fuzzy soalan
TRANSCRIPT
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4. Thelearningprocedrneof anewo-firzzysystemtakesthesemanticalpropertiesof thermderlyingfrtzarysysteminto accormtThis resultsin constraintsonthepossiblemodificationsapplicableto thesystemparameters'(1 marks)
5. A negro-fuzzysysternapproximatesan$n$dimensionat(unknounr)functionthat ispartiallydefinedby thetrainingdata'Thefrwy nrlesencodedwithin thesystemreprsx1tvagusamples,andcanbeviewedasprrototypesof the trainingdda"Anerno-firzzysystemshouldnotbeseenas akind of (firzzy) bxpertsystem"andit basnothingto dowith fuzuylogic inthe narrowsense'
(l ma*s)
Q2. Fuz'ycontrolsystemis apptiedfor conlrolth"-9,t
@ control$y$emtypeisryryp andeachvariablehavi fivememberslrip"frnctionsin tiangularfunctionEach*"*U.ryhip fi-i*ioo nambsrespctivelyare\p (negativebig),N (negative),Z (zsro)'P(positive),andPB(positivebig).Universediscourserelatd witheach name,*ft" following:
o N/[-2, -1,0J -olo Z:f-2,0,21Vto P; [0,l,2J \o PB:[ ,2,3]
Changeinsrror:o NB:[{,4,-4o N: [4, -2,0Jo Z:l-2,0,21o P:[0,2,4]o PB:[2,4'6]
Or{put:' o NB: [-3,-2,-llo N: [-2,-1,0]o '*t!O,q , 'o P:[0,l' 2Jo PB:[1,2,3]
'. f
,\ fL-2 -r \ l
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4
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Maxiurm vahn of all qtffikn is t'
(b)Drawtbemombershipflmctio!rylai$dtableinpoint(a)
Answer:
(l0mds)
.t' I't
(4 ma*s)
. II
II
t '
,Y , -2l -1 0,1,1 5
Enormber*iP grryh
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lrd,
3 4 i5
.0.&/u ' 71*
-6 -5 -4
Changein errormemboshiPgraPh
ControlsignalmembershiPgraPh
(amarks)
(amuks)
(c) Formulateall rulesfire relatedwith efror is -1.5andchangein errort{.t
Answer:
IF erroris Z Al'{D changeinerror is PBTI{EN u is P
IF erroris N AI'ID changein eror is PB THEN u is Z
IF errorisNB AND changeinerror isPB THENuisNB
(rule 1)(l marks)
(rule2)(1 marks)
(rule 3)(l marks)
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A@ offiol rysfiemh tiag$Itr rembership frretim ad tbree member$ip firetionsbelow arefiring:
IF erroris zero AI.ID changeinenCIris positivebig TIIENqTFUI is positiveIF ernDrisnegativebig AI.ID chmgeinerrs ispositirrcbig THEI{ugrtisaegdivebigIF errorisnegativeAllD changeinenor ispositive tligilGN output is zsro
Evaluarirylio frrzrl.,ysetusingminimumcriteria md thecrisp'orspr*sigealusingcoatnoidof gravity (COG)for changein enor is 2.5andenor is -1.5ifuniverse discotnsefor *roerroris I-2,0,2], negativeerror is [-3, -1.5,0], positivebig error is [4, A.5, -ll, changeinermr is V.5, 4,5.5], z,ercoutputis [4, 0, 4J,positiveoutputis f2, 4,6], andnegarivebigorsp$ is [-E,{.5, -5]
Ans\irr:-EquationofZ forerror[o e
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f o e-r
(l maks)Implied fiil?zysetfrom Rule with minimumctite.ria(1) (IF erroris Z AIID changein error isPB TI{ENuisP}
Fa,p= mrrlQu",,{e),p*,, u(&)) = min(p,, (-l .5),tt*,"u(4.5D= min(0.25,0.6?)= 0.25(1.5maks)
(1.5marks)
Equationof PB for changein errcrf o e
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E-
(1.5marks)centreb=4.5andareafp} =rr{,-+)=do-rr-+) =a'8267r ' - ' \ 2) \ z ) (1 marks)Irnpliod frrg4.ysetfrom Rulewift minimumcriteria(2) (IF enor is N At.lD changein eror isPBTHEN u is Z)
Impliedfrrg;ysetfromRulewithminimumcriteria(3)0F erroris NB AI{D changein errorisPBTHENu is NB)Poln = mmQu",* (e),P* ss(fu)) = min(p",* (-l'5), p*.", (4'5)= min(0.33,0.67)= 0.33
(1.5marks)
1
0.533
-54-3-2-1 0 I
po.z=min(p,o (e),p*su(de)) = min(p"o?1'5)' p asn(2'5).
=min(1'0'67)=0'67(1.5ma&s)
(1.5marks)centreb=oandarcaJr(i)=4r-+)={o"ut g=35544
-5.4-3-24O
1l
(l marks)
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Valuecrisp Defuzzification:
(1.5marks)
Q5.
COG methodDefuzzification
It, [rte), 'w=-@= (4X0.87s)+(-6.s{0.8267)+(0)(3.s644)=2.47960.875+0.8267+3.5644(1.5mmks)
A multilayer neuralnetwork is representedin FigureQ3.Thenetwork is trainedusingBackproppgationleamingalgorithmwith initial condition asbelow:xr = 1, xz=1, xj =1, t =lr4 =0.5wr=0.01,wz=-0.A1,W3=0.11,wu=A.21,W5=-0.11,W6= 4.2, wt =4,15,wr = 0.31Activation functionfor hiddenandoutputlayer is f (net) l+ e'*'
1rl
1?