fuzzy soalan

8/7/2019 fuzzy soalan

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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

-v

NSN abQAOEthQc"

&\ a?

\,{

4


2/7

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


3/7

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)

6

-3-2-1 0 1 2 3


4/7

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


6/7

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?

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