fuzzy_6828

GV: L Hoi Long 1

Fuzzy logic

Phn 2

GV: L Hoi Long 2

Fuzzy?

Nhng hnh di y c mu g?

GV: L Hoi Long 3

Fuzzy?

Cc c gi p?

GV: L Hoi Long 4

Fuzzy?

Ti v bn, ai cao?

GV: L Hoi Long 5

Fuzzy logic

Khi nim v fuzzy logic c thai nghnbi gio s Lotfi Zadeh ca i hc UC Berkeley 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 tnh kh nng lp lun ca con ngi.

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 (Rene Dubos)

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality (Albert Einstein)

GV: L Hoi Long 7

Fuzzy logic

L lun chnh xc ch l mt trng hp giihn ca l lun xp x (approximate reasoning)

Mi th ch l vn ca mc (matter of degree)

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 truynca cc rng buc n hi

Bt c mt h lun l (logic) no cng cth lm m (fuzzify)

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

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

GV: L Hoi Long 10

Bi tp 1

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

1

0

Gi tin

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 xitrong tp fuzzy A

nn xxxA /...// 2211

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

?

GV: L Hoi Long 13

Mt s khi nim trong l thuytfuzzy

Support

-cut

Tp fuzzy li (convex)

Tp fuzzy thng (normal)

S fuzzy

GV: L Hoi Long 14

Support ca tp fuzzy

Gi A l mt tp fuzzy thuc X, support ca A (k hiu supp(A)) l mt tp con cng (crisp) ca X sao cho:

}0)({) xAXxAsupp(

x1 x2

1

0

A

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

GV: L Hoi Long 15

-cut

L mt tp phi fuzzy (k hiu l [A]) c nh ngha nh sau:

cl(supp(A)) l khong ng ca supp(A)

0 ifsupp(A)

0 if

)(

})({

cl

tAXtA

GV: L Hoi Long 16

Bi tp 2

Hy tm -cut (0

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]

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.

GV: L Hoi Long 19

Fuzzy number

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

GV: L Hoi Long 20

Fuzzy number

GV: L Hoi Long 21

S fuzzy tam gic

otherwise

ata if

at-a if

0

1

1

)(

ta

ta

tA

-cut ti =0.5?

GV: L Hoi Long 22

S fuzzy hnh thang

othewise

btb if

bta if

at-a if

0

1

1

1

)(

ta

ta

tA

-cut ti =0.5?

GV: L Hoi Long 23

Cc s fuzzy khc

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

Cc s fuzzy khc u c th s dngtrong cc trng hp ph hp khc

Bell

Gaussian

Sigmoid

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)

GV: L Hoi Long 25

Php giao 2 s fuzzy

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

Xt all for

)()(

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

tBtA

tBtAtBA

GV: L Hoi Long 26

Php hp 2 s fuzzy

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

Xt all for

)()(

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

tBtA

tBtAtBA

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

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)

GV: L Hoi Long 29


Tnh giao hon (commutativity)

Tnh kt hp (associativity)

Tnh phn phi (Distributivity)

ABBA

ABBA

CBACBA

CBACBA

)()(

)()(

)()()(

)()()(

CABACBA

CABACBA

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 then if

AA ))((

GV: L Hoi Long 31

Luyn tp

6

3.0

5

7.0

4

4.0

3

8.0

2

5.0

6

6.0

5

2.0

4

6.0

3

5.0

2

1

B

A

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

BA

B

A

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 qua Y.

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

n

n

xx

xx

xxA

)(...)()(

2

2

1

1

n

n

yx

yx

yxAfB

)(...)()()(

2

2

1

1

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 X sao 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

GV: L Hoi Long 34

Extension principle

V d: hy tm nh x ca A qua

f(x)=x2 - 3

23.0

19.0

08.0

14.0

21.0

A

GV: L Hoi Long 35

Extension principle

Nu hm f l mt nh x t khng giann chiu X1X2Xn ti khng gian Y sao cho y=f(x1,x2,,xi) v A1,A2, , Anl n tp fuzzy trong X1, X2, , Xn. Tpfuzzy B l kt qu ca nh x f cnh ngha bi:

)(,0

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

12121

y

yxy

iAiyfxxxxxx

B

inn

1-

1-

f if

f if

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

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 R2c nh ngha

),(),(

),(),,(minmax),(

21

2121

zyyx

zyyxzx

RRy

RRy

RR

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 vR2 c nh ngha

),(),(

),(),,(max),(

21

2121

zyyx

zyyxzx

RRy

RRy

RR

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 X n Y thng qua Cartesian product ca X v 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 ),(),(),,(

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 skin)

x tng ng y

Nu x bng (l) tnh cht 1, th y l tnhcht 2 (lut if then)

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}, trnhby mi quan h fuzzy ca nhit -tnh trng iu ha

2

8.0

1

5.0

3

1.0

2

7.0

1

4.0

yyB

xxxA

GV: L Hoi Long 42

Php tng hp quan h fuzzy

Nu c 2 hay nhiu cc quan h fuzzy R1=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 hp2 quan h ny

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

2

8.0

1

4.0

zzC

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 theocc cng thc

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))(/(/

yBxAzBAyxz

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)

0k if

0k if

) ,ka,ka,ka(ka

kakakakaAk

1234

)4,3,2,1(

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) vB=(3,4,5)

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

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)

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

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

GV: L Hoi Long 52

Bin ngn ng (linguistic variable)

m phng suy ngh ca con ngi

Tng hp thng tin v trnh by didng fuzzy

V d: Tui = {tr, trung nin, gi}

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

Nhn nh = {khng chnh xc, tngi, chnh xc}

Tc = {chm, nhanh, rt nhanh}

GV: L Hoi Long 53


V d nu chng ta c bin linguistic v tui (T) nh sau:

Rt tr - T

GV: L Hoi Long 54


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

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 kAX

k /)(

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)

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

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

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)

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 di5 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

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

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

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

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

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

GV: L Hoi Long 67


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

A1 B2B2

x1 y

A2

x2

A1 B1

B1

A1y

A2

A2

min

y

A1 A2

B

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 rngnu 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

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

GV: L Hoi Long 70

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

C 3 m hnh suy lun fuzzy thngc cp:

Mamdanis

Sugenos

Tsukamotos

Cc m hnh ny khc nhau cchx l u ra (then )

Trong qun l xy dng thng sdng Mamdanis

GV: L Hoi Long 71

Mamdanis

M hnh Mamdanis c th c gi lm hnh singleton output membership function

Sau qu trnh x l vi fuzzy, c cctp fuzzy cho tng bin u ra mchng ta cn phi gii m

c s dng rt rng ri

GV: L Hoi Long 72

Mamdanis

V d:

GV: L Hoi Long 73

Mamdanis - Ph m(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 phm kt qu cui cng c th sdng n

Kt qu gii m l a ra mt con strn tp crisp

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


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 cacc gi tr c gi tr thnh vin lnnht

y

SoM LoM


GV: L Hoi Long 76

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

y

MoM


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 trngtrng tm qun tnh(??) (gravity) ca phn cn gii m (thng sdng)

y

BoA CoA


GV: L Hoi Long 78

Bi tp 9

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

GV: L Hoi Long 79

Cc bc trin khai m hnhMamdanis

1. Xc nh tp hp lut fuzzy

2. Fuzzy ha u vo s dng hm thnhvin

3. X l cc thng tin u vo fuzzy ha theo cc lut fuzzy

4. Xc nh kt qu (l cc output tngng) ca cc lut fuzzy

5. Thng tin input mi => xc nh hnhdng ca phn phi output tng ng

6. Tin hnh ph m

GV: L Hoi Long 80

Sugenos

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

GV: L Hoi Long 81

Sugenos

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)

GV: L Hoi Long 82

Sugenos

Mi lut trong m hnh s c 1 u ral crisp

Kt qu u ra cui cng l bnh quntrng s (weighted average) ca ccu ra ca cc lut

Trng s l kt qu ca ton t pdng ln cc hm thnh vin ca lutIF

GV: L Hoi Long 83

Sugenos

Nguyn l ca m hnh Sugenos

GV: L Hoi Long 84

Sugenos (v d)

GV: L Hoi Long 85

Sugenos (v d)

M hnh singleinput

M hnh 2-input single-output

2-xy THEN large is x IF

4-0.5xy THEN medium is x IF

6.40.1xy THEN small is IFx

2yxz THEN large is y AND large is x IF

3xz THEN small is y AND large is x IF

3-yz THEN large is y AND small is x IF

1yxz THEN small is y AND small is IFx

GV: L Hoi Long 86

Bi tp 10

Hy v minh ha m hnh Sugenoscho m hnh single-input slide trc. 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 tin cn thit.

GV: L Hoi Long 87

Tsukamotos

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 quntrng 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

GV: L Hoi Long 88

Tsukamotos

V d: 2-input single-output

x

y

x

y

z

z

w1

w2

z1

z2

21

2211

ww

zwzwz

A1 B1

A2 B2

C1

C2

GV: L Hoi Long 89

So snh 2 m hnh Mamdanis vSugenos

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 cchtng hp v ph m ca tng mhnh khc nhau

Mamdanis d thc hin hn

GV: L Hoi Long 90

Thun li ca m hnh Mamdanis

Trc quan

c ng dng rng ri

Rt ph hp khi s dng d liu do

dnh gi ca ca con ngi

GV: L Hoi Long 91

Thun li ca m hnh Sugenos

Hu hiu trong tnh ton

Rt ph hp vi cc m hnh c tnhtuyn tnh

Ph hp vi cc k thut ti u vthch nghi

m bo tnh lin tc ca khng gianu ra

Ph hp vi phn tch ton hc

GV: L Hoi Long 92

Ti sao li s dng fuzzy

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

GV: L Hoi Long 93

Ti sao li s dng fuzzy

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 t

nhin, giao tip ca con ngi

GV: L Hoi Long 94

Khi no khng nn s dng fuzzy

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

GV: L Hoi Long 95

S tng t gia fuzzy v ANN

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

GV: L Hoi Long 96

S khc nhau gia fuzzy v ANN

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 tontrn d liu mu

GV: L Hoi Long 97

Chc thnh cng

fuzzy_6828

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