Bai Thu Hoachi

7/31/2019 Bai Thu Hoachi

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M UTi cha bao gi dm m n s thnh mt hin tng khp th gii. Nhng iuti k vng khim tn hn nhiu.. l pht biu tr li phng vn caLofti

Zadeh (cha ca Logic m) trn tp ch Azerbaijan International v ch ni tip Cuc phiu lu ca Logic Mvo nm 2003.

Tht vy, ngy nay Logic m tr nn rt ph bin bi ng dng thctin ca n vo cc thit b gip chng thng minh hn. Nhiu quc gia tin tin v ang nghin cu ng dng ngy cng nhiu Logic m vo cc thit b chng ngy cng gn gi hn trong sinh hot thng nht ca con ngi nh: Nht, M, c, Trung Quc

Mt thit b in hnh p dng Logic m l my git. Khi s dng mt mygit, vic la chn thi gian git da vo s lng qun o, kiu v bn mqun o c. t ng ha qu trnh ny, chng ta s dng nhng phn t sensors pht hin ra nhng tham s ny (v d: th tch qun o, v kiu cht bn).Thi gian git c xc nh t d liu ny. Khng may, khng d c cch cngthc ha mt mi quan h ton hc chnh xc gia th tch qun o v bn vthi gian git. Chng ta gii quyt vn thit k ny bng cch s dng lgic m.

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CHNG 1. TNG QUAN V LOGIC M Logic m c hai cch hiu khc nhau:- Theo ngha hp c th xem logic m l h thng logic c m rng t logic a

tr (khc vi logic c in da trn i s Bool).- Tng qut hn, logic m hon ton gn lin vi l thuyt v tp m. Mt lthuyt lin quan n vic phn nhm cc i tng bi mt ng bao m, vicxc nh mt i tng c thuc vo mt nhm hay khng s da vo gi tr cahm ph thuc cho bi nhm (gi tr u vo khng cn phi l gi tr s m cth l ngn ng thng ngy)

Nh vy, c th ni logic m hiu theo ngha hp ch l mt trng hp c

bit ca logic m tng qut. Mt iu quan trng l ngay c khi hiu logic m theongha hp th nhng thao tc trong logic m cng khc v ngha ln phng php so vi logic c in da trn i s Bool.

Mt khi nim rt thng dng trong logic m l bin ngn ng. Bin ngnng l nhng bin cha gi tr l ch thay v l s. C th hiu logic m theo nghatng qut l mt phng php tnh ton trn cc gi tr ch thay v l tnh ton trngi tr s nh cc trng phi c in. Mc d cc gi tr ngn ng vn khngchnh xc bng cc gi tr s nhng n li gn vi trc gic ca con ngi. Hnna, vic tnh ton trn cc gi tr ngn ng cho php chp nhn tnh m h ca dliu nhp do dn n gii php t tn km hn.

1. Bin ngn ng Bin ngn ng l phn ch o trong cc h thng dng logic m. y,

cc thnh phn ngn ng m t cng mt ng cnh c kt hp li. V d nh

trong trng hp m t nhit , khng ch c rt nng m cn hi nng,trung bnh, hi lnh v rt lnh u m t nhit . Chng c gi l cctp ngn ng, mang mt khong gi tr no ca bin ngn ng v c v trncng mt th.

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2. Lut hp thnh m 2.1. Mnh hp thnh

Cho hai bin ngn ng v . Nu bin nhn gi tr m A c hm lin thuc A(x) v nhn gi tr m B c hm lin thuc B(y) th hai biu thc:

= A,

= Bc gi l hai mnh K hiu hai mnh trn l p v q th mnh hp thnh

p q ( t p suy ra q)hon ton tng ng vi mnh hp thnh mt iu kin

NU = A th = B,Trong mnh p c gi l mnh iu kin v q l mnh kt lun.Mnh hp thnh trn cho php t mt gi tr u vo x0 hay c th hn l t

ph thuc A(x0) i vi tp m A ca gi tr u vo x0 xc nh c h s thonmn mnh kt lun q ca gi tr u ra y. Biu din h s tha mn mnh qca y nh mt tp m B cng c s vi B th mnh hp thnh chnh l nh x:

A(x0) B(y)2.2. M t mnh hp thnh

nh x A(x0) B(y) ch ra rng mnh hp thnh l mt tp m mi phn t

l mt gi tr ( A(x0), B(y)), tc l mi phn t l mt tp m. M t mnh hpthnh t l m t nh x trn.

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Sau y, nh x A(x0) B(y) s c gi l hm lin thuc ca lut hp thnh.

Trong ton logic c in, gia mnh hp thnh p q v cc mnh iukhin p, kt lun q c quan h sau:

p q p q0 0 10 1 11 0 01 1 1

Ni cch khc: mnh hp thnh p q c gi tr logic ca p v q, trong ch php tnh ly gi tr logic o v v ch php tnh logic hoc.Biu thc tng ng cho hm lin thuc ca mnh hp thnh s l:

A B -> MAX {1- A(x), B(y) }Hm lin thuc ca mnh hp thnh trn c c s l tp tch hai tp c s

c. Do c s mu thun rng A B lun c gi tr ng (gi tr logic 1) khi p sai

nn s chuyn i tng ng t mnh hp thnh p q kinh in sang mnh

hp thnh m A B khng p dng c trong cc vn thc t. khc phc nhc im trn, c nhiu kin khc nhau v nguyn tc xy dng

hm lin thuc A B(x,y) cho mnh hp thnh A B nh1. A B(x,y) = MAX {MIN{ A(x), B(y)}, 1- A(x)} cng thc Zadeh,

2. A B(x,y) = MIN {1, 1- A(x) + B(y)} cng thc Lukasiewicz,

3. A B(x,y) = MAX {1- A(x), B(y)} cng thc Kleene-DienesTuy nhin, nguyn tc ca Mamdani: ph thuc ca kt lun khng c lnhn ph thuc ca iu kin l c tnh thuyt phc nht v hin ang c sdng nhiu nht m t lut mnh hp thnh m.T nguyn tc ca Mamdani c c cc cng thc xc nh hm lin thuc sau

cho mnh hp thnh A B:

1. A B(x,y) = MIN { A(x), B(y)} cng thc MAX-MIN

2. A B(x,y) = A(x). B(y) cng thc MAX-PROD

Cc cng thc trn cho mnh hp thnh A B c gi l qui tc hp thnh.

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2.3. Lut hp thnh MAX-MINLut hp thnh MAX-MIN l tn gi m hnh (ma trn) R ca mnh hp

thnh A B khi hm lin thuc A B(x,y) ca n c xy dng trn qui tc

MAX-MINTrc tin hai hm lin thuc A(x), B(y) c ri rc ha vi chu k ri

rc nh khng mt thng tinTng qut ln cho mt gi tr r x0 bt k:

x0 X ={ x1, x2,, xn }ti u vo, vector chuyn v a s c dng:

aT = ( a1, a2,, an)trong ch c mt phn t ai duy nht c ch s i l ch s ca x0 trong X c gitr bng 1, cc phn t cn li u bng 0. Hm lin thuc:

trnh s dng thut ton nhn ma trn ca i s tuyn tnh cho vic tnh B(y)v cng tng tc x l, php tnh nhn ma trn c thay bi lut max-minca Zadeh vi max (php ly cc i) thay vo v tr php nhn v min (php lycc tiu) thay vo v tr php cng nh sau:

2.4. Lut hp thnh MAX_PRODCng ging nh vi lut hp thnh MAX-MIN, ma trn R ca lut hp

thnh MAX_PROD c xy dng gm cc hng l m gi tr ri rc ca u ra

B(y1), B(y2),, B(ym) cho n gi tr r u vo x1, x2,, xn. Nh vy, ma trn R s c n hng v m ct.

rt ngn thi gian tnh v cng m rng cng thc trn cho trnghp u vo l gi tr m, php nhn ma trn aT.R cxung c thay bng lut max-min ca Zadeh nh lm cho lut hp thnh MAX_MIN.

2.5. Thut ton xy dng R

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Phng php xy dng Rcho mnh hp thnh mt iu kin R: A B,theo MAX-MIN hay MAX-PROD, xc nh hm lin thuc cho gi tr m Bu ra hon ton c th m rng tng t cho mt mnh hp thnh bt k no

khc dng: Nu =A th =BTrong ma trn hay lut hp thnh R khng nht thit phi l mt ma trn

vung. S chiu ca R ph thuc vo s im ly mu ca A(x) v B(y) khi rirc cc hm lin thuc tp m A v B

Chng hn vi n im mu x1, x2,, xn ca hm A(x) v m im mu y1,

y2,, ym ca hm B(y) th lut hp thnh R l mt ma trn n hng m ct nh sau:

Hm lin thuc B(y) ca gi tr u ra ng vi gi tr r u vo xk cxc nh theo:

B(y) = aT.R viAT = (0,0,,0,1,0,,0)

V tr th k

Trong trng hp u vo l gi tr m A vi hm lin thuc A(x) th

hm lin thuc B(y) ca gi tr u ra B:

B(y) = (l1, l2,,lm)Cng c tnh theo cng thc trn v

Trong a l vector gm cc gi tr ri rc ca cc hm lin thuc A(x)ca A ti cc im

x X = { x1, x2,, xn } ,tc l

aT = ( A(x1), A(x2), , A(xn))u im ca lut max-min Zedeh l c th xc nh ngay c R thng qua

dyadic, tc l tch ca mt vector vi mt vector chuyn v. Vi n im ri rc x1,x2,, xn ca c s ca A m m im ri rc y1, y2,, ym ca c s ca B th t hai

vector:

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suy ra:

R = A. T

B

trong nu qui tc p dng l MAX-MIN th php nhn c thay bng phptnh ly cc tiu (min), vi qui tc MAX-PROD th thc hin php nhn nh bnhthng.

2.6 Lut hp thnh ca mnh nhiu iu kin Nu mnh hp thnh vi d mnh iu kin:

Nu 1= A1 v 2= A2 v v d= Ad th = B

bao gm d bin ngn ng u vo 1, 2, , d v mt bin u ra cng c mhnh ha ging nh vic m hnh ha mnh hp thnh c mt iu kin, trong lin kt v gia cc mnh (hay gi tr m) c thc hin bng php giaocc tp m A1, A2,, Ad vi nhau. Kt qu ca php giao s l tha mn H calut. Cc bc xy dng lut hp thnh R nh sau:

- Ri rc ha min xc nh hm lin thuc A1(x1), A2(x2), , Ad(xd),

B(y) ca cc mnh iu kin v mnh kt lun.- Xc nh tha mn H cho tng vector cc gi tr r u vo l vector t

hp d im mu thuc min xc nh ca cc hm lin thuc Ai(xi), i= 1,,d.Chng hn vi mt vector cc gi tr r u vo

trong ci, i= 1, , d l mt trong cc im mu min xc nh ca Ai(xi)th

H = MIN { A1(c1), A2(c2), , Ad(cd)}- Lp R gm cc hm lin thuc gi tr m u ra cho tng vector cc gi tr

u vo theo nguyn tc:

B(y) = MIN {H, B(y)} nu qui tc s dng l MAX-MIN hoc

B(y) = H. B(y) nu qui tc s dng l MAX- PROD

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Lut hp thnh R vi d mnh iu kin c biu din di dng mt likhng gian (d+1) chiu.

3. Gii m

Gii m l qu trnh xc nh mt gi tr r y no c th chp nhnc t hm lin thuc B(y) ca gi tr m B (tp m). C hai phng php giim ch yu l phng php cc i v phng php im trng tm, trong c s ca tp m B c k hiu thng nht l Y.

3.1. Phng php cc iGii m theo phng php cc i gm 2 bc

- Bc 1: Xc nh min cha gi tr r y. Gi tr r y l gi tr m ti hmlin thuc t gi tr cc i ( cao H ca tp m B), tc l min:

G = {y Y/ B(y) = H}- Bc 2: xc nh y c th chp nhn c t G

G l khong [y1, y2] ca min gi tr ca tp m u ra B2 ca lut iukhin

R 2 : Nu =A2 th =B2

trong s hai lut R 1, R 2 v lut R 2 c gi l lut quyt nh. Vy lut iu khinquyt nh l lut R k , k {1,2,, p} m gi tr m u ra ca n c cao lnnht, tc l bng cao H ca BGii m bng phng php cc i

thc hin bc hai c ba nguyn l:- nguyn l trung bnh- nguyn l cn tri

- nguyn l cn phi Nu k hiu:

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th y1 chnh l im cn tri v y2 l im cn phi ca G3.2. Nguyn l trung bnh

Theo nguyn l trung bnh, gi tr r y s l

Nguyn l ny thng c dng khi G l mt min lin thng v nh vyy cng s l gi tr c ph thuc ln nht. Trong trng hp B gm cc hmlin thuc dng u th gi tr r y khng ph thuc v tha mn ca lut iu

khin quyt nh.Gi tr r y khng ph thuc vo p ng ca lut iu khin quyt nh

3.3. Nguyn l cn triGi tr r y c ly bng cn tri y1 ca G. Gi tr r ly theo nguyn l cn triny s ph thuc tuyn tnh vo thon mn ca lut iu khin quyt nh.Gi tr r y ph thuc tuyn tnh vi p ng vo lut iu khin quyt nh

3.4. Nguyn l cn phiGi tr r y c ly bng cn phi y1 ca G. Cng ging nh nguyn l

cn tri, gi tr r ly theo nguyn l cn tri ny s ph thuc tuyn tnh vo thon mn ca lut iu khin quyt nh.

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Gi tr r y ph thuc tuyn tnh vi p ng vo lut iu khin quyt nh3.5. Phng php im trng tm

Phng php im trng tm scho ra kt qu y l honh caim trng tm min c bao bi

trc honh v ng B(y)Cng thc xc nh y theo phng php im trng tm nh sau:

trong S l min xc nh ca tp m B

Gi tr r y l honh ca im trng tm

Cng thc trn cho php xc nh gi tr y vi s tham gia ca tt c cctp m u ra ca mt lut iu khin mt cch bnh ng v chnh xc, tuy nhinli khng c ti tha mn ca lut iu khin quyt nh v thi giantnh ton lu. Ngoi ra mt trong nhng nhc im c bn ca phng phpim trng tm l c th gi tr y xc nh c li c ph thuc nh nht,thm ch bng 0. Bi vy trnh nhng trng hp nh vy, khi nh ngha hm

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lin thuc cho tng gi tr m ca mt bin ngn ng nn sao cho min xcnh ca cc gi tr u ra l mt min lin thng.

3.6. Phng php im trng tm cho lut hp thnh SUM-MIN

Gi s c q lut iu khin c trin khai. Vy th mi gi tr m B tiu ra ca b iu khin th k l vi k = 1, 2,, q th quy tc SUM-MIN, hm

lin thuc B(y) s l:

3.7. Phng php cao

S dng cng thc tnh y trn cho c hai loi lut hp thnh MAX-MIN vSUM-MIN vi thm mt gi thit l mi tp m Bk (y) c xp x bng mt cp

gi tr (yk , Hk ) duy nht, trong Hk l cao ca Bk (y) v yk l mt im mu

trong min gi tr ca Bk (y) c:

Cng thc trn c tn gi l cng thc tnh xp x y theo phng php cao v khng ch p dng cho lut hp thnh MAX-MIN, SUM-MIN m cn cth cho c nhng lut hp thnh khc nh MAX-PROD hay SUM-PROD

4. Cc bc thit k h iu khin m dn gin- Bc 1: Xc nh cc bin ca qui trnh (cc bin vo, cc bin trng thi v cc bin ra)

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- Bc 2: Chia khng gian nn thnh cc tp m, gn mi tp m mt nhn ngnng (cc tp m bao gm tt c cc phn t trong tp nn)- Bc 3: Gn hoc xc nh mt hm lin thuc cho mi tp m

- Bc 4: Gn cc mi quan h gia cc tp m ca cc bin vo v cc tp m ca cc bin ra v hnh thnh mt c s lut m - Bc 5: Chn cc h s t l ph hp cho cc bin vo ra chun ha csac binvo on [0,1] hoc [-1,1]- Bc 6: M ha csac bin vo b iu khin- Bc 7: Dng suy din m suy ra ng ra ng gp t mi lut- Bc 8: Kt hp cc ng ra a ra t mi lut

- Bc 9: Gii m tm gi tr r cho ng raTrong mt b iu khin m khng thch nghi, phng php s dng v kt

qu ca chn bc trn l c nh, trong khi tong mt b iu khin m thchnghi, chng c th thay i da trn mt s lut ti u b iu khin.

Mt b iu khin m n gin c cc tnh cht sau:1. C nh v ng nht cc h s t l ng vo v ng ra2. C mt c s lut m vi cc lut c nh v khng tng tc ln nhau. Tt

c cc lut c cng mc chc chn v tin cy v bng 13. Cc hm lin thuc c nh4. C mt s hn ch cc lut, s lut ny tng theo hm m khi s bin vo

tng ln5. Metaknowlegde c nh, bao gm phng php suy din xp x, kt hp

cc lut m v gii m

6. iu khin mc thp v khng c cu trc phn lp lut iu khin

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CHNG 2: NG DNG LOGIC M VO BI TON MY GIT1. Xy dng b iu khinChng ta xy dng h thng m nh sau:

C hai tr nhp vo :( 1) Mt cho bn trn qun o( 2) Mt cho loi cht bn trn qun o.Hai u vo ny thu c t phn t sensors quang hc. bn c xc nh bis trong sut ca nc. Mt khc, loi cht bn c xc nh t s bo ha, thigian n dng t n s bo ha. Qun o du m chng hn cn lu hn chos trong sut nc t n s bo ha bi v m l cht t ha tan trong nc

hn nhng dng khc ca cht bn. Nh vy mt h thng phn t sensors kh ttc th cung cp nhng input cn thit c nhp vo cho b iu khin m cachng ta. Nhng gi tr cho bn v loi cht bn l c chun ha ( phm vi t 0 ti100) c cho bi gi tr phn t sensors.Vi bin ngn ng bn c cc tp m

Bn t (D.Small)Bn va (D.Medium)Bn nhiu (D.Large)

Vi bin ngn ng loi cht bn c cc tp m M t (K.NotGreasy)M va (K.Medium)M nhiu (K.Greasy)

Vi bin ngn ng kt lun xc nh thi gian git c cc tp m Git rt ngn (T.VeryShort)Git ngn (T.Short)Git va (T.Medium)Git lu (T.Long)Git rt lu (T.Very Long)

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2. Xy dng tp lutQuyt nh lm cho kh nng mt m l b iu khin c lp lut trong mt tphp nhng quy tc. Ni chung, nhng quy tc l trc gic v d hiu,

Mt quy tc trc gic tiu biu nh sau : Nu thi gian bo ha lu v s trong sut t th thi gian git cn phi

lu.T nhng s kt hp khc nhau ca nhng lut v nhng iu kin khc, chngta vit nhng quy tc cn thit xy dng b iu khin my git.

Gi x: ch bn (0


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D.Small(x) = [ 1-x/50 nu 0


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T.Long(z) = [0 nu 0


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Nu nhp tr input x0 =40 ( bn), y0=60 (loi cht bn)D.Small(x0) = 1/5D.Medium(x0) = 4/5D.Large(x0) = 0

K .NotGreasy(y0) = 0K .Medium(y0) = 4/5

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K .Greasy(y0) = 1/5W1 = min(D.Large(x0), K .Greasy(y0)) = min(0,1/5) = 0W2 = min(D.Medium(x0), K .Greasy(y0)) = min(4/5, 1/5) = 1/5

W3 = min(D.Small(x0), K .Greasy(y0)) = min(1/5, 1/5) = 1/5W4 = min(D.Large(x0), K .Medium(y0)) = min(0, 4/5) = 0W5 = min(D.Medium(x0), K .Medium(y0)) = min(4/5, 4/5) = 4/5W6 = min(D.Small(x0), K .Medium(y0)) = min(1/5, 4/5) = 1/5W7 = min(D.Large(x0), K .NotGreasy(y0)) = min(0, 0) = 0W8 = min(D.Medium(x0), K .NotGreasy(y0)) = min(4/5, 0) = 0W9 = min(D.Small(x0), K .NotGreasy(y0)) = min(1/5, 0) = 0

Cc Wi gi l cc trng s ca lut th i

Theo l thuyt hm thnh vin ca kt lun cho bi cng thc:

C(z) = W2*T.Long(z) + W3*T.Long(z) + W5*T.Medium(z) + W6*T.Medium(z)C(z) = 2/5*T.Long(z) + T.Medium(z)

Bc tip theo l ta phi gii m t hm thnh vin ca kt lun bng cnh tnhtrng tm ca hm C(z) l060z C(z) d(z) = 705.6V Moment C(z) l060 C(z) d(z) = 19.6VyDefuzzy(z) =705.6/19.6=36Do nu bn v loi cht bn l 40 v 60 th thi gian cn git l 36 pht.

CHNG 3: KT LUN

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Trong chng 2, chng ta xy dng b iu khin v cc thnh phn can ng dng Logic m v mt thit b dn dng thit yu trong i sng hngngy ca chng ta, l my git. ng dng trn l mt v d in hnh. Trong

tng lai khng xa Logic m s cn c ng dng trong nhiu lnh vc hn nanh: kinh t hc, nhn vn hc, tm l hc, tm sinh l hc, ngn ng hc, chnhtr, x hi hc, v v s ngnh khc s dng n n. cng chnh l pht biuca Zadeh, cha ca Logic m.

TI LIU THAM THO

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[1] Trn c Quang (bin dch),Tr tu tnh ton Tip cn bng Logic, tp 1+ 2, NXB Thng K 2002.

[2] George J. Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic Theory and

Applications, Prentice-Hall International Inc. 1995.[3] Phan Xuan Minh, L thuyt iu khin m , Nh Xut Bn Khoa Hc

K Thut.[4] tp ch Azerbaijan International ngy 04/3/2003, Trnh Hip dch

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