This document discusses the fundamentals of fuzzy logic control systems. It begins by defining fuzzy logic as a problem-solving control system methodology that uses linguistic variables and fuzzy rules to map inputs to outputs. It then outlines the typical elements of a fuzzy logic system, including fuzzy sets, linguistic variables, fuzzy rules, fuzzy inference, and defuzzification. Finally, it provides an example of applying fuzzy logic to control the temperature in a simple heating/cooling system.

2. Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…
IntroductionIntroduction..
ApproachApproach..
ApplicationApplication..
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ApplicationApplication..
SummarySummary..
DemoDemo..

3. IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroduction
FuzzyFuzzy LogicLogic definesdefines thethe controlcontrol strategystrategy onon aa LinguisticLinguistic
levellevel..
ProblemProblem--solvingsolving controlcontrol systemsystem methodologymethodology..
What is Fuzzy Logic ?
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ProblemProblem--solvingsolving controlcontrol systemsystem methodologymethodology..
LinguisticLinguistic oror “Fuzzy"“Fuzzy" variablesvariables
ExampleExample::
IFIF (process(process isis tootoo hot)hot)
ANDAND (process(process isis heatingheating rapidly)rapidly)
THENTHEN (cool(cool thethe processprocess quickly)quickly)

4. IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroduction
DescribeDescribe thethe valuevalue ofof variablesvariables
Apparatus of Fuzzy logic is built on :
Fuzzy sets :
QualitativelyQualitatively andand quantitativelyquantitativelyLinguistic
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QualitativelyQualitatively andand quantitativelyquantitatively
describeddescribed byby fuzzyfuzzy setssets
Linguistic
Variables :
AA knowledgeknowledgeFuzzy if -
then rules :
LinguisticLinguistic valuesvalues toto numericalnumerical valuesvaluesDefuzzification :

5. IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroduction
Basic Elements of a Fuzzy logic system :
3.Defuzzyfication
Linguistic
level
Command Variables
(Linguistic Values)
Measured Variables
(Linguistic Values)
1.Fuzzyfication
2. Fuzzy Inference
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Defuzzyfication
level
Numerical
level
Measured Variables
(Numerical Values)
Command Variables
(Numerical Values)
1.Fuzzyfication

6. ApproachApproachApproachApproachApproachApproachApproachApproach
Preliminary Evaluation :
Problem Analysis before Project start !
EvaluationEvaluation CriteriaCriteria :
AssessmentAssessment asas toto whetherwhether FuzzyFuzzy logiclogic isis applicableapplicable forfor
thethe givengiven applicationapplication..
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HasHas fuzzyfuzzy logiclogic beenbeen previouslypreviously appliedapplied toto aa similarsimilar applicationapplication
WithWith success?success?
IsIs itit aa multimulti--variablevariable typetype controlcontrol problem?problem?
DoDo operatorsoperators andand engineersengineers possesspossess knowledgeknowledge aboutabout anyany relevantrelevant
interdependenciesinterdependencies ofof thethe processprocess variables?variables?
CanCan furtherfurther knowledgeknowledge aboutabout thethe processprocess behaviorbehavior bebe gainedgained byby
observationobservation oror experiments?experiments?
IsIs itit difficultdifficult toto obtainobtain aa mathematicalmathematical modelmodel fromfrom thethe process?process?

7. UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
ApproachApproachApproachApproachApproachApproachApproachApproach
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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8. The Rule MatrixThe Rule Matrix
Error (Columns)Error (Columns)
ErrorError--dot (Rows)dot (Rows)
Input conditionsInput conditions
ApproachApproachApproachApproachApproachApproachApproachApproach
--veve
ErrorError
ZeroZero
ErrorError
+ve+ve
ErrorError
--veve
ErrorError--
dotdotInput conditionsInput conditions
(Error and Error(Error and Error--
dot)dot)
Output ResponseOutput Response
ConclusionConclusion
(Intersection of Row(Intersection of Row
and Column)and Column)
dotdot
ZeroZero
ErrorError--
dotdot
NoNo
changechange
+ve+ve
ErrorError--
dotdot
Rule MatrixRule Matrix
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9. ComponentsComponents
An electric heating elementAn electric heating element
VariableVariable--speed cooling fanspeed cooling fan
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
SimpleSimple ProportionalProportional TemperatureTemperature ControllerController :
VariableVariable--speed cooling fanspeed cooling fan
FunctionalityFunctionality
Positive signal output: 0Positive signal output: 0--100% heat100% heat
Negative signal output: 0Negative signal output: 0--100% cooling100% cooling
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10. ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
Block Diagram of the Control System
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11. ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
WorkingWorking
Establish a meaningful system for representing theEstablish a meaningful system for representing the
linguistic variables in the Rule Matrixlinguistic variables in the Rule Matrix
"N" = "negative" error/ error"N" = "negative" error/ error--dot input leveldot input level"N" = "negative" error/ error"N" = "negative" error/ error--dot input leveldot input level
"Z" = "zero" error/ error"Z" = "zero" error/ error--dot input leveldot input level
"P" = "positive" error/ error"P" = "positive" error/ error--dot input leveldot input level
"H" = "Heat" output response"H" = "Heat" output response
""--" = "No Change" to current output" = "No Change" to current output
"C" = "Cool" output response"C" = "Cool" output response
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12. ApproachApproachApproachApproachApproachApproachApproachApproach
UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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13. 1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
System temperatureSystem temperature
What do I have to do to control the system?What do I have to do to control the system?
Proper balance and control of the functional devicesProper balance and control of the functional devices
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
Proper balance and control of the functional devicesProper balance and control of the functional devices
What kind of response do I need?What kind of response do I need?
Stable Environment temperatureStable Environment temperature
What are the possible (probable) system failureWhat are the possible (probable) system failure
modes?modes?
The lack of the “No change” regionThe lack of the “No change” region
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14. What is being controlled and how?What is being controlled and how?
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
Typical control system responseTypical control system response
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15. ApproachApproachApproachApproachApproachApproachApproachApproach
UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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16. ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
2.2. Determine the input and output relationshipsDetermine the input and output relationships2.2. Determine the input and output relationshipsDetermine the input and output relationships
Define the minimum number of possible input productDefine the minimum number of possible input product
combinations and corresponding output responsecombinations and corresponding output response
conclusionsconclusions
INPUT#1: ("Error", positive (P), zero (Z), negative (N))
INPUT#2: ("Error-dot", positive (P), zero (Z), negative (N))
CONCLUSION: ("Output", Heat (H), No Change (-), Cool (C))CONCLUSION: ("Output", Heat (H), No Change (-), Cool (C))
INPUT#1 System Status
Error = Command-Feedback
P=Too cold, Z=Just right, N=Too hot
INPUT#2 System Status
Error-dot = d(Error)/dt
P=Getting hotter Z=Not changing N=Getting colder
OUTPUT Conclusion & System Response
Output H = Call for heating - = Don't change anything C = Call for cooling
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17. ApproachApproachApproachApproachApproachApproachApproachApproach
UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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18. APPLICATION (Contd.)
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
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19. ApproachApproachApproachApproachApproachApproachApproachApproach
UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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20. 4.4. CreateCreate FLFL membershipmembership functionsfunctions thatthat definedefine thethe
meaningmeaning (values)(values) ofof Input/OutputInput/Output termsterms usedused inin thethe
rulesrules
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
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21. A sample caseA sample case
ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication
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22. ApproachApproachApproachApproachApproachApproachApproachApproach
UsageUsageUsageUsage
1.1. Define the control objectives and criteriaDefine the control objectives and criteria
What am I trying to control?What am I trying to control?
What do I have to do to control the system?What do I have to do to control the system?
What kind of response do I need?What kind of response do I need?
What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?
2.2. Determine the input and output relationshipsDetermine the input and output relationships
Choose a minimum number of variables for input to theChoose a minimum number of variables for input to the
FL engineFL engine
3.3. Use the ruleUse the rule--based structure of FLbased structure of FL
Break the control problem down into a series of rulesBreak the control problem down into a series of rules
4.4. Create FL membership functionsCreate FL membership functions
Define the meaning (values) of Input / Output terms usedDefine the meaning (values) of Input / Output terms used
in the rulesin the rules
5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest
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23. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Loading dock (Loading dock ( XXff ,, YYff ))
RearRear
( X( X , Y, Y ))
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FrontFront
ɸɸ
ϴϴ
Diagram of Truck and Loading zoneDiagram of Truck and Loading zone

24. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
TheThe goalgoal isis toto makemake thethe trucktruck arrivearrive atat thethe loadingloading dockdock
atat aa rightright angleangle ((ɸɸff==9090)) andand toto alignalign thethe positionposition (x,(x, y)y) ofof
thethe trucktruck withwith thethe desireddesired loadingloading dockdock (( XXff ,, YYff ))..
TheThe trucktruck movesmoves backwardbackward byby somesome fixedfixed distancedistance atat
Goal ?
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TheThe trucktruck movesmoves backwardbackward byby somesome fixedfixed distancedistance atat
everyevery stagestage..
TheThe loadingloading zonezone correspondscorresponds toto planeplane [[00,,100100]] XX
[[100100,,00]] andand (( XfXf ,, YfYf )) equaledequaled ((5050,,100100))
AtAt everyevery stagestage thethe FuzzyFuzzy controllercontroller shouldshould produceproduce thethe
steeringsteering angleangle ϴϴ thatthat backsbacks upup thethe trucktruck toto thethe loadingloading
dockdock fromfrom anyany initialinitial positionposition andand fromfrom anyany angleangle inin thethe
loadingloading zonezone..

25. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
TheThe threethree statestate variablesvariables ɸɸ,, xx andand yy exactlyexactly determinedetermine
thethe trucktruck positionposition..
TheThe coordinatecoordinate pairpair (x,(x, y)y) specifiesspecifies thethe positionposition ofof thethe
rearrear centercenter ofof thethe trucktruck inin thethe planeplane..
ɸɸ specifiesspecifies thethe angleangle ofof thethe trucktruck withwith thethe horizontalhorizontal..
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rearrear centercenter ofof thethe trucktruck inin thethe planeplane..
First specify controller’s input and output variables.
TheThe inputinput variablesvariables areare thethe trucktruck angleangle ɸɸ andand xx ––
positionposition coordinatecoordinate xx..
TheThe outputoutput isis steeringsteering angleangle signalsignal ϴϴ..
WeWe assumeassume enoughenough clearanceclearance betweenbetween thethe trucktruck andand thethe loadingloading dockdock soso
wewe cancan ignoreignore thethe yy –– positionposition coordinatecoordinate..

26. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
PositivePositive valuesvalues ofof ϴϴ representsrepresents clockwiseclockwise rotationsrotations..
Next specify Fuzzy set values of input and output
variables.
ɸɸ specifiesspecifies thethe angleangle ofof thethe trucktruck withwith thethe horizontalhorizontal..
NegativeNegative valuesvalues ofof ϴϴ representsrepresents countercounter clockwiseclockwise
rotationsrotations..
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AngleAngleAngleAngleAngleAngleAngleAngle ɸɸ
RB Right Below
RU Right Upper
RV Right Vertical
VE Vertical
LV Left Vertical
LU Left Upper
LB Left Below
XXXXXXXX--------position xposition xposition xposition xposition xposition xposition xposition x
LE Left
LC Left Center
CE Center
RC Right Center
RI Right
Steering AngleSteering AngleSteering AngleSteering AngleSteering AngleSteering AngleSteering AngleSteering Angle ϴϴϴϴϴϴϴϴ
NB Negative Big
NM Negative Medium
NS Negative Small
ZE Zero
PS Positive Small
PM Positive Medium
PB Positive Big

27. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Next specify Fuzzy Membership Functions.
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0 ≤ x ≤ 1000 ≤ x ≤ 100

28. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Next specify Fuzzy Membership Functions.
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--90 ≤90 ≤ ɸɸ ≤ 270≤ 270

29. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Next specify Fuzzy Membership Functions.
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--30 ≤30 ≤ ϴϴ ≤ 30≤ 30

30. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Next specify Fuzzy “rulebase” or bank of FAM rules.
xxxx
LE LC CE RC RI
RB PS PM PM PB PB
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ɸɸɸɸɸɸɸɸ
RB PS PM PM PB PB
RU NS PS PM PB PB
RV NM NS PS PM PB
VE NM NM ZE PM PM
LV NB NM NS PS PM
LU NB NB NM NS PS
LB NB NB NM NM NS

31. Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…
Next Defuzzification.
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CorrelationCorrelation –– minimum inference withminimum inference with centroidcentroid
defuzzificationdefuzzification methodmethod

32. Summary …Summary …Summary …Summary …Summary …Summary …Summary …Summary …
1.1. TheThe plantplant isis observableobservable andand controllablecontrollable :: state,state, inputinput
andand outputoutput variablesvariables areare usuallyusually availableavailable forfor
observationobservation andand measurementmeasurement oror computationcomputation..
Assumptions in a Fuzzy control system design :
2.2. ThereThere existsexists aa bodybody ofof knowledgeknowledge comprisedcomprised ofof aa setset ofof
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2.2. ThereThere existsexists aa bodybody ofof knowledgeknowledge comprisedcomprised ofof aa setset ofof
linguisticlinguistic rules,rules, engineeringengineering commoncommon sense,sense, intuition,intuition, oror aa
setset ofof inputinput –– outputoutput measurementsmeasurements datadata fromfrom whichwhich rulesrules
cancan bebe extractedextracted..
3.3. AA solutionsolution existsexists..
4.4. AA controlcontrol engineerengineer isis lookinglooking forfor aa “good“good enough”enough”
solution,solution, notnot necessarilynecessarily thethe optimumoptimum oneone..

33. Summary …Summary …Summary …Summary …Summary …Summary …Summary …Summary …
5.5. TheThe controllercontroller willwill bebe designeddesigned withinwithin anan acceptableacceptable
rangerange ofof precisionprecision..
Assumptions in a Fuzzy control system design :
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6.6. TheThe problemsproblems ofof stabilitystability andand optimalityoptimality areare notnot
addressedaddressed explicitlyexplicitly ,, suchsuch issuesissues areare stillstill openopen problemsproblems
inin FuzzyFuzzy controllercontroller designdesign..

34. Summary …Summary …Summary …Summary …Summary …Summary …Summary …Summary …
1.1. IdentifyIdentify thethe variablesvariables (inputs,(inputs, statesstates andand outputs)outputs) ..
The Steps in designing a simple Fuzzy control system :
2.2. PartitionPartition thethe universeuniverse ofof disclosuredisclosure oror thethe intervalinterval
spannedspanned byby eacheach variablevariable intointo aa numbernumber ofof FuzzyFuzzy subsets,subsets,
assigningassigning eacheach aa linguisticlinguistic labellabel (subset(subset includeinclude allall thethe
9/12/2013 Mahesh J. vadhavaniya 33
assigningassigning eacheach aa linguisticlinguistic labellabel (subset(subset includeinclude allall thethe
elementselements inin thethe universe)universe)..
3.3. AssignAssign oror determinedetermine aa membershipmembership functionfunction forfor eacheach
FuzzyFuzzy subsetsubset..
4.4. AssignAssign thethe FuzzyFuzzy relationshipsrelationships betweenbetween thethe inputs’inputs’ oror
states’states’ FuzzyFuzzy subsetssubsets onon thethe oneone handhand andand thethe outputs’outputs’
FuzzyFuzzy subsetssubsets onon thethe otherother hand,hand, thusthus formingforming thethe rulerule––
basebase..

35. Summary …Summary …Summary …Summary …Summary …Summary …Summary …Summary …
5.5. ChooseChoose appropriateappropriate scalingscaling factorsfactors forfor thethe inputinput andand
outputoutput variablesvariables inin orderorder toto normalizenormalize thethe variablesvariables toto thethe
[[00,, 11]] oror thethe [[--11,, 11]] intervalinterval..
The Steps in designing a simple Fuzzy control system :
6.6. FuzzifyFuzzify thethe inputsinputs toto thethe controllercontroller..6.6. FuzzifyFuzzify thethe inputsinputs toto thethe controllercontroller..
7.7. UseUse FuzzyFuzzy approximateapproximate reasoningreasoning toto inferinfer thethe outputoutput
contributedcontributed fromfrom eacheach rulerule..
8.8. AggregateAggregate thethe FuzzyFuzzy outputsoutputs recommendedrecommended byby eacheach
rulerule..
9.9. ApplyApply defuzzificationdefuzzification toto formform aa crispcrisp outputoutput..
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