mayhoc fuzzy

8/6/2019 MayHoc Fuzzy

1/36

SOM-LOGICM

-GIAIPHNGTRNHM


2/36

1.1.

TTppmm

nhngha:Altpmtrnkh

nggiannnX

nuA

cxcn

hbihm:

A

:X[0,1]

Trong:

Al

hmlinthuc(membersh

ipfunction)

A(x)llinthu

ccaxvo

tpmA.


3/36

2.

2.CC

ccphphpp

totonntr

n

tr

nttppmm

nhngha:ChoAv

Blhaitpm

trnkhnggiannn

X,c

cchmlinthucA,B.Khitacccph

p

tons

au:

AxB(x,y)=min{A(x),B(y)}

AxB

8

(x)=

0

7

X(x)=1

X

6

AB

=A(x)+B(x)-

A(x)B(x)

AB

5

A=

1-A

A

4

AB

(x)=min{A(x),B(x)}

AB

3

AB

(x)=max{A(x),B(x)}

AB

2

A(x)

B(x)

AB

1

nhn

ghahmlinthuc

Phptontrntpm

Stt


4/36

SS

mm

nhngha:

TpmMtrn

ngthngs

thcRl

ltpsmnu:

a)

Ml

chunho,tcl

cimxsaocho

M(x)=1.

b)

ng

vimiRl,tp

mc{x:M(x)}

lonngtrnR

l

Ngitathngdngccs

mdngtamgic,hnhthang

vdngGa

uss


5/36

SOSOM

M

((tttt))

CONGS

OM:

[a,b]+[d,e]=[a+d,b+e]

TRSOM:

[a,b]-[d,e]=[a-e,b

-d]

NHANS

OM:

[a,b]*[d,e]=[min(ad,

ae,bd,be]),max(ad,ae,bd,be)]

CHIASOM:

[a,b]/[d,e]=[min(a/d,a/e,b/d,b/e]),max(a/d,a/e,b/d,b

/e)]


6/36

Nguyn

Nguynllsuy

suyrrngng

ccaaZad

eh

Zad

eh

lmvicvicchth

ngcnhiubinvo,nguynlsuy

rngcaZ

adehlrtquan

trng.

nhngha:ChoAiltp

mvicchm

linthucAi

trn

khnggiannnXi,(i=1,2,,n).KhiytchcaA1xA2x

xAn

ltpmtrnkhnggian

nnX=X1xX2x

xXnvihm

lin

thuc:

A(x)=min{A1(x1),A2(x2),,An

(xn)}

Trongx=(x1,x2,,xn

)


7/36

Nguyn

Nguyn

llsuy

suyrrngng

GisvimibinuvoxilygitrlAi(i=1,2,..,n)viAi

ltpm

trnkhnggiannnXivhm

linthuclA

i(xi).

Hmf:X

Ychuynccgitruvo

Aithnhgitrura

B.KhiBsltpm

trnYvicch

mlinthuc

B(x)

ctnh

theocngthc

sau:

B(x)=m

ax{min(A1(x1),,An

(xn

)):xf-1(y)}

nuf-1

(y)

B(x)=0

nuf-1(y)=

Trongf-1(y)={x=(x1,x2,,xn

)X:f(x)=y

}


8/36

Suyrngph

pcnghaism

ppddngngnguyn

nguynllsuysuyrrn

g

ngchchngngtataccththchochongay

ngayn

h

n

h

nghnghaasuysuyrrngngphphppccngngc

ho

c

ho22ssmmbbn

g

n

gccchchssddngng

hhmm

haihaibibinn.z=.z=

f(x,y

f(x,y)=)=x+yx+y

nhnhnghnghaa::

ChoM,N

ChoM,Nll22ssmmcchhmmli

n

li

nthuthuccM(x

M(x),),

N(xN(x))

khikhiccngngsuy

s

uyrrngngM+N

M+NllttppmmtrntrnRR

cchhmmlinlinthuthu

ccxxcc

nhvnhviimmiissththcczzchochobbii::M(x

M(x)+)+N(zN(z)={

)={min(

min(M(x

M(x),),

N(yN(y)):)):

x+yx+y=z}

=z}

nhnhll:(:(Du

bois,

Du

bois,Prade

Prade1980

1980))NNuuM,N

M,Nll22

ssmmhhnhnhthang

thangthth

M+N

M+Nccngngll

ssmmhhnhnhthang

thang..

Tng

Tngttng

ngiitataccngngnhnh

nghnghaaphphptrptrs

uy

s

uyrrngngvvphphpp

nhn

nhn

suysuyrrngng


9/36

SOSOH

O

H

OC

MCM

Sohocm

d

atrenhaitnhchatcuaconsom

:

Moitapmcungnhmoisomcothecneurabi-cutsay

u

vadu

ynhat.

-cutscuaso

mlakhoangongthc(0,1]

Goi*lamottrong4{+,-,

.,/}

[a,b]*[d,e]={fxg/afb,dge}

Nhnghoat

ongso

hocmd

atrenkhoang

ong.

GoiA=[a1,a2],B=[b

1,b2],C=[c

1,c2],O=[o1,o2],

1=[1,1

]taco:


10/36

SOSOH

O

H

OC

MCM

1.

A+B=

B+A,

A.B=B.A

2.

(A+B)+C=A+(B+C),

(A.B).C=A.(B

.C)

3.

A=0+

A=A+0,

A=1.A=A.1

4.

A.(B+C)A.B+A.C

5.

Neub.c0bB,cCthA.(B.C)=A.B

+A.C

6.

0A-A

va1A/A

7.

NeuA

EvaBFth:

A+BE+F

A-BE-F

A.BE.F

A/BE/F


11/36

Lo

gic

Lo

gicmm

gigimmbb

ttssphphthuthuccvvoocccphcphppttnhnh

minmax,do

minmax,dollmm

tng

tngmmmmdd

oovvlinhlinhhohott

tron

tronviviccgigiiicc

ccbbiitotonnththccttng

ngii

tatammrrngng

phphppllyyminm

ax

minm

axththnhnh22llpptt--norm

normvvtt--cono

rm

conormcc

ttngngccppphph

nnttiingnguu..

Nh

Nhvvyychch

ngngtatasskhng

khng

ccmmttiissttppmmduyduynhnhtt,,

vv

trong

trongnhnhnghnghaaiissttpp

mmtatalun

lunccthth

thay

thaymin,ma

x

min,ma

xbbngng

tt--norm

normvvtt

--conorm

conormiingng

uunhau

nhauvvthuthu

ccmmttttppii

ssmm

khkhcc


12/36

1.

1.

PhPhpp

phph

nhnh

nhnhnghnghaa::

HHmmn:[0,1]

n:[0,1][0,1]

[0,1]khng

khngtngtng

ththaamn

mniiuukikinn

n(0)=1,n(1)=0,

n(0)=1,n(1)=0,ggiillhhmmphphnhnh..

MMttvviivvdd

::

--HHmmphph

nhnhchuchunnn(xn(x

)=1)=1--xx

--HHmmphph

nhnhn(xn(x)=1)=1--xx22

--HHphph

nhnh(Sugeno,19

97)

(Sugeno,19

97)NN(x(x)=(1

)=(1--x)

/(1+

x)

/(1+x),x),vvii>>

--11

HHmmnnllphph

ppphphnhnhmmnhnh,,nnuunngigimmchchttvvn(n(x

n(n(x))=

x

))=xmmii

x.x.


13/36

2.

Ph

2.

Phphph

i(ti(t--norm)

norm)

Ph

Phphphi(i(vvnqueng

nquengililph

ph

pAND)

pAND)ll1t1tr

ongc

r

ongccpcphhptpto

o

nlogic

nlogic

ccbbnnh

nnht.t.

Nc

Ncngl

nglcscs

nhng

nhnghha

p

a

phhpgiaoc

pgiaoca2a2

ttpmpm..

nhng

nhnghha:a:

H

HmT:[0,1]

mT:[0,1]22

[0,1]l

[0,1]lmmtttt--normn

normnuthuthamamncnccc

iiuki

ukinsau:

nsau:

a)a)T(1,x)=x,

T(1,x)=x,

vvimimi0i0xx11

(T(Tnnttiphiphntntnnvv))

b)b)T(x,y

T(x,y)=)=T(y,x

T(y,x),),vviimmii00

x,yx,y11

(T(Tcctt

nhnhgiao

giaohohonn))

c)c)T(x,y

T(x,y)=)=T(u,v

T(

u,v),),vviimmii00

xxuu1,01,0yyvv

11

((Khng

Khnggigimmtheo

theottngngbibinn

))

d)d)T(x,T(y,z

T(x,T(y,z))=))=T(T(x,y),z

T(T(x,y),z))vv

iimmii00x,y,z

x,y,z

11

(T(Tccttnhnhkk

tthhpp))

TTnhnhngngtiu

tiutrntrnchchngng

tatasuysuyrarangay

ngayT(0,x).

T

(0,x).Hn

Hnnnaa

tintin

d)d)mmbboottnhnhththcctritrinndu

y

du

ynhnhttchochohhmm

nhinhiuubibinn..


14/36

MMttvviivvdd

::

--

Min(

Min(Za

deh

Za

deh1965)

1965)::

T(x,y

T(x,y)=)=min

(x,y

min

(x,y))

--

DDngngttc

h

c

h

::

T(x,y

T(x,y)=)=xyxy

--

tt--norm

normL

ukasiewiz

L

ukasiewiz::

T(x,y

T(x,y)=max{x+y

)=max{x+y--1,0}

1,0}

--

Minnilp

otent(Fodor19

93):

Minnilp

otent(Fodor19

93):

T(x,y

T(x,y)=)=m

in(x,y

m

in(x,y))

nnuux

+y

x

+y>1>1

=0=0

nnuux

+y

x

+y11

--

tt--norm

normyy

uunhnhtt(drastic

,product):

(drastic,product):

Z

(x,y

Z

(x,y)=)=min(x,y

min(x,y))

nnuumax(x,y

max(x,y)=1)=1

=0=0

nnuumax(x,y

max(x,y)Q=

P=>Q=PvQPvQ..

nhnh

ll::VVii

bbttkktt--normT,

normT,tt--conorm

conormSSvvphphppphphnhnhmmnhnh

nnnnoo,,

IIS1S1llphphppkk

ootheo

theoththaanhnhnghnghaaphphppkkooth

eo

theo..

PhPhppkkootheo

theo

ththhaihaisausauyyllyyttlgic

lgictrtrcccc

mm((intuitionistic

intuitionistic

logic)

logic)

nhnhnghnghaa::ChoT

ChoTlltt--norm,

norm,

hhmmIITT(x,y

(x,y))xxccnhnhtrntrn[0,1]

[0,1]22bbngngbibiuu

ththcc

IITT(x,y(x,y)=)=sup{u:T(x,u

sup{u:T(x,u))y}y}

nhnh

ll::VVii

bbttkktt--normT

normTnn

oo,I,ITTccnhnhnghnghaanh

nhtrntrnll

phphppkkoo

theo

theoththaanhnhnghnghaaphphppkkoo

theo

theo..


20/36

PHPHNG

TRNH

M

NG

TRNH

M

Xet2dangphngtrnhm:

Dan

g1:A+X=B

KhongthesuyraX=B

A,

Thatva

y,viA=[a1,a2],B=[b1,b2],B-A=[b1-a1,b2-a2]

A+B=[a1,a2]+[b1-a2,b2-a

1]=[a1+b1-a2,a2+b2-a1][b1,b2]=

B

atX=[x

1,x2],

taco[a

1+x1,a2+x

2]=[b1,b2]

a1+

x1=b1

x1=b1a

1

a2+

x2=b2

x2=b2a

2

VXla1khoangvix

1x2b1-a1b2-

a2thconghiem

Luconghiemlax=[b1-a1,b2-a2]


21/36

PHPH

NGT

RNHM

NGT

RNHM

((tttt))

*Cachg

iaiquye

t2:

(0,1],

A=[

a1,a2],B=[

b1,b2]va

X=[

x1,x2]

phng

trnhconghiem

i/

b1-a1

b1-

a2,(0,1

]

ii/

b1-

a1

b1

-a1

b2-

a2

b2-

a2

(

]

U

1,0

=

X

X


22/36

PHPH

NGT

RNHM

NGT

RNHM

((tttt))

Dang2:A.X=B

at

A=[

a1,a2

],

B=[

b1,b2]

va

X=[

x1,x2]th

nghiemphng

trnhmtonta

i,tngngvi

Neunghiem

phngtrnhtonta

i

(

]

U

1,0

=

X

X

(

]

22

22

11

11

22

11

1,0

,

ab

ab

ab

ab

ab

ab


23/36

CACACPHECPHEP

TO

P

TOAN

TREN

AN

TREN

TATA

PMPM

Phephp:

Phepgiao:

Phepbu:

Phepkeotheo:

GoiA,Bla

haitapmtrongtapX

(

)

(

)

(

)

(

)

(

)

X

X

X

X

X

B

A

B

A

B

A

,

max

=

=

(

)

(

)

(

)

(

)

(

)

X

X

X

X

X

B

A

B

A

B

A

,

min

=

=

(

)

(

)

X

X

A

A

=1

(

)

(

)

(

)

(

)

(

)

[

]

X

X

X

X

B

A

B

A

B

A

,

1

max

=

=


24/36

HEHELUA

LUATMTM

HELU

ATM

IF

THEN

Theoluatro:Ift>30,a>15

thenv=30

0

Nguyenlyxlycacbaitoan

m:Input

ro

thsemhoaeapdungluatro

m

Dlieuvaoro

mhoaetmluatapdu

ng

t

orohoae

apdu

ng.R

o

m

ro


25/36

HEHELUA

LUATMTM

Nhatlaquo

cquaautien

ngdu

ngheluatmeieukhientau

ienngamTokyoraithehemaymo

cthongminh

intellige

ntmachinesystemHT+IT

(hightech+informationtechnology)

Vdu:ngdu

ngtronghoa

tongcuacacmaygiat

Neuquanaoban+nhieuth

xaphongnhieu+mayquaylau

Neuquanaosach

+nhieuth

xaphongt+mayqua

ylau

Neuquanaoban+tthxaphongnhieu+mayquayva

co36luat


26/36

Phng

Phngtrtrnhnhf

uzzy

fuzzy

Cho

Chohai

hai

ssfuzzyL

fuzzyL--RRll

a=[

a=[la,ra

la,ra]]vvb

=[

b

=[lb,r

b

lb,r

b],],xxtt

phng

phngtrtrnhnhfuzzy

fuzzysau

s

auvviix=[

x=[lx,rx

lx,rx

]]llssfuzzy

fuzzycc

nn

ttmm..

a+

x

a+

x=b=b

Ta

Taccthth

ththcchihinnphphppccngngvvtr

triirriingngnhnh

tt

hai

haivv

suy

suyrarax=[x=[lx,rx

lx,rx]]nhnhsau

sau::

[la,

[la,rara]+[lx,

]+[lx,rxrx]=[lb,

]=[lb,rbrb]]

[la+lx

[la+lx

,,rara++rxrx]=

]=[lb,

[lb,rbrb]]

la+lx=lb

la+lx=lbvv

rara++rxrx==rbrb

lx=lb

lx=lb--lalavvr

x

r

x==rbrb--rara


27/36

ccchchg

i

g

iiinnyykhng

khnghhchuy

chuynnmmtt

ssfuzzy

fuzzyttvvtrtrii

sang

sangvvphph

iiho

hoccngngcc

llii,,iiuunnyytng

tngttnhnhgigi

ii

phng

phngtrtr

nhnhlogic.

Theo

logic.

Theo

nhnhnnxxtt,,ta

taccphng

phngp

h

p

hpp

ttngngququtt

gigiiiphng

phng

trtrnhnhfuzzy

fuzzynhnh

sau

sau::

B1:

B1:ThThcchihinnttttccccccphphpptotonnvvt

r

t

riicho

choraramm

ttss

fuzzya=[

fuzzya=[la,ra

la,ra]]

ThThcchihi

nnttttccccccphph

pptotonnvvp

h

p

hiicho

choraramm

ttss

fuzzyb=[

fuzzyb=[lb,r

b

lb,r

b]]

B2:

B2:ngngn

h

n

httccaahai

haivvcho

chotatammttphng

phngtrtrnhnhiiss

cc

hai

haiphng

phngtrtrnhnh

la=lb

la=lbvv

rara==rbrb

GiGiiihai

haiph

ng

ph

ngtrtrnhnhbbyy

tatacckkttququ

ccnnttmm


28/36

Nhng

Nhngi

iuunnyylliikh

ng

kh

ngththcchihinn

ccddddngng

iivvii

phphppnh

n

nh

nvvccququn

hi

n

hiuutr

trngnghh

ppxxyyrara..

MMttcc

chch

ttngngququttnnuua=[

a=[la,ra

la,ra]]vvb=[

b=[lb,r

b

lb,r

b]]thth

a.b

a.b==

[[min(la.lb

,ra.r

b,ra.l

b,la.rb

min(la.lb

,ra.r

b,ra.l

b,la.rb),),

max(la.lb

,ra.r

b,ra.l

b,la.rb

max(la.lb

,ra.r

b,ra.l

b,la.rb)])]

XXttcccctr

trngnghhppcccc

ssfuzzya

fuzzyavv

bbdng

dnghay

haym

m

nghim

nghim

ngngttththcc

44tr

trngnghhppxx

yyrara..

GG

iic=c=a.b

a.b,,

tata

cc::

iiuukikinn

lclc

rcrc

a>0,

b>0

a>0,

b>0

la.l

b

la.l

b

ra.r

b

ra.r

b

a

0)

(a>

0)

1.

1.

TTmmn

ghi

nghimm

x>0

x>0

Ta

Tacc

[la,

[la,rara]*[

]*[lx,rx

lx,rx]+

[

]+

[lb,r

b

lb,r

b]]

=0=0

[la*lx,

[la*lx,rara**rxrx]+]+[lb

[lb

,,rbrb]]

=0=0

[la*lx+lb,

[la*lx+lb,rara**rxrx

++rbrb]]

=0=0

la

*lx+lb=0

la

*lx+lb=0vv

rara**rxrx++rbrb=0=0

lx

=

lx

=--lb/la

lb/lavvrxrx

==--rbrb//rara


30/36

VVx>0

x>0nn

nn

lx>0

lx>0vv

rxrx>0>0

--lb/la>0

lb/la>0vvrb/ra

rb/ra>0>0

lb0vv

rara>0)

>0)

b

nx>0c0c

honghi

honghimn

mn

y

,

y

,tac

tac::

lx>0

lx>0

((--lb+

lb+ll)/2*la

)/2*la

--lblb--ll>0>0

lb

mayhoc fuzzy

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