic is same as

imprecise logic

Fuzzy logic is a new way of

expressing probability.

Fuzzy logic will be difficult to

scale to larger problems.


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Sets and Fuzzy Sets

Classical sets either an elementbelongs to the set or it does not.Classical sets are also called crisp(sets).

Fuzzy Set Theory: An object

is either in a set, not in a set, orpartially in a set.

In fuzzy sets, membership is

based on a degree between 0and 1

0 = item not in set1 = item is in set

If degree is between 0 and 1,then this de ree is the de ree


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Membership Functions

To determine what is the membership value ofan object in a set, refer to membershipfunctions of the objects attribute(s).

For example, we may define our membershipfunctions for the three sets Short, Mediumand Tall

Attribute is heightShort

Medium

Tall

0.0

1.0

0.5

1.4 1.5 1.6 1.8 1.9 2.0

1.55

Height (meters)

Membership


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Crisp Logic Operations

AND

OR

NOT

A B A and B

0 0 0

0 1 0

1 0 0

1 1 1

A B A or B

0 0 0

0 1 1

1 0 1

1 1 1

A not A

0 1

1 0


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Fuzzy Logic Operations

NOT: If Fuzzy Statement A is m true, then the

statement Not A is (1.0 m) true.

AND:

If Fuzzy Statement A is m true, andFuzzy Statement B is n true, then theFuzzy Statement A and B is ktrue,where k= min(m,n).

OR: If Fuzzy Statement A is m true, and

Fuzzy Statement B is n true, then theFuzzy Statement A or B is ktrue,


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Rules

Crisp rule:

Example: If Self is Tall and Enemy isShort, then Attack.

The Condition of a Rule:

The condition for this rule is: If Self isTall and Enemy is Short

Fuzzy rule:

Example: If Self is Tall and Enemy isShort, then Attack.

The condition of the rule once again is: IfSelf is Tall and Enemy is Short

Suppose that Self is 0.3 Tall, and Enemy is0.6 Short, then this condition is 0.3 True.


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Building Fuzzy Systems

Fuzzification

Inference

Composition

Defuzzification

Fuzzy Input

Fuzzy Output

Crisp Output

Fuzzification

Rule Evaluation

Defuzzification

Crisp Input

Input

Membership

Functions

Rules

Output

Membership

Functions


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Where is Fuzzy Logicused?

Fuzzy logic is used directlyin very few applications.

Most applications of fuzzylogic use it as the

underlying logic systemfor decision supportsystems.


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Fuzzy SystemApplications

Cement Kiln - first expertsystem to use fuzzy logic

Sendai Subway - mostcelebrated fuzzy logic system

Bullet train between Tokyo andOsaka


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Applications Cont.

ABS Brakes

Expert Systems Video Cameras

Dishwashers

Washing machines

Bus Time Tables


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TEMPERATURECONTROLLER

The problem

Change the speed of a heater fan,based on the room temperature and

humidity. A temperature control system hasfour settings

Cold, Cool, Warm, and Hot

Humidity can be defined by: Low, Medium, and High

Using this we can define

the fuzzy set.


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BENEFITS OF USINGFUZZY LOGIC


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Why Use Fuzzy Logic?

An Alternative Design Methodology WhichIs Simpler, And Faster

Fuzzy Logic reduces the design

development cycle

Fuzzy Logic simplifies design complexity

Fuzzy Logic improves control performance

Fuzzy Logic simplifies implementation

Fuzzy Logic reduces hardware costs


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Limitations of FuzzyLogic

Stability

Learning

Fuzzy Logic control may not scale wellto large or complex problems

Verification and Validation requiresextensive testing (as in any expertsystem).


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CONCLUSION

Fuzzy logic provides analternative way to represent

linguistic and subjectiveattributes of the real world incomputing.

It is able to be applied to controlsystems and other applicationsin order to improve theefficiency and simplicity of thedesi n rocess.


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Fuzzy Logic Seminar

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