Fag Inene Sqstms (FIs)
Kuk-based systu.dusy moleb, and
gnnally
known
as
fusy erpeat ysims
tg indeena Systemy (FIs).
The key wit os a du3sy logc Sln is FIS.
’FIS
"IF.... THEN' Kues along wcth connec oay
Kon AND. fos making necessay deasion zuls.
The inut to FIs may be dussg o CAisp , but
set.
te atput taom FIs in aluays
Constuc ton 4wonking paincipk a< FIS.
DataRule
4|base base
knowledge base
|Fgitcahon
inpuat
Defiggkatonatpd
Caisp)it
|unit
In<eene
Tnje aence
Decision- Making
unt
Fuzag
Block diagramaQf FIS.
(Cp)
A AS n constucttd ) ve
dunctiol bleeus
lhey au:
)A Aue bae tht costains
contains numekoLus
IF: THEN
Ruls.
13
d434
)A data base that dekines the membenship tnchons
Q4 d34 set wsed in dussy kus.
9)3) Desision-making unt that pejoum opescaton
the Ruley.
9 Fugijicahon inexenca unit that Conveat the caus
quanities into dugs4 quastitie
5) De tggification iexena unit ttt conv ith ths
figgy quontitiu into cisp quanti tiey
Iritially, in the duzaiticaton untt, the caisp inpt
is conveatd into duzqH inpct. Vaiow
tusshcato
nethods aue
emploed o this. A4tex this paoess;
&ule based u douad Bat base and Kule bue au
collec tively called kaowledqe base Fndlly.
de<uzatication paoes1 iin (amied out to produc
Cisp adput. Mainly the dusy uls cau lonud
to the aule base and Suitable deas ion aae made
tn the decisiòn - making nit.
Methods Q FIs
Tvu cu two important types af FIS
I Mamdani FIS
Suqono FS.
lhe dyeAeNCe by the tuo method
lis is the
Consequnt of fugay ule
Fuz3y sets ae wed as kule (onseqest in
Mamdani FIS
- Linzan guncton o nput vcaiables ae ucd ag
Rule consequnts is Sugeno's maihod.
’Mamdois kule dind a qeatex acceptante in
al niversai oppzozimatoxs than Sugeno's
mocal
Mandani FIS.
p menbership funchions au ezpected to be
fay sets. Ajtex aggagaton paoas, each cutpud
vauable conitains a duaH ets, hene deyugifcaton
is cmpoxtant at the otpd stge
steps to comput otpud jom this FIS.
tg3y kules.
a<
Set
a
Deleamine
kp-I:
fuxhony
merdbership
tp
using
tgg4
ifp
the
ep-: Nake
to the
acconding stengy
ul
a
shing
C
establi
oa
step 3 : Combine the duajied p
dg kues
by
ule
the
q
consequant
stap4: DeteAmin tha
output
the
ond
staength
Rule
tha
comlbining
monsbekship duncton.
stap5:
ofp
as
get
to
Consequnta
Conbine all the
distaibution.
sup 6 :Finally
bution
distai
ocdpt
a de<ajed
obtoinec.
Rule
sBungih
Then
Jand
3
1
Then
Rule
stugth
1
Fpd distaibution
ouput clistaibutn
1
I Momdani FIS.I
Consider a too-inpud Madanu FIS wth tu00
ules The modal dusifieu the hwo inputa by
inding tte inteasec tion a wo (isp ingut valua.
wcth input membeaship unctin .The minumm
onoaation is wed to Computu the dussy input
ind or conmbining he too daated input to
obBas kue stengh. The output mambeaship
jncton is cipped at te suk stength. Fioaly
#u marimun
the two
ules
operaba is wed to comput the
"oa o Combining the odpt
>The duz34 kue aue joumed wing E-THEN'
state ment and AND /OR COnnectves .( The consegueny
the
ule can be obtaind in too steps:
) by computig the kule sthengih completely
wsing the tusziyed yp faom the fuzy Combitoy
a) bg cippcg the ouput membexslaip unchon at
the aul
The outputs a al the jusgy Rles
Reule aa (ombid
to cotais ona jzg otput distibuton Faom F5,
t in desid to gt only one chisp aput. the
(usp o dotined {rom dauugihcaton ploan. The
Conmon tchniqus of dajugificaton wsed
Cerstea a mass ozland Mean ol maimum
(Ts Method)
9 1akagi -Su qpno Fuggy Model rs
The fomad o< the fussy
ul ot a Sugno
ug34 model in
24)
io the astu
ante cedents
whee A,B aue tugy set in
Z=e4) is a caisp hncton in ine
F
B THEN
x is A cnd y iss B
(onsequent
polynonmial
Vaiabey I and
ast oncdea polynomial,
dast-oadea Sugeno u3s4 modal
1f f4) is Constant , e get geuo-oAda Suge
model
moce! w.
mocde
Sugeno
Wndea
>Fusy indeaence paOI)
sbp1 : Fgfyg the input
- hee , tue
p
the Slm ae made quy
he
opeaator
juzy
the
$tep a : Applying
fusdt ope Aatox tnut be aplied to t
if 3-x and 5-y then outpud à z= aztbytc
Fok Saqero model oa 3eAo oxded, the outpt evel
z is a Constant
Compaaison blen
b/o Mamdani 4 suqeno Method.
t odput membeaship dunchon :
The main diyeaente
bjop them is on the bauig
4otput munbeaship duncton The Suqpno olp
(outont
mmbeaship dunctio ae eithea inea o COatt
Agquga tion and Defuzzificaton Proadua:
lics in the
aho
them
bla
dyeence
Ihe
h334 ues. and due to the Same
Ccnsequune
hctn agguqation and dejuiijcanion procedua
also diger
3 Mathemahcal Rule
Mou mathe matical
Sugeno
ues eçst Jou the
ule than the mamdani kule
4Adjustade Paxametes :
mou
has
kollea
cot
suqeno
lhe
contolet.
Mamdani
the
than
parameteRs
Irpd
Munbeiship
duncton
Inpud1
AND
Ruu sungth
Thputa
Znpud membeaship
duncion oudped Membenship iur
Z-xtbytc
Model
suqnoThe main advortages a Mamdani Mehed,
1 ct has
HAZ
.
wcdespaad acceptance
it is wll - Suitable dor human yp
Hai
Advantags af Suqyno Mcihods.
IH (omputahonally eyjicient
QIH
uniaa
weitn
wel
woxk1
iu compact and
and ada
techrique
opimizahon
tachnique,
tlive tzchnque
9 Tt in best Sud foA mathematical anay su.
4It has guuanteed continauity o4 the ofp Sujaa,
14.3 Architecture and Operation of FLC System
The basic archicecrure of a fuzzy logic controller is shown in Figure 14-2. The principal componencs of an
FLC sysem are: afuzzifier, afzy rule base, afuzy knowledge base, an inference engine and adefuzzifier.
It also includes parameters for normalization. When he ourpur from he defuzifier is not acontrol acion
for aplant, then the system is afuzzy logic decision system. The fuzzifier present converts the crisp quantities
into fuzzy quancities. The fuzy rule base sores the knowBedge about the operation of che process of domain
experise. The fuzzy knowledge base stores the knowledge about all che inpur-output fuzzy relationships. It
incudes the membership funcions defining the input variables to che fuzzy rule base and the outpur variables
to the plant under control. The inference engine is che kernel of an FLC system, and it possess che capability
simulate human decisions by performing approximare reasoning to achieve adesied control strategy. The
defuzzifier converts che fuzzy quaniies into crisp quantities from an inferred fuzzy control acrion by che
inference engine.
Fuzzy
knowtedge
base
inpus
Normalization
input scaling
factors
Fuzzy
rule base
k)Defuzzifier (y)
HFuziier k(*) Interence
engine
Normafizalion
oulput scaling
Sensors
factors
Flgure 14-2 Basic architecrure of an FLC system.
X Outputs
Plant
Slates
The various steps involved in designing afuzzy logic controller are as follows:
IStep 1: Locate the input, outpuc and state variables of the plane under consideration.
Step 2: Split che complece universe of discourse spanned by each variable into a number of fuzzy subsets,
assigning each with alinguistic label. The subsets include all che clemens in the universe.
Step 3: Obtain che membership funcion for each fuzzy subset.
Step 4: Asign che fuzzy relationships between che inputs or staes of fuzzy subsets on one side and che
oucpucs of fuzzy subsets on ocher side, chereby forming che rule base.
Step 5: Choose appropriare scaling factors for che input and ourput variables for normalizing che variables
between [0, 1] and [-1, 1] interval.
Step 6: Carry out the fuzzifcation process.
Step 7: ldentify ehe ourput contributed Erom cach rule using fuzzy approximae reasoning.
Step 8: Combine the fuzzy oucputs obained from each rule.
| Scep 9: Finally, apply defuzzification to form acrisp output.
The above sceps are performed and executed for asimple FLC system. The following design elemens are
adopred for designing ageneral FLC system:
1. Fuzzificaion srategies and che interpretation of afurzifier.
2. Fuzzy knowledge base:
normalization of the parameters involved;
paritioning of input and ourput spaces;
selection of membership functions of a primary fuzy set.
3. Fuzy rue base:
selection of input and output variables;
source from which fuzzy control rules are to be derived;
ypes of fuzzy control rules;
compleceness of fuzzy control rules.
4. Decision-making logic:
proper definition of fuzzy implicacion;
interpretation of conneccive "and";
interpreraion of connective "or";
inference engine.
5. Defuzification strategies and che incerpretation afa defuziñet.
When all the above five design paramerers are fixed, che FLC system is simple. Based on all his, che features
ofa simple FLC system are as follows:
fixed and uniform input and output scaling facrors for normalization;
fxed and noninteractive rules;
fuxed membership funcions;
only limited number of rules, which increases exponentialy wich che number of input variables;
fixed expertise knowledge;
no hierarchical rule strucrure and low-level control.
) Creetc a Radog Toihial stak.
(R) Kvalngto titnes.
) Reproduce (Mentathion)
6) let qensah'a.
pofulaly
tautaehorae
elGe
X lele
Eneoding
$pee
Acfal
golutiy txcoing
(lonpikhiau
Spate)
&Bepi: recle a arog Iolhialae: An
do chomoromes ) This is unlike the sikehyfo
Skp2: kvazle itnas: Avae tor fitnes ts asiseclt east, solu h
(Ciomosowe)depeneing on hou) clox it acually ts to Bolngte poloy
(Ans arirtng to tue answe ofAe desired rode). Tese Maslios
43
etG lot to e otused witu "anwers'l to the pblm:tnk of
ORdles to Lash the awswen. )
ko ; Reprodute (ancl ehilerey Muae): The chuomeoes ith a
ngover"):
vesakytolains aeluto tiat
|nihalpofaton
I|Cress ovet
]Mulahoy
(emia
No
Yes
Best ndirduas
Sutput
wrepoveinchvoumaones
Filne
chvomotOwe
2
3
Finas venetr' ComeRpoveine eewctones
Fitnes
chomoSOe
3
b:otlotIO
tiners-proportovste seletoy CRoulelte wheel Raulirg
Rokte uwnel samplng
Fitneu -preportavate elutay
D
Cocer e-bilcowotemes ithke tz lloswne prepethes:
2) popubhey 6ize Ne
45
(3) 1E B SDáse geleded , crevsever s penfenccl.
B:0ol|0 E :l01 10100-p:00lLoO0
Bestfit shinp froy prerions peptoy slet ltthe
Rtnes ofpopulehn
alowi
4/4 =35
Tables showw the ttnes rale tor the Corekondig
ewenpsomes q fisuo shows tae Roulelte ested selerhny
ae.
(0 Entaig (eding)
salectoy (Retonbinay)
) Mutktioy
-Knceding is a proe of repreeng
-Thh precss Can be pevted usig bits
eay trees/ avays
rts er
- he entodinp depevts maioy on solving the pulg.
5-Gne a eveccle
a) Biay kneodine
tnkges ae
-iofe no. f real nea. can le vepetekd.
- No- cf real noi. repreeulecl itvcaer coth ching length.
cuveweUSoe, 2
yor
octol
of
p
wede
shines
wes
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Comgome 1
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15423314
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A-)
Co-9,
nag
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chomosowe 1
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n
Repieendeol
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of
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Konehines Cone ehons hane to he tlone alter qeresa oeneon is
Covplele Ty pemathty enlne eveRychomeOme
a
pemutMentecing ts dy wetal for ciceng fvreoeme.
covetev
Krn tttuig plyome types of-cvotsoves
Mutr
wet e wace to leawe he ciromosone lonnstent(ie;tae
Chomeemed
||55
cvomeseme 2 6
3
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Conveeted to plolmy for m no.}real noR orclakrs
Yaes can
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ehronegome A (. 2324 5.3243 O4556 23213 2:45A
comaome BABDJEIFJDHDIERJFDLD FFEGT
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9) Tree Enedng
tinmexpreein forgvete
eyelnp
ert
wed
wainly
is
eneodinç
Fht
(2) Selectto y
Mahiná
fol
New
populahoy
chanco that ay toeval
beker
hunehmie
ttnex
te
ises
-he
Cutl he eleeted':
which he
tb
degree
die
as
oletrec
is
preue
Me elehm
knes oves Beuttewive enesehbns.
-There ae 2 dypes of elechioy schewe s -
)Proport'on ate -bascd selechts y -eilneavek
G)dial -havcol selechoon
-froportoake-beccl geleehay peka ou itivrcuals baecd
eyoy ther Atnes aus rekhveo thetthes of the oto itvidd
hthepopehoy:
taw Fitre butupoy taeir rank withiy Hhe popuetn
Weakseleaty will resut y sloo roluchion.
(a) Roulette nlheel selecioy
-The extetd ane of ay bdiyeuel s todtycal's Ptnes
divil cel by beaeel fitsen of te poplady. eh idi utue ]
lice
1s aus gned a slice ottthe Rouletehal, tte Sze ofte
being proportoval tbAheidiviclel's ftney.
Reuletkcwheetis easter toingpemantbut s voEy
-the kade of evelutiy deevd onthanananee op hes
the popaty
Thus techitpe Ranclomy seles a poment Remthe popdethon
e move dirvupive tou Ralek heel alecioy
Rauk lehoy Banks dae poplahay scNevy Chcwegw
-.Fao kers
p qeleiay pres
e when t e folne
Nanncc
low
() Touryawunt selectiovM
etournament seletey staegy proves eletve resuye
ly indivtnals
by hollig a tonaentowpehiho am
wththe
a bcst idividnal Rohe tournanetstheone
ilut ftnes, who is the oiner of Nu: etten
Tourrammn ompeiticvs
mating Pool.
he winer a
ekl into te
regealcdwl e macng poel for
goneseting ew cftpinpsAled.
Pool congpsine the toumaminer hag hige
them
alenge poputay fihes
wlieh tis
Thetonament orttang
Selechioy pekline
The fra diferente provides theSucceclene
geres.
Gt to inwe tue Rthes of te
Ths meted y mone efkrient
leads to ayoi
ctoy.
(e) Boltaannseletoy
Cortols tte sede t seleehay atoeling to m preeet-selhecle
dud wheh qhacally lead'y to ay intraue. ig the
slecioy preite
) Stocste oriveral ampling
-prevides Kovo bins c Mininal spraacl.
of
-The indivduek ane wepplto cantiguo Regneh
eava in ize
line suehthateohindiv idluals sesnt
to it Atnes eacty a y Roule He
hecl selechiey.
- Here camaly spaed porsts areplacclover tee ine,
to be seletec' .
tdalg
y
irdi
dhereare.
wanyas
ng
tly Wiag
doined
oy
eelaed.
etel offte teley
ane
chilol
2
child
1
farent
2
farentI
tont
cVoSOves
hing hages severely tavets,else
it
Teo
(6)
qood
te
ssite
Leterchose,
lbe canchdray
Liis SAnges
Cros
ave sitg nettohe
seleed pointis Crossovet
aovytardody
cehompeol.
cro% tere,
a
onea
pY
esaodie
it
Crossoles
the oth
olfspring
pool, mehng ttte
parens
ions
cuts
are
cut comesome
te affensecfoys
maiae,
doose
tanelomy
ome
Single-post
cooves
bter
applr'ec
thewm
aking
2
hking
rom
the
Taoo
4
4)
Rrst
creaes
a
that
h hore
opetor
i7 -crDssoes
cilel Producinga
ofces
roces,
of
ol
teCrossOVr
s
CressoVex
80
(O MuHipcirt cossoves
^-poin
cress ove
ase sdectel Randosy aou
acicle c intmeray
eehonged.
Parent211
oo lo 11 o
elitl1|Lo
10
child 2
C) Utovm eroyoven
t can e nohec
fat
ile poduerne cild l,shenthone
prodncing frowyfent 2, , hanfre
nthe mak the qene is cpied
lepud fomte parentl.
Pment
pares 2
cild 2
e) thvec - RaventvossoVes
e
1s talkey fotae ofspngtemwe
e toit- em, the ttuel
eveutH
Panent2
farent3
chitd
(
shutRle eOsONeN,
Befeve Vartabes ae
ase
Kandorysuftc)
to lbott emet After orsbves , he vaidegi t e cttspng
ane
whuled
) PreCedence Presevatve Chossorer CPPx)
-Used invehile oting pns
seheduling polms tet
2
Selet pawentno-lt/)\2
A
) orteved ros oveN
PrentI
citd1
4-2
3
3 6 5
31%5
21
clill
powent
irdenctauged.
cild
ChromogOme
Mulaty
parent
too)eilel
pading
bit
ihy
ersenet
faud
pavet
Is
(o cluomosoe
tofliped
for
in 1 4generted
thecome, ehromo mttoy
clisibuting
qenete
covering
he
fer asbell
Raoy
vole te playsMutety
re of
Mutatioy
3
o
4)
chilol
2
756
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t
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porent
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231
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child
2
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sent2
84
C) Revesng
A
Vanclay
tuxihoy ave vevoseol
clitd cawomosome s prducd.
lchild
The,
an'ons
t-The GA Sbps whenteSpeitec)
Ws-hays bas erelved.
2) Eapsed Tine
-The qeett procen will enol osheasfeatd
Aione hey elapol
chowge
Atney Peor
med
Soes ifene it no
te objetvetnehn fera sspuote
6) slall toz lmit-Te
io tucobletvo kuretay durng an rkel
Gonit
ane
(3) Gmof Fitney
4) 84eltoun Fitres