Fuzzy Unit 1

8/10/2019 Fuzzy Unit 1

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Nidhika BirlaA.P, Dept. of Electronics Engg.

Sendai subway: 16 stations and 13.5 km route, designed byHitachiWashing machines that measure weight, saturation time andwater clarity in order to set program cyclesPortable camcorders with automatic focus and anti-jitterVacuum cleaners that measure air dust to set suction powerMicrowave ovens that measure temperature, humidity,weight of food to set time and power.



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Sugeno designed a voice controlled system to operatean unmanned helicopterAnti-Lock Braking Systems: Nissan, Mitsubishi. Honda,Mazda, Hyunday, BMW, Bosch and PeugeotSuspension, transmission and fuel injector systems areusual.Hitachi uses approximately 150 rules to trade inJapanese bonds and futuresYamaichi Securities uses hundreds of rules to manage a

stock fundAnaesthesia Control and Fuzzy Data Analysis for Cardio-Anaesthesia

Airconditioning

Mitsubishi,Hitachi, Sharp

Avoids temperature oscillationsand saves energy

Electronicfuel injection

NOK/Nissan Injection based on throttle, O2tax, water temperature, RPM, etc

Steel Nippon Steel Mix inputs and controls time andtemperature

Golf Maruman Golf

Club

Chooses clubs

Lifts Fujitec Improves response time based ontraffic



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“AI is the activity of providing suchmachines as computers with the ability todisplay behaviours that would be regardedas intelligent if it were observed inhumans” (R. McLeod)

“AI is the study of agents that exist in anenvironment, perceive and act.” (S. Russeland P. Norvig)

AI emphasizes symbolic processingActs on higher levels of intelligenceAI seeks to understand



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Acts on lower levels of IntelligenceUses learning extensivelyPattern recognition and heuristics playimportant roles

Fuzzy Logic

Artificial Neural Networks

Evolutionary Systems

Swarm Intelligence

Hybrid Systems



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Fuzzy Logic

Artificial Neural Networks

Evolutionary Systems

Swarm Intelligence

Hybrid Systems

Logic that deals mathematically with impreciseinformation usually employed by humans.

Multi-valued logic that extends Boolean logicusually employed in computer science.



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Used to alleviate difficulties in developing andanalysing complex control systems.

Function approximator

Decision systems

Who is greater than 1.80 m?

Who is tall?

Who weighs more than 60 kg?

Who is heavy?

The driver was heavy and tall.



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Macedonian philosopher who livedbetween 384 e 322 ACStudied under Plato in the AcademyCreator of formal logicHis father Nichomachus was court physician to KingAmyntasAssociates the spirit of observation and aclassification instinct

He was considered during the middle ages the philosopher He shaped much of the western mind.



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Objects are separated on very clear categoriesOne object either belongs to a category oranotherEither you are or notHelps to separate objects into well definedcategories.

Every language is vague. All traditional logic habitually assumes that precisesymbols are being employed. It is therefore not applicable to this terrestrial life, but only to animagined celestial one.Everything is vague to a degree you do not realize till you have tried to make it precise.

Bertrand Russel



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As far as the laws of Mathematics refer toreality, they are not certain; and as far as they are certain, they do not refer to reality.

Albert Einstein

Happy peopleSmall roomsHigh temperaturesFaster carsHigh tax ratesHigh people



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Bertrand Russel, while trying to formalize Mathematichad difficulties due to the liar’s paradox.

“I am lying.”If Eubulides‘ statement was true, then he is lyingwhen he says “I am lying” and so he isn't, i.e. hisstatement is false.If his statement is false, then he isn't lying when hetells us he is, and so his statement is true.

Consider the set of all sets that are notmembers of its own set. Is it a member of thisset?

If it is a member then it is not, but if it is notthen it is.



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Variable: AGEMiddle-Aged : 40 Years ≤ AGE < 55 YearsOld-Aged : AGE ≥ 55 Years

Is a person with age 54 Years 364 Days 23 Hours59 Minutes 59 Seconds Old-Aged?

NO

Is a person with age 55 Years Old-Aged?

YES

Middle - Aged

Old - Aged

Age

Age

M . G .

M . G .

1

1

40 55

40 55Age

Age

M . G .

M . G .

1

1

40 55

40 55

60

60

35

707575

0.5

0.5

57



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Lotfy Zadeh. “Fuzzy Sets”, Information na Control,1965Principle of Incompatibility

As the complexity of a system increases, our ability tomake precise yet significant descriptions about itsbehaviour diminishes until a threshold is reached beyond which precision and significance (or relevance) becomealmost mutually exclusive characteristics.

Lofty Zadeh

Vagueness (Russel 1923)Einstein (1937)

“As far as the laws of mathematics refer to reality,they are not certain, and as far as they are certain,they do not refer to reality”.

Fuzzy logic invention:Lotfi Zadeh (1965), although the ideas can be

traced back to earlier works (1962).Zadeh (1968-73), fuzzy algorithms,fuzzy decisionmaking, Principle of incompatibility, fuzzy control.



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Fuzzy follow up:Mamdani , first practical demonstration (1974 )

Applying Fuzzy Logic for control of steam engine

First fuzzy controller, Holmblad 1978.First commercial applications in 1981.Establishing of International Fuzzy SystemAssociation (IFSA). (1984)

In 1994, Japan exported products worth $35 billionthat use fuzzy logic !

Traditional or Crisp LogicNoYes

Fuzzy LogicNoSlightlySomewhat

Sort of A fewMostlyYes, Absolutely





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Meas u re Fu zzi fi ed Meas ur e

Temp = 35 º Temp = high, µ high (t)=0.8Temp = 48º Temp = high, µ high (t)=1.0

Age = 35 Idade = middle, µ middle (i)=0.8Grade = 10.0 Grade = A, µ A(t)=1.0

Grade = 8.5 Grade = A, µ A(t)=0.87

Fuzzy logic provides a method to formalizereasoning when dealing with vague terms.It is based on possibility theory.



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Fuzzy systems are knowledge-based or rule-based systems.The heart of a fuzzy system is a knowledge baseconsisting of the so-called fuzzy IF-THEN rules.A fuzzy IF-THEN rule is an IF-THEN statement inwhich some words are characterized bycontinuous membership functions.

XX Y=F(X)Y=F(X)

Function F(x) is unknownFunction F(x) is unknown



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FuzzificationModule

InferenceEngine

DefuzzicationEngine

Knowledge Base(Rule Base and

Data Base)

CrispInputs

CrispOutputs

Maps inputvalues in crisp

sets to values infuzzy sets

Simulatesdecision making

capability of human brain

Converts thefuzzy output tocorrespondingcrisp output

Database providesnecessary definitionsof linguistic variables

and fuzzy datamanipulation

Rulebaserepresents in astructured way

the controlpolicy of the

domain expert



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Fuzzy logic is flexible.Fuzzy logic is based on natural language .Better way of dealing with

Ill-defined systems, imprecise knowledge, incompleteinformation, complex and non-linear systems.

Use rules that express imprecision of the real world.Easy to understand , test and maintain.Easy to be prototyped.Robust . It operates even when there is lack of rules orwrong rules.

Circumvents the need for rigorous mathematicaltreatment.Provides a better way of dealing with the linguisticexpressionsCan be blended with conventional techniques.Reduction of development and maintenance time.



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Need more tests and simulation as stabilitystudying criteria is not available.Shortage of trained personnel.Difficult to establish correct rules.Lack of precise mathematical model .

If you find Fuzzy Logic is not convenient , trysomething else.If a simpler solution already exists, use it.



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Is fuzzy logic probability ?

Find a fuzzy product description.

Find fuzzy development tools.

Fuzzy Mathematics

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Fuzzy Unit 1

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