FuzzyLogic - Northeastern University
FuzzyLogicOutsideresourcesì
FuzzySets§ ecapableofhighlyadapBvecontrol.”§ Acceptsnoisy,impreciseinput!
3Fuzzy Logic IntroductionFuzzy Inference System
FuzzySetsì ndedtohandletheconceptofparBaltruthì luteFalsenessand1.0represenBngabsoluteTruth.ì dealswithrealworldvagueness
Linguisticvariable,linguistictermì .ì ll,tallbutnotverytall,quitetall,moreorlesstall.ì Tallisalinguis(cvalueorprimarytermì Hedgesarevery,moreorlesssoon
ì IfageisalinguisBcvariablethenitstermsetisì T(age)ì young,notyoung,veryyoung,notveryyoungì middleaged,notmiddleagedì old,notold,veryold,moreorlessold,notveryold
youngmiddleagedold1.0µ0.0Age
OperationsABA BA B A
FuzzyRulesì Bonandjudgment.ì Afuzzyif- ofdiscourseXandY,respecBvely.ì onsequent.
Examples,forsucharuleareì Ifpressureishigh,thenvolumeissmall.ì Iftheroadisslippery,thendrivingisdangerous.ì Ifthefruitisripe,thenitissoY.
ExampleAirCondiBoningControllerExample:ì IFColdthenStopì IfCoolthenSlowì IfOKthenMediumì IfWarmthenFastì IFHotthenBlast
FuzzyAirConditioner01009080BlaFaIf HotthenBlastststIf WarmthenFast7060Med5040If Just RightthenMediumiumSloIF CoolthenSloww30if Coldthen Stop20oSt10p0HotWarmJusRig thtldCoCool1045505560657075808590
40iu mSlow3020oSt10p0ldHotWarmJu sRig thtCoCool1045505560657075808590
14Fuzzy Logic IntroductionFuzzy Inference System
15Fuzzy Logic Introduction Fuzzy Inference System.Mamdani Method In 1975, Professor Ebrahim Mamdani of LondonUniversity built one of the first fuzzy systems to control asteam engine and boiler combination. He applied a set offuzzy rules supplied by experienced human operators.
16Fuzzy Logic IntroductionFuzzy Inference System
17Fuzzy Logic Introduction Fuzzy Inference System oAn exampleì Two inputs (x, y)ì One output (z)ì Rules:Rule1:C1Rule2:C2Rule3:C3Ifx is A3 ory is B1 Thenz isIfx is A2 andy is B2 Thenz isIfx is A1Thenz is
18Fuzzy Logic Introduction FuzzyInferenceSystem o Inputx:research fundingo Inputy:project staffingo Outputz:riskì Rules:Rule1:Ifresearch fundingisadequateorproject staffingissmallThenriskislowRule2:Ifresearch fundingismarginalandproject staffingislargeThenriskisnormalRule3:Ifresearch fundingisinadequateThenriskishigh
19Step 1: Fuzzification
20Step 2: Rule Evaluation
21Applying to the membership erentways:
22Step 3: Rule Evaluation
23Step 4: methodscanalsobeused
Why Fuzzy Logic?§ Advantages§ Mimicks human control logic§ Uses imprecise language§ Inherently robust§ Fails safely§ Modified and tweaked easily
Why Fuzzy Logic?§ Disadvantages§ Operator's experience required§ System complexity
fthisapproach?
Fuzzy Logic Introduction Fuzzy Inference System. Mamdani Method In 1975, Professor Ebrahim Mamdani of London University built one of the first fuzzy systems to control a steam engine and boiler combination. He applied a set of fuzzy rules supplied by experienced human operators. 15
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