Download - Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
2/22
Sub-topics:
Motivation
History
Fuzzy logicrepresentation
Crisp set Vs Fuzzy set
Membership functions How Fuzzy logic is
applied?
Applications
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8/2/2019 Fuzzy Logic Seminar
3/22
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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8/2/2019 Fuzzy Logic Seminar
4/22
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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
7/22
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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8/2/2019 Fuzzy Logic Seminar
8/22
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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8/2/2019 Fuzzy Logic Seminar
9/22
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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8/2/2019 Fuzzy Logic Seminar
10/22
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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8/2/2019 Fuzzy Logic Seminar
11/22
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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8/2/2019 Fuzzy Logic Seminar
12/22
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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
15/22
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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8/2/2019 Fuzzy Logic Seminar
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Applications Cont.
ABS Brakes
Expert Systems Video Cameras
Dishwashers
Washing machines
Bus Time Tables
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8/2/2019 Fuzzy Logic Seminar
17/22
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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8/2/2019 Fuzzy Logic Seminar
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BENEFITS OF USINGFUZZY LOGIC
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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
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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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8/2/2019 Fuzzy Logic Seminar
22/22