fuzzy_logic_6828

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GV: L Hoi Long 1

Fuzzy logic

Phn 2

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GV: L Hoi Long 2

Fuzzy?

Nhng hnh di y c mu g?

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GV: L Hoi Long 3

Fuzzy?

Cc c gi p?

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GV: L Hoi Long 4

Fuzzy?

Ti v bn, ai cao?

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GV: L Hoi Long 5

Fuzzy logic

Khi nim v fuzzy logic c thai nghnbi gio s Lotfi Zadeh ca i hc UCBerkeley vo nm 1965

Cho php gii quyt vn thng tin

khng chnh xc (imprecision) hay khngchc chn (uncertain)

L thuyt fuzzy cung cp mt c ch x lcc thng tin c tnh ngn ng (linguistic)

nh l nhiu, thp, trung bnh, rt Cung cp mt cu trc suy lun tng t

nh kh nng lp lun ca con ngi.

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GV: L Hoi Long 6

S chnh xc c chnh xc?

Precision is not truth (Henri Matisse) Sometimes the more measurable

drives out the most important (ReneDubos)

So far as the laws of mathematicsrefer to reality, they are not certain.And so far as they are certain, they

do not refer to reality (AlbertEinstein)

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GV: L Hoi Long 7

Fuzzy logic L lun chnh xc ch l mt trng hp gii

hn ca l lun xp x (approximatereasoning)

Mi th ch l vn ca mc (matter ofdegree)

Kin thc ch l mt tp hp ca cc rngbuc m c tnh n hi trn mt tp hpcc bin

Suy lun ch l mt qu trnh lan truyn

ca cc rng buc n hi Bt c mt h lun l (logic) no cng cth lm m (fuzzify)

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GV: L Hoi Long 8

Fuzzy set

Gi X l mt tp khng rng(nonempty set)

Mt tp fuzzy A trong X c ctrng bi mt hm thnh vin(membership function) A (hay l A)

]1,0[: XA

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GV: L Hoi Long 9

Fuzzy set

V d: Nu gi chiu cao t 1,7m lcao trong tp crisp (cng nhc), tpfuzzy ca ngi c coi l cao cc trng bi hm thnh vin nhsau

1,5 1,7

1

0

Chiu cao

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GV: L Hoi Long 10

Bi tp 1

Vi iu kin no c chp nhn,hy v hm thnh vin ca tp fuzzyth hin gi bn mt xe t l r

1

0

Gi tin

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GV: L Hoi Long 11

Fuzzy set

Nu X={x1, x2,,xn} l mt tp huhn (finite) v A l mt tp fuzzy,chng ta c th s dng k hiu sau trnh by:

i/xi th hin mc thnh vin ca xi

trong tp fuzzy A

nn xxxA /...// 2211

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GV: L Hoi Long 12

Fuzzy set

V d nu ta c X={-2,-1,0,1,2,3} vA l mt tp fuzzy c th trnh bynh sau:

4/0.03/0.02/6.01/0.10/6.01/3.02/0.0 A

?

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GV: L Hoi Long 13

Mt s khi nim trong l thuytfuzzy

Support -cut Tp fuzzy li (convex) Tp fuzzy thng (normal) S fuzzy

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GV: L Hoi Long 14

Support ca tp fuzzy

Gi A l mt tp fuzzy thuc X, supportca A (k hiu supp(A)) l mt tp concng (crisp) ca X sao cho:

}0)({) xAXxAsupp(

x1 x2

1

0

A

....................) Asupp(

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GV: L Hoi Long 16

Bi tp 2

Hy tm -cut (0

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GV: L Hoi Long 17

Convex fuzzy set

Mt tp fuzzy A thuc X c gi lli nu cc tp con mc (-level)l mt tp li ca X [0,1]

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GV: L Hoi Long 18

Tp Fuzzy thng

Mt tp fuzzy c gi l thng(normal) nu tn ti gi tr xX saocho A(x) = 1.

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GV: L Hoi Long 19

Fuzzy number

Mt s fuzzy A l mt tp fuzzy vihm thnh vin lin tc, li v thng

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GV: L Hoi Long 20

Fuzzy number

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GV: L Hoi Long 21

S fuzzy tam gic

otherwise

ataif

at-aif

0

1

1

)(

ta

ta

tA

-cut ti =0.5?

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GV: L Hoi Long 22

S fuzzy hnh thang

othewise

btbif

btaif

at-aif

0

1

1

1

)(

ta

ta

tA

-cut ti =0.5?

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GV: L Hoi Long 23

Cc s fuzzy khc

S fuzzy dng tam gic v hnh thanghay c s dng.

Cc s fuzzykhc u c th s dngtrong cc trng hp ph hp khc Bell Gaussian Sigmoid

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GV: L Hoi Long 24

Mt s php logic thng s dngvi s fuzzy

Php giao (intersection) Php hp (union) Php ly phn b (complement -

negation)

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GV: L Hoi Long 25

Php giao 2 s fuzzy

Giao ca 2 s fuzzy A v B c nhngha nh sau:

Xtallfor

)()(

)}(),(min{))((

tBtA

tBtAtBA

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GV: L Hoi Long 26

Php hp 2 s fuzzy

Hp ca 2 s fuzzy A v B c nhngha nh sau:

Xtallfor

)()(

)}(),(max{))((

tBtA

tBtAtBA

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GV: L Hoi Long 27

Php b ca s fuzzy

Phn b ca tp fuzzy c nhngha nh sau (-A hoc ):

)(1))(( tAtA

?.........)(

?.........)(

AA

AA

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GV: L Hoi Long 28

Tnh cht ca fuzzy set

Tnh giao hon (commutativity) Tnh kt hp (associativity) Tnh phn phi (Distributivity)

Tnh hon nguyn (Idempotency) Tnh ng nht (Identity) Tnh bc cu (Transitivity) Tnh cun (Involution)

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GV: L Hoi Long 29


Tnh giao hon (commutativity)

Tnh kt hp (associativity)

Tnh phn phi (Distributivity)

ABBA

ABBA

CBACBA

CBACBA

)()(

)()(

)()()(

)()()(

CABACBA

CABACBA

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GV: L Hoi Long 30


Tnh hon nguyn (Idempotency)

Tnh ng nht (Identity)

Tnh bc cu (Transitivity)

Tnh cun (Involution)

AAAAAA and

XXAA

AXAAA

and

and

CACBA thenif

AA ))((

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GV: L Hoi Long 31

Luyn tp

6

3.0

5

7.0

4

4.0

3

8.0

2

5.0

66.0

52.0

46.0

35.0

21

B

A

Tm phn b ca A v B v giao ca A v B

BA

B

A

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GV: L Hoi Long 32

Extension principle

Ta c mt tp fuzzy A trn X vy=f(.) l mt hm s nh x t X quaY.

Lc ny nh ca A trn Y qua phpnh x f(.) l tp fuzzy B c dng:

n

n

x

x

x

x

x

xA

)(...

)()(

2

2

1

1

n

n

yx

yx

yxAfB )(...)()()(

2

2

1

1

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GV: L Hoi Long 33

Extension principle

Nh vy tp fuzzy kt qu B c thc xc nh thng qua cc gi tr caf(xi)

Nu f(.) l mt hm nh x many-to-one th s tn ti gi tr xm, xn thuc Xsao cho f(xn)=f(xm)=y, y thuc Y. Lcny gi tr hm thnh vin ca tp B sl gi tr ln nht ca (A(xn),A(xm))

)(max)()(1

xy Ayfx

B

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GV: L Hoi Long 34

Extension principle

V d: hy tm nh x ca A quaf(x)=x2 - 3

2

3.0

1

9.0

0

8.0

1

4.0

2

1.0

A

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GV: L Hoi Long 35

Extension principle

Nu hm f l mt nh x t khng giann chiu X1X2Xn ti khng gian Ysao cho y=f(x1,x2,,xi) v A1,A2, , Anl n tp fuzzy trong X1, X2, , Xn. Tp

fuzzy B l kt qu ca nh x f cnh ngha bi:

)(,0

)(,)(minmax)( )(),...,,(),,...,,(

12121

y

yxy

iAiyfxxxxxx

B

inn

1-

1-

fif

fif

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GV: L Hoi Long 36

Php tng hp (composition)

C 2 php tng hp: Max-min composition Max-product composition

Php max-min c s dng rng rinhng v mt s cc kh khn trongphn tch nn max-product l phptng hp c xut s dng nhmt php thay th

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GV: L Hoi Long 37

Max-min composition (sup min)

Gi R1 l quan h gia nhng thnhphn t X n Y. Gi R2 l quan hgia nhng thnh phn t Y n Z.Max-min composition ca R1 v R2

c nh ngha

),(),(

),(),,(minmax),(

21

2121

zyyx

zyyxzx

RRy

RRy

RR

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GV: L Hoi Long 38

Max-product composition

Gi R1 l quan h gia nhng thnhphn t X n Y. Gi R2 l quan hgia nhng thnh phn t Y n Z.Max-product composition ca R1 v

R2 c nh ngha

),(),(

),(),,(max),(

21

2121

zyyx

zyyxzx

RRy

RRy

RR

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GV: L Hoi Long 39

Quan h fuzzy (fuzzy relation)

Quan h fuzzy (fuzzy relation) l cc tpcon fuzzy ca XY, X+Y, nh x t Xn Y thng qua Cartesian product ca Xv Y. Mt quan h fuzzy R ang nh x tkhng gian Cartesian XY n on [0,1]vi cng (strength) nh x c thhin bi hm thnh vin ca quan h .Cng thc sau din t quan h fuzzy trnXY :

YXyxyxyxR R ),(),(),,(

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GV: L Hoi Long 40

Quan h fuzzy

V d mt s cc quan h fuzzy: x gn bng y (nu x v y l con s) x ph thuc vo y (nu x, y l cc s

kin)

x tng ng y Nu x bng (l) tnh cht 1, th y l tnh

cht 2 (lut if then)

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GV: L Hoi Long 41

Bi tp 3

Nu ta c nhit phng (A) c 3 mcnhit ln lt x={x1,x2,x3} vtng ng l tnh trng iu chnh myiu ha nhit (B) y={y1,y2}, trnh

by mi quan h fuzzy ca nhit -tnh trng iu ha

28.0

15.0

3

1.0

2

7.0

1

4.0

yyB

xxxA

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GV: L Hoi Long 42

Php tng hp quan h fuzzy

Nu c 2 hay nhiu cc quan h fuzzyR1=XY, R2=YZ, v chng ta cntng hp chng. Lc ny cc phptng hp Max-min v Max-product sc s dng

V d chng ta c quan h gia nhit v tnh trng my iu ha vquan h tnh trng my v tin inphi tr, v chng ta mun tng hp

2 quan h ny

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GV: L Hoi Long 43

Bi tp 4

V d chng ta c quan h R1 gianhit -tnh trng my (v d trn)v quan h R2 gia tnh trng my-tin in tr (C), hy tm kt qu ca

tng hp 2 mi quan h ny (nhit-tin in) (c Max-min v Max-product)

2

8.0

1

4.0

zzC

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GV: L Hoi Long 44

Tnh ton s vi s fuzzy

Bn php tnh c bn vi s fuzzy Php cng (addition) Php tr (subtraction) Php chia (division)

Php nhn (multiplication) Gi s chng ta c 2 s fuzzy A v B,

cc kt qu ca 4 php ton giachng c th c nh ngha theo

cc cng thc

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GV: L Hoi Long 45

Tnh ton s vi s fuzzy

Php cng (addition) fuzzy:

Php tr (subtraction) fuzzy

Php nhn fuzzy

Php chia fuzzy

)(),(minmax))(( yBxAzBAyxz



)(),(minmax))(/( / yBxAzBA yxz

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GV: L Hoi Long 46

Php ton vi s fuzzy hnh thang

Nu ta c 2 s fuzzy hnh thang(trapezoidal) c nh ngha nh slide phn u v c dng di (a1,b10)

A=(a1,a2,a3,a4) v B=(b1,b2,b3,b4) A+B=(a1+b1,a2+b2,a3+b3,a4+b4) A-B=(a1-b4,a2-b3,a3-b2,a4-b1) AB=(a1b1,a2b2,a3b3,a4b4) A/B=(a1/b4,a2/b3,a3/b2,a4/b1)

0kif

0kif

),ka,ka,ka(ka

kakakakaAk

1234

)4,3,2,1(

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GV: L Hoi Long 47

Bi tp 5

Tnh ton cc php +,-,*,/ cho 2 sfuzzy c dng A=(1,2,3,4) vB=(3,4,5,6)

Hai s fuzzy c dng A=(2,3,4,5) v

B=(3,4,5)

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GV: L Hoi Long 48

Php ton vi s fuzzy

Cc cng thc tnh ton nhanh l gnu: Nu cc s fuzzy hnh thang slide

trc khng dng (a1,b1

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GV: L Hoi Long 49

Php ton vi s fuzzy

Chng ta c th da vo cc phpton trn on ng [a,b] v [c,d]nh sau: [a,b]+[c,d]=[a+c,b+d] [a,b]-[c,d]=[a-d, b-c] [a,b]*[c,d]=[min(ac,ad,bc,bd),

max(ac,ad,bc,bd) [a,b]/[c,d]=[a,b]*[1/d,1/c]

=[min(a/d,a/c,b/d,b/c),

max(a/d,a/c,b/d,b/c)

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GV: L Hoi Long 50

Bi tp 6

Hy thit lp cng thc tnh ton cho2 s fuzzy tam gic dng c dng(a1,b1,c1) v (a2,b2,c2)

Hy tnh cc kt qu +,-,*,/ cho 2 s

fuzzy sau (-4,-2,0) v (-2,0,2)

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GV: L Hoi Long 51

Php ly trung bnh (average)

Nu chng ta c n responses (Ai -fuzzy). Chng ta cn ly tr trungbnh ca cc responses (Aav). Cchly nh sau:

nav AAAn

A ...1

21

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GV: L Hoi Long 52

Bin ngn ng (linguistic variable)

m phng suy ngh ca con ngi Tng hp thng tin v trnh by di

dng fuzzy V d:

Tui = {tr, trung nin, gi} Tui = {rt tr, tr, trung nin, gi, rt

gi} Nhn nh = {khng chnh xc, tng

i, chnh xc} Tc = {chm, nhanh, rt nhanh}

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GV: L Hoi Long 53


V d nu chng ta c bin linguisticv tui (T) nh sau: Rt tr - T

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GV: L Hoi Long 54


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GV: L Hoi Long 55


Khi s dng bin ngn ng, chng tac th dng phng php khuch i(intensify) cho ra cc nhn nhkhc t cc nhn nh fuzzy gc

V d: nhn nh gc gi, chng tac th dng cch khuch i tmtng i gi, rt gi

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GV: L Hoi Long 56

Khuch i

Khuch i c xem nh l th bini ca bin ngn ng ban u vc nh ngha nh sau:

2 khuch i thng c s dng lk=0.5 (gin n (dilation) v d: thn) v k=2 (c c (concentration) v d: rt) (xem ti liu)

xxA kA

X

k /)(

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GV: L Hoi Long 57

Khuch i

V d: Nu chng ta c bin fuzzy riro th chng ta c th tm c:t ri ro = Dil(ri ro) (k=0.5)rt ri ro = Con(ri ro) (k=2)cc k ri ro = Con(Con(ri ro))

(k=2*2=4)

h h i

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GV: L Hoi Long 58

Khuch i

V d: nhn nh gc gi, chng tac th dng cch khuch i tmtng i gi, rt gi

L t f If Th

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GV: L Hoi Long 59

Lut fuzzy If-Then

Lut if-then hay cn gi l pht biuc iu kin (conditional statement)c dng nh sau:

If (x1 is A1)

and (x2 is A2)and

then y is B

L t f If Th

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GV: L Hoi Long 60

Lut fuzzy If-Then

V d: If (chm tr > 1 tun) then (pht = 20

triu ) If (ri ro = cao) then (quyt nh =

khng thc hin)

L l f (f i )

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GV: L Hoi Long 61

L lun fuzzy (fuzzy reasoning)

Thng qua mt lut c xcnhn, chng ta c th rt ra mt ktlun (conclusion) t mt s tht(fact-truth) c ghi nhn.

V d: Lut: c xc nh l nu im thi di

5 th kt qu nh gi l khng t. S tht: mt hc vin t im thi soft-

computing di 5. Kt lun: hc vin khng qua mn

L l f (f i )

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GV: L Hoi Long 62


L lun: Rule: if (x is A) then (y is B) Fact: x is A Conclusion: y is B

M rng: Rule: if (x is A) then (y is B) Fact: x is A Conclusion: y is B

Nu A gn nh A, v B gn nh B


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GV: L Hoi Long 63


Mt s dng l lun: Mt lut (rule) cng mt iu kin

(antecedent) Mt lut gm nhiu iu kin

Nhiu lut v nhiu iu kin


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GV: L Hoi Long 64


Mt lut (rule) cng mt iu kin(antecedent) Rule: if (x is A) then (y is B) Fact: x is A

Conclusion: y is B

A B

B

A x y


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GV: L Hoi Long 65


Mt lut (rule) gm nhiu iu kin(antecedent) Rule: if (x1 is A1) and (x2 is A2)

then (y is B)

Fact: x1 is A1 and x2 is A2 Conclusion: y is B

A B

B

A1 x1 y

A

A2 x2

min


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GV: L Hoi Long 66


Nhiu lut (rule) gm nhiu iu kin(antecedent) Rule: if (x1 is A1) and (x2 is A2)

then (y is B1)

and (x1 is A1) and (x2 is A2)then (y is B2)

Fact: x1 is A1 and x2 is A2 Conclusion: y is B


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GV: L Hoi Long 67


Nhiu lut (rule) gm nhiu iu kin(antecedent)

A1 B2B2

x1 y

A2

x2

A1 B1

B1

A1 y

A2

A2

min

y

A1 A2

B

Bi tp 7

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GV: L Hoi Long 68

Bi tp 7

Cho tp fuzzy hnh thang A=(1,2,3,4)ca mt nh gi yu t ri ro v tpfuzzy B=(1,2,3) ca hu qu ca mcnh gi ri ro . Mt lut ni rng

nu ri ro l A th hu qu s l B. Hy v minh ha quan h fuzzy cho riro ny

Nu ri ro thc t c nh gi lA=(1.5,2,3.5,4). Hy v minh ha huqu ca nh gi ri ro ny

Bi tp 8

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GV: L Hoi Long 69

Bi tp 8

By gi hu qu trn l kt hp camc nh gi yu t ri ro A v mcnh gi ca yu t ri roA1=(2,3,4,5).

Hy v minh ha quan h fuzzy ny Nu ri ro thc t c nh gi cho A l

A=(1.5,2,3.5,4) v A1=(2,3,4.5,5). Hyv minh ha hu qu ca nh gi ri rony

Mt s m hnh suy lun fuzzy(fuzzy inference model)

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GV: L Hoi Long 70

(fuzzy inference model)

C 3 m hnh suy lun fuzzy thngc cp: Mamdanis Sugenos

Tsukamotos Cc m hnh ny khc nhau cch

x l u ra (then ) Trong qun l xy dng thng s

dng Mamdanis

Mamdanis

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GV: L Hoi Long 71

Mamdani s

M hnh Mamdanis c th c gi lm hnh singleton outputmembership function

Sau qu trnh x l vi fuzzy, c cc

tp fuzzy cho tng bin u ra mchng ta cn phi gii m c s dng rt rng ri

Mamdanis

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GV: L Hoi Long 72

Mamdani s

V d:

Mamdanis - Ph m(Defuzzification)

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GV: L Hoi Long 73

(Defuzzification)

Kt qu ca x l, tnh ton m bnthn n m Sau khi tnh ton v x l vi fuzzy

set, cng vic cui cng l phi ph

m kt qu cui cng c th sdng n Kt qu gii m l a ra mt con s

trn tp crisp


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GV: L Hoi Long 74

Mt s phng php gii m Smallest of Max Largest of Max Mean of Max

Centroid of Area (Center of mass -gravity) Bisector of Area

(Defuzzification)


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GV: L Hoi Long 75

Smallest of Max: l gi tr nh nhtca cc gi tr c gi tr thnh vinln nht

Largest of Max: l gi tr ln nht ca

cc gi tr c gi tr thnh vin lnnht

y

SoM LoM

(Defuzzification)


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GV: L Hoi Long 76

Mean of Max: l gi tr trung bnh cacc gi tr c gi tr thnh vin lnnht

y

MoM

(Defuzzification)


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GV: L Hoi Long 77

Bisector of Area: l gi tr ti dintch c chia lm 2 phn bng nhau Centroid of Area: l v tr tm trng

trng tm qun tnh(??) (gravity)

ca phn cn gii m (thng sdng)

y

BoA CoA

( e u cat o )

Bi tp 9

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GV: L Hoi Long 78

p

Hy ph m kt qu bi tp 7 v 8 phn trc

Cc bc trin khai m hnhMamdanis

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79/97

GV: L Hoi Long 79

1. Xc nh tp hp lut fuzzy2. Fuzzy ha u vo s dng hm thnhvin

3. X l cc thng tin u vo fuzzy

ha theo cc lut fuzzy4. Xc nh kt qu (l cc output tngng) ca cc lut fuzzy

5. Thng tin input mi => xc nh hnh

dng ca phn phi output tng ng6. Tin hnh ph m

Sugenos

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80/97

GV: L Hoi Long 80

g

Cn gi l m hnh Takagi-Sugeno Lut c bn ca m hnh:

IF x is A and y is B THEN z=f(x,y)

Trong f(.) l hm crisp

Sugenos

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GV: L Hoi Long 81

g

Hm f(.) c th c nhiu bc: Bc 0 (zero-order)

f(x,y) = C

Bc 1 (first order)f(x,y) = ax+by+C

(Rt t khi s dng)

Sugenos

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82/97

GV: L Hoi Long 82

Mi lut trong m hnh s c 1 u ral crisp Kt qu u ra cui cng l bnh qun

trng s (weighted average) ca cc

u ra ca cc lut Trng s l kt qu ca ton t p

dng ln cc hm thnh vin ca lutIF

Sugenos

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GV: L Hoi Long 83

Nguyn l ca m hnh Sugenos

Sugenos (v d)

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GV: L Hoi Long 84

Sugenos (v d)

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GV: L Hoi Long 85

M hnh singleinput

M hnh 2-input single-output

2-xyTHENlargeisxIF

4-0.5xyTHENmediumisxIF

6.40.1xyTHENsmallisIFx

2yxzTHENlargeisyANDlargeisxIF

3xzTHENsmallisyANDlargeisxIF

3-yzTHENlargeisyANDsmallisxIF

1yxzTHENsmallisyANDsmallisIFx

Bi tp 10

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GV: L Hoi Long 86

Hy v minh ha m hnh Sugenoscho m hnh single-input slidetrc. Hy t thm cc thng tin cnthit.

Hy v minh ha m hnh Sugenoscho m hnh 2-input single-output slide trc. Hy t thm cc thng tincn thit.

Tsukamotos

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GV: L Hoi Long 87

Tp fuzzy ca pht biu THEN c i dinbi mt hm thnh vin n iu

Mi lut trong m hnh s c 1 u ra lcrisp l gi tr ca hm thnh vin

Kt qu u ra cui cng l bnh qun

trng s (weighted average) ca cc u raca cc lut

Trng s l kt qu ca ton t p dng lncc hm thnh vin ca lut IF

t c s dng

Tsukamotos

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GV: L Hoi Long 88

V d: 2-input single-output

x

y

x

y

z

z

w1

w2

z1

z2

21

2211

ww

zwzw

z

A1 B1

A2 B2

C1

C2

So snh 2 m hnh Mamdanis vSugenos

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GV: L Hoi Long 89

S khc nhau c bn l hm thnhvin u ra ca Sugenos c th ltuyn tnh hay hng s

Kt qu ca lut fuzzy cng nh cch

tng hp v ph m ca tng mhnh khc nhau Mamdanis d thc hin hn

Thun li ca m hnh Mamdanis

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GV: L Hoi Long 90

Trc quan c ng dng rng ri

Rt ph hp khi s dng d liu do

dnh gi ca ca con ngi

Thun li ca m hnh Sugenos

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91/97

GV: L Hoi Long 91

Hu hiu trong tnh ton Rt ph hp vi cc m hnh c tnhtuyn tnh

Ph hp vi cc k thut ti u v

thch nghi m bo tnh lin tc ca khng gian

u ra Ph hp vi phn tch ton hc

Ti sao li s dng fuzzy

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92/97

GV: L Hoi Long 92

Kh d hiu v mt khi nim Kh mm do

X l tt nhng thng tin khng chnh

xc C th m hnh cc hm s c tnh

phi tuyn

Ti sao li s dng fuzzy

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93/97

GV: L Hoi Long 93

M hnh tt cc thng tin kinh nghim p dng kt hp vi cc k thut iu

khin truyn thng

Da trn ngn ng mang tnh tnhin, giao tip ca con ngi

Khi no khng nn s dng fuzzy

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94/97

GV: L Hoi Long 94

Fuzzy khng phi l mt v thn vnnng

i khi nhng cch hay phng phpx l n gin hiu qu hn

i khi vic thit lp nhng nh x tkhng gian u vo n khng gianu ra gp kh khn => chn cchkhc

S tng t gia fuzzy v ANN

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95/97

GV: L Hoi Long 95

c tnh cc hm s t d liu mu Khng yu cu m hnh ton L mt h ng Chuyn cc u vo s thnh cc u ra s X l thng tin khng chnh xc Cng khng gian trng thi To ra cc tn hiu b chn Hot ng nh mt b nh c tnh lin kt

S khc nhau gia fuzzy v ANN

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96/97

GV: L Hoi Long 96

Fuzzy s dng kin thc t tm ti to nn cc lut v lm cho chngph hp s dng d liu mu

ANN to nn cc lut da hon ton

trn d liu mu

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GV: L Hoi Long 97

Chc thnh cng

fuzzy_logic_6828

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