Table Of ContentSeleOctthMeeodrr gKaanu fmaRnena dTiintglse s
ReadinignsP lanning
Eddib tyJem aseA llJeanmH,ee sln edarn,Ad u sTtaitne
ReadinignsD isitbruteAdr tiicfiIanlt eilglence
Eddib tyAe laBno naddnL eGsa sser
ReadinignsK nowledgRee presentation
Eddib tyRe ondJ aB.lr cahmaadnnH ector Levesque
ReadinignsK nowledge AcquainsdiL teiaornn ing
EdtiebdyB urcGe.B uhcanaadnnD avCi.Wd i lkins
ReadinignsC ognitiSvcei ence
Eddib tyAe lnlC aolaldniE ndswr daS mith
ReadinignsC omputeVri sion
EdtiebdyM atriJnF. i sacnhOdls ecFrai rr schein
ReadinignsN aturLaaln guagPer ocessing
EdtiebdyB arabG arroKsarezn.S pcakJr onaesnB,do nLnyinWene b ber
ReadinignsM odel-basDeida gnosis
Eddib tyWe alHtamecsrh ,Le urcCao nsaodnJl oenh,nda eK leer
ReadinignsA rtifiIcnitaell ligaenndcD ea tabases
Eddib tyJe oMhynlo poaudlnM ocish aBerlo die
ReadinignsA rtifiIcnitaell ligaenndcS eo ftwaErneg ineering
EdtiebdyC hralReisac dnliR icdWh aatrers
ReadinignsU ncertaRiena soning
EdtiebdyG leSnhneaa rfn Jdu dPeeaa rl
ReadinignsM achien Learning
EdtiebdyJ uSdliea avdnlT ihko mDaeesir titch
ReadinignsS peecRhe cognition
EdtiebdyA lWeaxi abdneK la iL-eFeu
ReadinignsA rtifiIcnitaell ligence
EdtiebdyB onLnyinWene b baenNrdli JsN. li sson
ReadinignsQ ualitatRievaes onianbgo ut PhysSyisctaelm s
Eddib tyDe anSi.Wee lla ddnJ ohdaeKn lne er
Readinigns
FuzzSye ftso r
IntellSiygsetenmts
Edibtye d
DidDiuebro ainsdH enPrria de
UnivePrasuSilat bea tier
RonaRl.Yd a ger
IonCao llege
MorgaKna ufmann Publishers, Inc.
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Edoirat nPdr esnitMd eichBa.Me oglrna
ProjMeacntea mgenCto,p eyditing,
anCdo vDeers iPgornsf esiBoonoCakel n. Dt eevnreCrO,
AssitsanEtd itDooru gSlearsy
IdnexD idDiuebro is
CovAerrt J oPhenra sno,
"REFCLTIEON#SI "
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Ackneodwglments
C.A lsinEa.,T rillaansd,L .V alver(d1 e98 3)O.n SomeL ogical B.P.B uckleasn dF E.P etr(y1 982)A FuzzRye presentaotfi on
ConnectifvoerFs u zzSye tsT heorJyo uronfaM la themaAtniaclayls iDsa taf oRre latioDnaatla bsaesF.u zzSye tasn dS yste7m:s2,13 -226.
andA pplica9t3i1:5o -n2s6R,.e printweidt ht hep ermissiooftn h e Reprintweidt thh ep ermissoifot nh ea uthoarnsd p ublisher.
authoarnsd p ublisher.
S Chanas(1 982)F uzzSye tsi n Few ClassiOcpaelr ational
Baldwiann dB .W.P ilswor(1t 9h8 0)A.x iomatAipcp roactho ResearcPhr oblemsI.nM .M. Guptaa nd E.S anchez (Eds).
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ImplicatfioorAn p proximRaetaes oniwnigt hF uzzLyo gicF.u zzy ApproximRaetaes oniinDn egc isAinoanl yNsoirst,h -HollAamnsdt,e r
Setasn dS yste3m:s1.9 3-21R9e.p rintweidt ht hep ermissioofn dam,p p.3 51-363R.e printweidt thh ep ermissiooftn h ea uthor
thea uthoarnsd p ublisher. andp ublisher.
Baldwiann d N.C. Guild(1 980)M odellinCgo ntrollerSs.C hiua ndM .T oga(i1 988)A. F uzzLyo giPcr ogramming Envi
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permissoifot nh ea uthoarnsd p ublisher. Reason2i:1n 6g3,- 175R.e printweidt ht hep ermissioofnt he
authoarnsd p ublisher.
W. Bandiearn dL .K ohou(t1 980)F.u zzPyo werS etsa ndF uzzy
lmpilc atioOnp eratorFsu zzSye tsa ndS ystem4s:1, 83 -190. M. Delgadaon dS .M oral(1 987)O n theC oncepotfP ossibility
Reprintweidt thh ep ermissoifot nh ea uthoarnsd p ublisher. ProbabilCtoyn sistenFcuyz.z Sye tasn dS ystem21s3:,1 1 -318.
H.RB.e ren(j1 i9 921A ReinforcemLeenatr ning-bAarscehdi tecReprintweidt thh ep ermissoifot nh ea uthoarnsd p ublisher.
turef orF uzzLyo gicC ontroIln.t ernatJioounrnaoalflA pproximaAt.eD e Lucaa ndS . Termin(1i 9 72)A. Definitoifoa n Non
Reaso,n2 i6n7g-29R2.e printweidt thh ep ermissoioftn h ea uthor probabiliEsnttirco piynt heS ettionfgF uzzSye tsT heorIyn.f or
andp ublisher. matiaonndC ont.r2 o0l:301-3R1e2p.r intweidt thh ep ermissioofn
thea uthoarnsd p ublisher.
JC.B ezdeakn d1 .DH.a rri(1s 9 79)C.o nveDxe compositioonfs
FuzzPya rtitiJoonsu.r onfaM la themaAtniaclaylas nidsA pplicatiAo.nd si,N ola, PedrycSz.,S essaa,n dP. Z.W ang( 1 984)F.u zzy
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67:490-5R1e2.p rintweidt ht hep ermissiooftn h ea uthors anRde latiEoqnu atiuonnd ear C lasosf T rianguNloarrm sA: S urvey
publisher. and New ResultSst.o chas8t(2i)c:a9,9 -1R4e5p.r intweidt ht he
JC.B ezde(k1 976)A. P hysicIanlt erpretoaftF iuoznzI yS ODATA. permissoifotn h ea uthoarnsd p ublisher.
IEEET ransacotni Soynsst eMmasn,, a ndC ybernet6i:c3s87,- 390.D .D uboisH,.P radea,n dC .T esteamle(1 988)W eighteFdu zzy
Reprintweidt thh ep ermissoifot nh ea uthoarn dp ublisher PatteMrant chinFgu.z zSye tasn dS yste2m8s:,3 13-3R3e1p. rinted
G.B ortolaannd R .D egan(i1 985)A. R evieowf S omeM ethods witthh ep ermissoifotn h ea uthoarnsd p ublisher.
forR ankinFgu zzSyu bsetsF.u zzSye tasn dS ystem15s:,1 -19. D.D uboiasn dH .P rade( 1991)E.p istemEinct renchmaenndt
Reprintweidt thh ep ermissoifot nh ea uthoarnsd p ublisher. PossibiliLsotgiiccA .r tifIinctiealll i5g02 e2n3c-e2.39 R.e printed
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P.B oseM,. Galioburga,n dG .H amon (1 988)F.u zzQyu erying
withSO L ExtensioanndsI mplementaAtisopne ctFsu.z zSye ts D.D uboiasn dH .P rad(e1 987)F uzzNyu mbersA:n O vervieIwn.
andS yste2m8s:.3 33-3R4e9p.r intweidt ht he permisosfti hoen J.CB.e zde(kE d)A.n alyosfFi usz zIyn formationM-aVtohle matics
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thep ermissoifot nh ea uthoarnsd p ublisher.
B.B oucho(n1 987)F.u zzIyn ferenacnedsC onditioPnoasls ibility
DistributFiuoznzsS.ye tasn dS yste2m3s:.3 3-4R1e.p rintweidt h D.D uboiasn dH .P rad(e1 984)A. T heoreomn I mplication Func
thep ermissoifotn h ea uthoarn dp ublisher. tionDse finefdr omT rianguNloarrm sS.t ochas8(t3i)c:a2.6 7-279
Reprintweidt thh ep ermissoifotn h ea uthoarnsd p ublisher.
M. Braaea ndD .AR utherf(o1 r9d7 9)S electioofPn a rameters
frmo aF uzzLyo giCco ntrolFluezrzS.ye tasn dS yste2m:s1,8 5-199.D .F ile(1v 9 9)1. F uzzMyo delinogfC ompleSxy stemIsn.t ernational
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Buckl(e1 y9 87)T.h eF uzzMya thematiocfFs i nancFeu.z zSeyt s
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andS yste2m1s:,2 57-2R7e3 printweidt ht hep ermissiooftn h e S.F ukamMi.,M izumotaon.d K .T anak(1a 9 80)S omeC onsider
authoarn dp ublisher. ationosn FuzzCyo nditioInnafle renFcuez.zS ye tasn dS ystems,
Acknowledgmxein ts
4:243-27R3e.p rintweidt ht hep ermissioofnt he authaonrds R.K ruse1 982)T.h eS tronLga w ofL argNeu mbersf orF uzzy
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publisher. Random Varialb11lfeos.r mScaiteinoc112es 3,3 -241C.o pyrig1h9t82
byE lsevSiceri enPcueb lishCion.gI, n cR.e printweidt thh ep er
L.W. Funga ndK .SF.u (1 977)C.h aracterni zoafta i Colasosf
missioonft hea uthoarn dp ublisher.
FuzzOyp timaClo ntrPorlo blemIsn.M .M.G uptaG,. NS.a ridis,
andB .R.G aine(sE ds.F)u,z zAyu tomaat11ad D ecisPiroo11c esseRs.,C .LT.e e(1 972)F.u zzLyo giacn dt heR esolutPiroinn cipJloeu r-
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missioonft hea uthoarnsd p ublisher. 1972A,s sociatfioorCn o mputiMnagc hinerIyn,cR .e printweidt h
thep ermissoioftn h ea uthoarn dp ublisher.
BR. Gaine(s1 978)F.u zzayn dP robability UncLeorgtiacisn.t y
l11formaa11tdiC oo1111 tr3o8l1:5. 4 -169R.e printweidt ht hep ermisL.L esmoL,. S aittaan,d Torass(1o 9 82)L.e arnionfgF uzzy
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sioonf t hea uthoarn dp ublisher. ProductiRounl efso Mre dicaDli agnosIinsM .. M.G uptaa ndE .
Sanche(zE ds.A)p.p roxiRmeaatseo niinDn egc isAi11oa11l yNsoirst,h
R.G ile(1s 9 88)T.h eC oncepotfG radoef M embershiFpu.z Szey ts
HollanAdm,s terdapmp,. 2 49-26R0.e printweidt ht hep ermis
a11dS yste2m5s:,2 97-3R2e3p.r intweidt ht hep ermissiooftn h e
sioonf t hea uthoarnsd p ublisher.
authoarn dp ublisher.
Magreza nd Smets(1 975)F.u zzMyo dusP onensA: N ew
I.AG.o guen(1 969)T heL ogico fI nexaCcotn ceptSsy.11 theseP, P
ModelS uitabfloerA pplicatiionnK sn owledge-bSayssetde ms.
19:325-3R7e3p.r intweidt ht hep ermissioofnt hea uthoarn d
lnternaJtoiuorn11oaaflIl n telSlyisgteen4mt:1s 8,1 -20R0e.p rintweidt h
publisher.
thep ermissiooft nh ea uthoarnsd W iley-Lai dsisv,i sioofJn o hn
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Information oBnaP soesds ibiDliisttyr ibutli11otnesrn. atJioou11ra-l &
11aolf G eneral S9y:s4t3-e5mR8se.,p rinted twhiept ehr missioofn E.HM.a mdania ndS . Assi(1l 9i7a)5n. A n ExperimeinnLt i nguis
tiScy ntheswiist ah FuzzLyo giCco ntrolllnetr.e rnaJtoiuorn11oaafll
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ManM-achiSnteu di7es:1 ,-1 3R. eprintweidt ht hep ermissioofn
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RobotA rm PlayinTgw o-Dimensional PiGnagm-eP.oF nugz zy
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FuzzCyl ustering oBna tsheedC oncepotf l ndistinguishability
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RelatioInE.E ET ransacotniP oantst Ae11ranl yasnidMs a chilnnet elli
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i11 ExperSty stemNso,rt h-HollaAnmds,t erdamp,p . 33-46. M. MukaidonZo.,L S.h en.an dL .YD.i ng(1 989)F.u ndamentals
of FuzzPyr ologl.11 ternatio11aolfA ppJroouxrinRmaealat seo 11i11g,
Reprintweidt thh ep ermissoifot nh ea uthoarn dp ublisher.
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Kilbny F uzzLyo gicI.nM .M.G uptaa ndE .S anche(zE ds.F)u.z zy
l11formaa11tdiD oe11c isPiroo11c esNsoerst,h -HollAamnsdt,e rdapmp,. C.VN.e goitaan dD .AR.a lesc(1 u9 75)R.e presentaTthieoonr ems
forF uzzy ConcKepytbse.r n4e:1t 6e9s-.1 74R.e printweidt ht he
389-399R.e printweidt ht hep ermissioofn t hea uthorasn d
permissiooftn h ea uthoarns dp ublisher.
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J.K acprzMy.k F,e drizaznid.H .N urmi(1 990)G.r oupD ecisionH .T.N guyen( 1 984)O.n Modelinogf L inguisItnifco rmation
UsingR andomS etsl.n formaStciioe11n3 c4e:2,6 5-27C4o.p yright
Makinwgi tFhu zzMya joritRieepsr esenbtyeL di nguisQtuiacn ti
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i11gT ooflosAr r tificial Velr11ltaTegOl Yl Rihgeei11nclea.nK do.l np,p . permissoifot nh ea uthoarn dp ublisher.
126-145R.e printweidt ht hep ermissioofn t hea uthorasn d A.M.N orwicahn dl .BT.u rkse(1n 9 84A). Modeflo rt heM easure
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A. Kaufma(n1 984)F uzzZye ro-BaBsued getiTngI.M S/Stiu11d ieIsm plementatFiuoznzS.ye tasn dS yste1m2s1:,- 2 5R.e printweidt h
the Ma11agSecmieenn2tc0 e:s49-.7-4 87R. eprintweidt ht hep ermisthep ermissoifotn h ea uthoarnsd p ublisher.
sioonf t hea uthoarn dp ublisher. S.AO.r lovs(k1 y9 78)D.e cision-Mawkiitnhag FuzzPyr eference
J.K ellGer.H. o bsonI. W ootonA.. N afariaenhd,K .L uetkemeyerR elatioFnu.z zSye tasn dS ysteIm1·s5 ,5 -167R.e printweidt ht he
permissoifot nh ea uthoarn dp ublisher.
(1 985)F.u zzCyo nfidenMceea sureisn M idlevVeils ioInE. EE
Tra11sac0t11i So11yss temMsa.11 .a 11dC ybernet1i5c(s4,) :580-58S5V. .O vchinnik(1o 9v8) 1. S tructuorfeF uzzByi naryR elations.
Reprintweidt thh ep ermissiofot nh ea uthoarnsd p ublisher. FuzzSye tasn dS yste6m:1s 6,9 -19R5e.p rintweidt thh ep ermission
oft hea uthoarn dp ublisher.
W.J.MK.i ckearntd E .HM.a mdani(1 978)A.n alysoifsa Fuzzy
LogicC ontrolFleurz.zS ye tas11 dS ysteIm( sI),: 29-4R4e.p rinted Procyakn dE .HM.a mdani(1 979)A. L inguisSteilcf -Organiz
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witthh ep ermissoioftn h ea uthoarnsd p ublisher. ingP rocesCso ntrolAluetro.m aPteircgaa,m oPnr esLst d. O xford,
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B. Kosko(1 988)A.d aptivIenf erenicnFe u zzKyn owledNgeet
worksI.nM .M.G uptaa nd Yamakaw(aE ds.F)u.z zCyo mputi11ga:u thoarnsd p ublisher.
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pp.2 99--30R6e. printweidt ht hep ermissiooftn h ea uthoarns d 11aolf M athemaAt11iaclayalsn idAs p plica11t4i:o4110s9,- 4R2e2p.r inted
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D.H. KarnadfD t. A. Bue1l98l3 )F.u zzSye tsa ndG eneralizeAd. R amer(1 989)C onditioPnoasls ibiMleiatsyu reIsn.t ernational
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Ackwnloedgments
xii
A Rosenfe(1l 9d8 4T)h eF uzzGye ometroyfI magSeu bsetPsa.t Tsukamo(t1 o9 79A)n ApproacthoF uzzRye asoniMnegt hod.
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oft hea uthoarn dp ublisher FuzzSye tT heoarnyd A pplicaNtoirotnhs-,H ollAamnsdt.e rdapmp,
137-14R9e.p rintweidt thh ep ermissiooftn h ea uthoarn dp ub
M.R ouben(1s 9 89S)o meP ropertoifCe hso icFeu nctioBnass ed
lisher
on ValueBdi narRye latioEnusr.o peJaonu rnaolf O perational
Resear4c0h3 .0 9-321R eprintweidt ht hep ermissioofn t he M. Umano( 1 982)F REEDOM-0 A FuzzDya tabasSey stemI n
authoarn dp ublisher M.M.G uptaa ndE .S anche(zE ds)F.u zzIyn formaatnidDo enc ision
E.H Ruspin(1i 9 70)N umericMaelt hodfso rF uzzCyl usteringP.r ocesNsoerst.h -HollAamnsdt,e rdampp. 339-347R.e printed
witthh ep ermissoioftn h ea uthoarn dp ublisher
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enceP ublishCion,gI n c.R eprintweidt ht hep ermissiooftn h e WG. Weea ndK S Fu( 1 969A) FormulatoifoF nu zzAyu tomata
authoarn dp ublisher andi tAsp plicataisao nM odelo fL earniSnygs temIsE.E ET rans
actioonnS sy steMmas.n ,a ndC yberne5t:i2c1s5.- 2R2e3p.r intweidt h
E.S anche(1z 9 77S)o lutiionnCs o mposiFtuez zRye lation Equa
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tionAsp plicattioMo end icaDli agnosiinBs r ouweriLaong icIn.
M.M.G uptaG.. N.S aridainsd.B .RG.a ine(sE d)s.F uzzAyu tomata Wenst0(p1 976)F uzzSye tS imulatiMoond elisn a Systems
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M.S ugen(o1 977)F uzzMye asureasn dF uzzIyn tegralSsu-rA Whale(n1 984)D ecisiMoank inugn deUrn certaiwnittyhV ari
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veyI.n M .M.G uptaG,N Saridainsd.B .RG.a ine(sE ds)F,u zzy ousA ssumptioanbso uAtv ailaIbnlfeo rmatIiEoEnET. r ansactions
AutomaatnadD ecisPiroonc esNsoerst,Hh o llanNde.w Y orkp.p 89- onS ystemMsa.n .a ndC yberne1t4i8c8s8.- 90R0e.p rintweidt ht he
102R.e printweidtt hh ep ermissoifot nh ea uthoarn dp ublisherp ermissoifot nh ea uthoarn dp ublisher
M. Schneidaenrd A .K ande(l1 988)P ropertoifet sh eF uzzy D.W illaeaynsd N .M alvach(e1 981T)h eU seo fF uzzSye tsf or
ExpecteVadl uaen dt heF uzzEyx pecteIdn terivnaF lu zzEyn vi theT reatmeonftF uzzIyn formatbiyoC no mputeFru.z zSye tasn d
ronmenFtu.z zSye tasn dS yste2m6s3. 7 3-38R5e.p rintweidt ht he System5s 3.2 3-328R.e printweidt ht hep ermissioofn t he
permissoifot nh ea uthoarnsd p ublisher authoarnsd p ublisher.
W Silve(1r 9t7 9S)y mmetrSiucm matioAn C lasosf O perationsR .RY.a ge(r1 988)O n OrdereWde ightAevde ragiAnggg regation
on FuzzSye tsI.E EET ransacotniS oynsst emMsa.n .a ndC ybernetiOcpse.r atoirnsM ulticriDteecriisai onmakIiEnEgET. r ansacotni ons
9(I0 )6 57-65R9e.p rintweidt thh ep ermissoifot nh ea uthoarn d SysteMmasn,, a ndC yberne1t8i1 c8s3.- 19R0e.p rintweidt thh ep er
publisher missioonft hea uthoarn dp ublisher
R Slowinsakndi Teghem.,(1 988)F uzzVye rsuSst ochastiRc .RY.a ge(r1 992)O n theS pecifiocfia t Pyo ssibiDliisttyr ibu
I Ir
Appraochetso M ulticriLtienreiaaPr r ogrammiunngd erU ncer tionFu.z yz Setasn dS yste5m0s2 ,7 9-29R2e.p rintweidt ht hep er
taintNya vaRle seaLrocghi st3i5c,ps p. 673-69R5e.p rinted wimtihs sioonft hea uthoarn dp ublisher.
thep ermissiofot nh ea uthoarnsd W iley-Lai dsisv.i sioofJ no hn
R.R.Y age(r1 987)U sinAgp proximaRteea sonitnogR epresent
WileyS onsI.n c.
& DefauKlnto wled.gA ertifiIcnitaell li3g19e 9n-c1e1.R2 e.p rintweidt h
Takagain dM .S ugen(o1 985)F uzzIyd entificoafSt yisotne ms thep ermissoifot nh ea uthoarn dp ublisher
T
andi tAs pplaitciontsoM odelinagn dC ontroIlE.E ET ransactions
R.RY.a ge(r1 98)1. AN ew MethodolofgoyrO rdinMaul ltiobjec
onS ystemMsa.n a ndC yberne1t5i1:c1 s6.- 13R2e.p rintweidt ht he
tivDee cisioBnass edon FuzzSye tsD.e cisSicoine n1c2e:s5.8 9-600.
permissoifot nh ea uthoarnsd p ublisher
Reprintweidt thh ep ermissiooftn h ea uthoarn dp ublishTehre
H.T anaka,T sukiyamaan.dK .A sai(1 982)A FuzzSyy stem DecisSicoine njcoeusr niaslp ublishbeyd t heD ecisiSocni ences
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ModelB aseodn t heL ogicSatlr uctuIrnRe ..R Y.a ge(rEd ).F uzzy Institluotcea.t aetdG eorgiSat atUen iversity
Seta ndP ossibility TheDoervye-lRoepcmPeeennrttg sa,m oPnr ess,
S YasunobSu .M iyamotaon.d H .l har(1a 9 83)F uzzCyo ntrol
New Yorkp.p 257-27R4e.p rintweidt ht hep ermissiooftn h e
forA utomatTirca iOnp eratiSoyns temIn Proceedoiftn hge4s t h
authoarnsd p ublisher.
IFAC/IFIP/IFORS ICnotnefrenraoetnniC cooenn atlri onTl r ansportation
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IEEET ransactoino Snyss temMsa.n andC yberneIt i30c2 s7.- 331.p ermissoifot nh ea uthoarnsd p ublisher
Reprintweidtt hh ep ermissoifot nh ea uthoarn dp ublisher
LA Zadeh(1 981)P ossibiTlhietoyra yn dS ofDta taA nalysIins
R.M.T onga nd Bonison(n1 e9 80A) LinguisAtpipcr oactho L.C obba ndR .T hral(lE ds)M.a thematFircoanlt oifeS rosc iaanld
PA
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oft he authaonrdp su blisher
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and B Kiszk(aE d)s .A pproximRaetaes oniinnE gx peSryts tems.a ndp ublisher.
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North-HollAamnsdt.e rdapmp,. 1 57-16R6e.p rintweidt ht he M. Zemankov(1a 9 89)F ILIPA FuzzIyn telliIgnefnotr mation
permissoifot nh ea uthoarnsd p ublisher
Systemw ith LearninCga pabilitiIensf ormatSiyosnt ems.
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guishabiilnti hteyS ettionfgF uzzLyo giIcn. Kacprzaynkd R .R Reprintweidt thh ep ermissoifot nh ea uthoarn dp ublisher
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Yage(rE.d )s M.a nagemDenetc isSiuopnp oSryts teUmssi nFgu zzSye ts HJ Zimmerma(n1 985)A pplicatioofnF su zzSye tT heoryt o
andP ossibilitVye rTlhaTegUo Vr,Ry h,e inlaKnadi.n p,p .1 98-212.
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Reprintweidt thh ep ermissoifot nh e authaonrdps u blisher
righ1t9 85b y ElseviSecri encPeu blishCion,g I ncR.e printed
witthh ep ermissoifot nh ea uthoarn dp ublisher
Chapter
1
Introcdituon
byD idiDeurb oiHse,n rPir adaen,d R onalRd.Y ager
Fora lontgi mcel,a ssliocghaialcbs e efnle tt oo poionutta ,n dt or egrtehta",tL ogichiaavtneos mo u ch
liemdi tafrsa mae wofromkro delailfnlag c oefth su man negletchtseet du odfy nostu psecttihneg
vagueness,
reaisnoagnn,d mroeercnett lhyue n iquenpersosbi alboift iym protapnatri ttp laiynsm athematthiocuagTlhh ti.s"
theoarsym oad elc afpotruu rnicnegr taanvidan gtuyse sn,e poionftv iewwa sa lseox pressosmeedt liamtee r by
habse eqnu estiaoswn eeldMl a.n ayt mtpethsa vbee en BertrRaunsds (e1l239l) I.n s pei otft hceo nesriadble
madee,s peciinat lhlicyse ntufroayru, g mentthien gi ntefroemrsu til ptle-vlaolgurieacdis si entd h 1e39 0bsy
reprteasteincoanpaalb iolfli otgioiercsf , op rr oposiJnagLn u kasiicaeznw hdi ssc hoowlh od evelloopgewidic tsh
non-admdodietloisfvu en caeirntOtnye. t ohmfeo srta dicailn terrmyet driuavtahl u,e i(tsw )ast heA merican
anfdur itofftu hle astemt petwsa isn iiattbeyLd o tZfia dehp hilosMoapxBh lear(c 1k39 7w)h o pfriorpstos soe-dc alled
in1 96w5i tthhp eu blicoafht iipsoa np "eFru zSzeyt s.""c onsipsrtoefni(cltyeah sne"c esotffo zurzsmy e mbership
Satrtfrionmg itdheeoa fg radmueamlb erishtha ibspe ,e n functiionon rsd)toe "rc haravcatgesuryeim zbeo Clasl.c"u li
thbea sfoirs baol tohg oifgc r adiutaypl riornpt eiaensd af ovra guper edichaavtbeee se snu ggeedbs ytH .W ey!
newp,ai rctulsairmlpayln ed evffeeu,cn tciertcaailnctuyl (us14,90 )b,yA .K apl,a naHn.Fd.S chto( t19,5w 1he)re the
cal"lPeods siTbhieloirtyZy"a dbe(yh1 89)7fo,rh andlibnags fuizcz syec to nnecatlirveaeapsdpe yaS re.Oe s tasiewicz
thneo tioofnp so ssibainldci etryt a(ionnrte yc essi(t1y19)1,9 9 2)9f or daentrdae ifelrcseet nsor elawtokersdT. h e
gradually. Frenclhi ngYuvieGsset ni tlhom(m16e98 c)o intehtdee rm
Together, afnudpz ozsys isbteihtlesoio rtfyyfa e r "ensefmlbolue" F r(etnhcceoh ut nerpfaorfrtu zszeyt ),
framewtoord ke awli tphr ediwchaotsseeas t isfaicsat iwoni thboeuitn agw aroefZ adeh('16s95 )fu zzsye ts.
matotfedr e graenewd i tmho daleixtepisressui nncge rtaiGnetnyt ilhuosmetmdhe te e rfmo nra mianp ga iorfn ested
gruadalPloys.s imbeialsiutarynend se cesmseiatsyua rrees s ubs(eEt1.s E2,)w itEhl E2,i no rdteord istinguish
no-nadditsievtfe un ctiotnhse;f omrer are �
betwe"ecne nitnretarlpr teitoan(siE"nl) tohfce o ncept
max-decompfoodrs iajsbulnec tainodtn h lea tatreer
midne-compofsoacrbo jlnnuec tiBoenrfo.ei ndictahtei ntgh us desc"rpieberdi,po hnaee(nrsidaE n 2l- "El )·
Interesetnionuiggtlh y t ihsme a thematKiacrila n
maifna coeftf su zszeyat nspd o ssibiliatntdyr ytihnego ry,
Mengwerh oi,n 1 915,w ast hfei rsuts ett hote e rm
toc layr tihfe miasisnur eaiss etdh ifisrna mewiotr k,
"ensemfblloue" t hteii nto lfae p apeirnF recnhH.e
seemasp pprroiattome e ntisoonmf eo ruenrnewrhso
consiwdheariteks dn owinnt hfuez zsyel tei rtatausr e-m ax
discuisdseoearfods r madle finivteircoyln osts ote h bea sic
prodtuarcnts iftuizvrzeey il oatnbsu,wt i tahp or babilistic
notions ibnyZt aredodhTu.hc eeidr cwaobenr vkise waesd
inteetraptrHiiowsno .r iknp roabbilgiesotmiecdt erayl s
testimotnhiceeo sn cdeoernfv elopreedsc ehbaeyrwr isth
witthr ianignuelqaura litthyle o cwahotefipn oo ni anrtes
diffebraecnoktug nrdess,p elcliiynta hsee cohnadl ft hoifs
assocwiiattpher dob bialdiittsryi buftuitnoicnoI ntws a.s
centufroyr, mocdaeplasob flhe a ndltihnkegi nodf
motivbaytt ehdne o nr-astniti(viiant s yt rsiecnts e) of
knowltehdhagutem amnasnp uil(aite.i ele.lf,-i dcnlead sses,
equailnaip thyy sciocnatli nwuhueamrne,e lemmeanybt e
impreocrui nscee rptaiienoc fei sn fornmr,au tlpieeosr vaded
indistinfrgoumti wsoh aobttlhhecae atrn s d ibes tinguished
witvha gueonree xscsie opnts).
fromo nea nothaesdr i,s cubsysP eodi ncMaorree.o ver
Mengewro'rosk n p robbialimsettirci c splaectdoe s also
thienr toducotfis oon- catlrlieadn ngourlmaasnr dc o
TheE mergencoef F uzzyS etsa nd
normwsh,i chha vbee eenx tenssitvuedlbiyye B d.
PossibilTihteyo ry
SchewizaenrAd . S kl(a18r93 a)n,wd h ilcahth earvt eu rned
outtob eb asoipce raftoorr sfs ueztzsyC h(aspe2t)ee .r
Aboauh tu ndyreeadar gso ,A mtehrei pchainl osopher
Menge(r91 66a)c knloewdgseodm ree lationship
CharPleeisrw caeso noef t hfei risntt h meo deamg teo
betweheiinsd eoaf" cloudp-oliinkoter"s" h, a szeyt "
2 ChapIt eIrno tdruction
(Mengetrra'nss lafotri" oenn semfblloeua "n)dt, h ied ea,B enven(u1t9i6 o9f)g, e neirzaeildn formation measures
recenetxlpyr eastst ehdat ti moefa, f uzzy Isnfe atct.th e whicahr e lnoon gneerc essaardidliytb iuvteo ,nl y
ideoafg radmeedm berswhaissp u ggesbtyMe edn gerd ecomposwaibtlrhee spetcoat t riangcuol-anro rm
himsetlotf h (eE asGte)r mamna thematDi.cK ilaanu a (incluthdeci ansogef m axo peration).
whob,e twe1e9n6 a5n d1 972d,e veloapnee xdt ensiveA sw ec an botht hied eoaffu zzsye tfosrd escribing
see
theoorfmy a ny-vasleutesd h tamhsua ctih n c ommowni th vaguper edicoartc elsa swsietsih m precilsoeclayt ed
fuzzsye tth eoarlyb,e wiitta h m ormea thematicbaolulnydaarnidet hsne,e efdo arn on-additive calculus of
orientrteeadt m(een.tKg l.a,u1 a9,6 6S)e.Ge o ttw(a1l9d8 4)u ncertbaaisnoetndmy a xa nmdi no peratiwoenrbser ewing
foarn e xtenascicvoeuo nftt h oef tfoerng otwtoernkb sy beforet hien trodoufctt hnieoo nt ioofan f su zszeyat n dof
Klau(aa nfdo rt heigree nsisa)l,o nwgi tah fulla possibmielaistuybry eZ adeihn 1 96a5n di n1 978
bibliography. respectiHvoewleyv.Ze ard,e whh,o h adm adiem portant
TheE ngliescho nomGi.sL t. S .S hackilsea contributtosi yosnst eamnsdc ontrol enbgeifnoereer ing
particnuoltaarpblrlyee c uorfsp oors sibtihleiotIrynya . 196h5a,bs e etnh fier sttob ec onvinced
serioefws o rksst aritnit nhlgea t1e9 40Ssh,a ck(l1e9 49, ". t.h.at thc eo nventqiuoannatli tteacthinvieoq fu es
195159,6 119,7 h9a)ps r opostoe rde plparcoeb abwiiltiht y systaenma lysiinstr insuincsaulifoltryde eda ling
are
an ewc oncienpo tr dteohr a vaem orsea taicstfomroyd eolf withhu manissytsitceo mrsf, o trh amta ttaenry,
uncertianie nctoyn omHiceis n.t rod"udceegdr oefe s systwehmo sceo mpleixsci otmyp artaobt lheao tf
potenstuiraplr wihsiec,eh"s timtaowt hea t eexvteenntts humanissytsitce Tmhse. basisc ofnotre ntthiiosn
ariem possainbdlu es,et dh mea ximuamn dm inimum resotnsw hat mbiegc hatl ltehdpe r ipnlceoif
operatfioocrno sm bintihndege greaensda, p otential inocmpatibSitaltiietndyf o.r mtahleels ys,e onfc e
surprciusrevw eh icuhp t oa c omplementtoa1 t iiso n thipsr inciistp hlaaets t hceo mpleoxfai s tyys tem
nothibnugat p ossibdiilsittryi ibnuZ taidoenhs 'esn se. increaosueras b,i ltiotm ya kep reciansde yet
Moreovheerd ,i scusastel de ng"tuhn certaasi nty signifsitcaatnetma ebnotiusttbe s h avidoirm inishes
probabvisl".iu tnyc"e ratsap ionstsyi bIinls iptioytf.te "h e untait lh resihsro eladc behyeodn wdh icphr ecision
inteorfess otm leo giciinah nisws o r(ke .Hga.m,b lin, ands ignifi(coarrn eclee vabnecceo)ma el most
1959t)h,me a themaotfSi hcasc ktlhee'oswr eyr nee ver mutuaelxlcyl ucshiavrea cte(Zraidset1hi9,c7 s3.)"
complewtoerlkyoe udt . ThenZ adeh (1973)a naa ldtveocrnaaattipevpsero ach
Independtehnept hliyl,o soLp.hJCe.or h e(n1 973) ". .b. aseodnt hper emitsheat th kee ye lements in
advocattheemd i nimuomp eratfiooren s timatthien g humatnh inkairneng o tn umbebrustl, a beolfs
so-caglrlaeddoe fi nductive supptootr hte attafcuhzezsdye ttsh,ai tsc ,l asosfeo sb jeicntw sh icthh e
conjunocftt wioporn o posfritoimto hngesr adaesss ociated transfriotmim oenm bersthoni opn -membeirss hip
witeha cohf t hem. Some ytehaepr hsi lloastoeprh er gradruaatlth ehraa nb rupt. tIhnpede erevda siveness
NichoRleassc h(e1r9 7p6r)o poast ehde oorfpy l ausible off uzziinneh susm atnh oupgrhotc essusgegse sts
reasownhienrgpe r oposiatrioeor ngsa niiznle ady eorfs thamtu coh ft hleo gic behind huimsa n reasoning
vari"opulsa usidbeiglrieTtehyse".sd ee grewehsi,ci hno ur notth trea dititownoa-lv aolreu veedmn u ltivalued
terminaorlreoa gtyh" ecre rtdaeignrteyae rspe,r "o pagated logibcu,ta logiwci tfhu zztyr utfhusz,z y
bym eanosfi nferernuclewe hsi cahrs ei mitlota hroe n es connecatnifudvze zsry,u loefis n ference."
appeariintn hgse y ntapcatriotcfp ossibilloigsiatc i,c A si tc anb es eefrno mt hese qutowot atZiaodnesh,' s
logwihco ssee manctiocmsp leatgerlweyie t pho ssibilmiottyi vaatinobdna scg krounwde rqeu idtieff erfreonmtt h ose
theo(rsyeC eh apt5e)Tr.h ec onsequpernicnect ihpailtse oft haeb ove-tmieonnaeudt hHoeri sn.t rodutchceeod n cept
usegdoe sb actkoT heophraad sitsucsoi,fpA lrei staontdl eo,fa fu zzsye cto mpleitnedleyp enodfet nhtepliryro posals
expretshstaehtsce e rtaaitnttayct hoae c do nclucsainonno ti no rdteorp rovait doeo flo rre preseanntdri enags oning
bew eaktehra tnh aotft hwee akest premitsos weiststheh anevt aiiallia nbfloer mianta im oann nseirm itlota hre
drawitnhcgeo ncluFsoiromna.tl hlciyas,bn e e xpreisns edw ayh umanesx preksnso wleadngdse u mmardiaztea .
termosfa necesmseiatsyu Nr aes N,( B)m in(N(A)Z,a dehc'aslf lo nro n-convetnetcihonniahqlau sbe ese n
<::
N(A B)w)h erAe B ist hmea teriimapll ic(ait.ieo.ns, o metimmeiss understood,a tte hsbeepg eicninaialnnlgdy,
� �
"noAt o rB " )T.h iisn equaclainbt eyo btaiansea d interparsae nte exda mpolfpe e rmissivetr ytihntigon king
consequoefnt cheem in-decompoosfan beicleistsyie tsyc apes ttrhiec otfnm eastsh emartaitchse,r a sta h an
measurfoerst hceo njunction. serioautst emtpoto verttahkeel imitpeodw eorf
Thes pecciaasloe fa S hafe(r1'9s7 6ba)c, o nsonanetx pressiovfee xniessmtsoi dnegal nsmd e thodIsns. p iotfe
plausifbuinlcit(tiwyoh net nh feoc aell emewnhtisc h gitvhee e arleyn courageamnedsn utp poorfts ome
birttoht hissef tu nctaironene steidsm) a,t hematicmaaltlhye matliickiReai ncsh ard Boerll olgmiacnli iaknes
identtioZc aadle h('1s9 7p8o)s sibmielaistuSyrh ea.f er'Gsr igoMroei stihlwe,o rkosfZ adeahn,dh ifso llowers,
contour f(ucnocrtrieosnpsto ont dhiepn lga usiobfi lihtayvo ef teennc ounstkeerpetdi mciissimn,t erparnedt ations
singletobnesv )i ecwaaensda fuzzsye mte mbershiupn warracrnitteidfrc oimms amn syc holwahrisfl,ue z szeyt
functaipo oinn,fit r smta dbey K ampdee F eri(e1t9 80)a.n dp ossibtihleioatrnyyd t heaiprp licartaiiostnehsde
Shilk(r1e9t7m'1as)x itive amreaean soutrheesr examipnlteeo rfooe fts hte SresZe.a deh (fo1r9h 9io0sw) n a ccoounn t
possibilmietays-ulriienkste,r odiuntc heicdsa sfreo ma theev oluotfifu oznz yl ogiAcf.t aelr motshti ryteya rs,
puremlayt hemapotiincotafv l i eAwl.s woo rth-mentiZoandienhgo 'rsi giindaela hsa veb lossomiendt ao
ist hei ntrodubcytK iaomnp,ed eF eriFeotr,ta en d comprehecnosripovufems e thoadnsdt oolfosr h andling
ChapIt Ietnrr otdiuocn3
botchl assweistg hr adumaelm bersahnidnp o nknowle(deg.lega .co,kf p ercissiloonp,p ilniemsist,a tion
probbialiusntcritencat iAyb.o uttw toh ousarnedsse archoeftr hse nlaatnugrau,lab guertsa )tahsea r woafye xpsriensg
havceo ntriabttu htee dt hoero ratephtlpeii cc alteivoenl sgr.a duiatlIynt. h saetsn ef,u zszeydts o n ohta veex actthley
Thep apecrosl leicntt heedrs eeai dngcsa bne s eeansa samceo nrcnea so thaeprp roatcohv easg uenFeosrs .
rperesentasatmipvleio nftg h eciornb turtiions. instaKn.Fc ien(,e1 97p5r)oo psetsh astta temeabnotaus t
vagpuree dibec attaekt eobe n t ruiaef n odn liytf h ehyo ld
fora lplo ssiwbalyoesf m akitnhgpe r edipceractieIs te .
What FuzzyS etsA reA bout enabtlhecesl assliocgairlce allas thiiobepntsw eeavn a gue
prediAc aantdie t nse gatnioonn-t Aob ep erservBeyd .
Thceo ncoefapf tu zzy sweittt hhdr eee apslresen taticoonn trfuazsztsy e atpp licattaikaoedn vsa notaftg hele i mited
ofc laswsheossbo eu ndaraireneso t qdueitteiern meIdt. overilnabegptp weenA annodn -aAn dmo rgee nelryoa fl
useasc haractfeurnicstttiaiiokcnnv g,a luuessu ailntl hye this okfoi vnedr lnagip nfp zuizpya rttiioinnos r dteohr a ve
inte[r0v,aI1lmt) a .ya lsboea f inoirdt een urmaebsleet oaf s moottrhsa iintofnr oomn ec latsosa nothPearr.i kh
lineoarrdleylr eevdeH losw.e vtehrve a luasteniteo enbd e (198q3u)e sttihopeno ss siboifpl rietcyi sely assessing
neitlhienrea orrldye (rael da ttiisec neo uagsh pooiuntt edde groeeftrs u tfohra v ague preIdnpi rctaacitech.eo ,w ever
earilnty h dee vleopmoefnfu tz zsye tnso)bor u nde(de .g.m,e mbersdheigpr eesm ahianavlneoy r dimneaaln iInng .
thsee mi-roepaeilnn te[r0v,a+lhoo a)bs e euns ed aw itoht hweorr disit s t hoer deriinndgu bcye dt he membership
cositn teetrpart.i oFno)r simpalsiscutimhteuey s ,oe f wed egrbeetewse etnhe el emetnhtaistsm eaninrgaftuhle,r
thien te[r0v,ai1lnt) h foel lowIinna fg u:z czlya ssosm,e thatnh eex avcatl oufet hdee egresT.h iissi na gerement
elemetnhtaastr ec ondseireads" mraginoarl" "l essw itthhq eu alintaattiuvorefte h bea soipecr iaotntsh aarte
accepet,aa"br glei vaed ne groefem embertshhiaipts useodnt hedseeg r(emeismn a,x ancdo mtphlee mentation
intermebdeitawre0ye ( nn on-bmeermshainpd1) ( fullt o1 a sa no rderr-srieonvpgee raitn[i 0o,n1O ]b)v.i oau sly
membehri.spF )uzzya rsgeee tnasel rulsye fodrre presentfiunzgmz eym bershipw ifldulenpe cntodin to hnce o ntienx t
linguliasbetlTishc.i c sa nb ev iewaesde xpresasni nvga riwoauysFs i.r tshtue,n vierosfed isrcso(eui .teh.e,
uncertaabionuttcy l tehaerm -ecauntio nfg lthaebB eult. domaoifnt hmee mbersfhuinpc thiaotsno b) e d efined
thiem portpoainntit st hatthv ea luasteiitoss n u ppotsoe d( e.tagl.l,ni esnso stt h sea emt hifonrga m ano rfo ra tr ee).
bec ommotnot heva riloiuns guliasbteitlchsa a tr e Secoinmtda ,yd epenodnt hoet hcelra swsheisac rhue s ed
involivnaeg di vperno ebmlT.h iisst h ceo mmensurabtiolc iotyvte hrde o maFionir.n stawnictrehepe, sc tt oa g iven
assump,wt hiioucnnhd eralltilhef eszu zsye ltei rtataunrde doma"isnm,a dloelsn" o t meexaanc tthlseya mteh ing
habse efonu ndde batabbysl oe moep ponetnott hste h eory.t hree maivnocianbgu lianrcyl oundle"yslr ageo"ri rsi cher
Iti st ob ec onesriedda caosn venierneta saonnda balnecd o ntaboitnh" sm ediaunmd""a l rg.eL"a syt,alf uifz zy
assumpitnmi aonnsy i tuaDteiloentsti.hn aigss s umptimoenm bersfhuinpc tmiaoyvn a ry fromp erosntoeo n
woullde atdod iifcfulwthieecnso mbinmienmgb ershainpo tHhoewre.v er,i rse wlahyila mtpo rtainnpt r acittsio c e
functionnasm,e ilty uissu ailmlpyo sstiomb elreg e cortrlecrye epsretnhtpe i ecoefks n owlepdrgoev ibdyae nd
complperteeor ridneagsns o,t beydA rro(w1 96i3ns) o ciaelx pearntcd a pttuhrmeee anihneig n tetnod sg tiohv ies
choitchee ory. ownw ordWsh.e thtehrei rsaeu nivecrosnasle onns utsh e
A fuzszeymt e mberfsuhnicpet nicoonad p erse fceer enmeanionfag l insgtuieicx preslsiik"oetn a mlaln i"s
amontgh peo ssiibnltee rtpiroeontftsa h ceo rrespondainnogt mhaetrt er.
labe.l A fuszecztay an l sboed efibnyee dx amplificatFiuoznz,sy e ts be ciannt erpirnde itfeefdne tr wTahyes .
rankeilnegm eanctcso rtod tihnegi r twyiptirhce ascpltei tmyo scto mmovni eiwst os emee mbersfhuinpc taisao ns
tot hceo nceupntd erltyhifenu zgzy s e(tp rotioctaylpw ayo fa ssesdseignrgoe fes sa tisfoarpc rteifeornefo nrc e
elemernetcset ihvgeer eamteemsbte rgsrhaisdp)Fe .u zzy thed iffeernte lemse notr intperarettiso.nT he
sentast aulralpyp eiannr o n-sstpreiccitf siI.cmt aa tybi eo ncommensurhaybpioltiohtnetys h diees g roefsae tiss faction
sofcto nstraoirfn ltesx riebqlueie rnetfomsr whsilcihg hwti trhe stpt eocv arifouuzssz eyt s mapkoesss itibotl e
violactaibeno tnosl er(aet.teghd.de ,ea dliintseo dabyu,t combifnuez zsye tisna meaninwgafyuG.le neral
tomorirsso twai clcle patalbtlheol ueggshoos d )o,re lastipcr incfiopfrlu ezssz eymt e mberfsnuhcitpi eolni citation
clasosfoe bjse catpsp,r oxidmeastceri opftt iyopnoesfs restoore tx ismteitnhgoi dnms e asuremen(tKr atnhtezo ry
situattowi hoinca hg i ven prcocaebnde ua rpep loire d,e ta l1.9,7 1A) p.o iwnotr tmhe ntioanbionfugut z szeyt
evepnr oceduwrietfshu zzsitlayti-ends trouncsIt.nie ach combinaetsipoenc,ii nat lhlneyu merseitctailin stg h,e
casfezu zsye ts praeg sreardavuneads l m ootthar nsitieoxni stoefan p caen oopfld yif freenfta miolfio epesr ators,
from coaneteg oriyn taon othaenrda voiadbsr upti ncludviarnigo euxst ensoifol nosg iocnaells i ke
disconttihnwauotiu tlbideec sa usbeytd h aes signomfe nctoj nunctainoddni jssu ncttoigoentswh,ie tra hv egrianagn d
precbiosuen dafroirte hse cdoenrsesdiu bsets. coTmhpee onrsyoa petriaotnTsh.i vsa rioeftc yo mbination
specifictahtubiseo cnosmm oer e raonbadud sattpi vIen. operatmiaoyhn esls po ldvief uflitcliiektseh f elo lowing:
thciass feu zzyp rsoevtaist d oeo folrb ridgtihngeag p Smitahn dO sher(s1o9n8 g4i)v teh eex amptlhea" ta
betwetehpener ceicvoendt ionfut ihwteo yr alndhd u man peercftblryo wanp plsee"e mtsob em oret ypiocfta hle
disccroegtnei rteipvrete asteinIonpn a.r tifczuuzlsyae rt,s c ojnunicotbnr owanpl pet haonfe itbhrero wonra plpe.
helwpi tihn tceirnfngau merdiactaa lsa ynmdbo lliacb els.H owevtehrei,xs ampallesp oo inotutsth awth ewne
are
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4 ChapIt eIrno tdruction
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onoef C. havbee en repcoeinnottule(tyde .Fga.r,id neaC!se rarnod
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nestoerdd insaurbys eFtusz.zs ye cto unnjctiaonnds p ossidbsiitlriitbyfou rte iaoconhbj ectths,ee to bjoefc ts
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8). possisbaltyit shrfeey q uir"eXimeAsn" at n d ftzuhzesy e t
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satiistBf.ey c aIlu(sAe;;:) N: ( Afo)r e acohb jtet,ch lea tter
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thfeu zzinoefsF s.O nt hoen hea ntdh eex pre"sXsi iso n Degreeosf T rutha nd Incomplete
F"c atna kpel aicnae sitwuhaetrtiehov ena loufXe is Information
preciksneolwaynn wde e stitmhaeetx et enwth ittcohh i s
valiusec ompatwiibttlhhe le a bFe (lw homseaen ing At tphoiiisnts te emtsi melayn stwtoeh rqe u estion
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satitshfirieessq eumieronrt caqnu ableia fs"i yeodu ngy"e alrast tehrpe,e pe rcstihvaers a tchhearn gfeudzl;zo yg ic
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coindseraes"d y outnogt "hd ee gr0e.ei8 n coan dseiredr edaingissb, o tah l ogoifcg radpuraolp eratnide s
cont.e xt) incompilnefotrem aWthieonn .o nlpyer dfuizczaayrt ee s
Ont hoet hhearn" dXi s aFl"sm oa ym ea"na lli st hiantv olovnelmdyu, il ptle-vlaolguaiercdnes e ed(ewdh at
knowanb otuhtve a loufeX ,i s tXh iasFt " ( whiotut Haaccka ltlhs'e f isrtsatog fef uzzificWahteino n').
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corproensdtsoa situaotfii nocnpo elmtei nformatpieornv awdietudhn certaanidtn rtu-ytv halbueecso imlel
(pervwaidtiehmd p recisuinocanei rnattansy di) t,u ianti konn own aarnmedo delblyfe udz zy souftb hsee tusn it
whiwceh cano rodtnehlrpey o ssviabllouefe X sa ccordiinngt eWrhvaaatlr c.ea l'lfuezdtz ryhu -tvalbyuZ easd'te urnh
tot heliervo efpl l ausiobrpi olsistiybW ihleanifu tzyz.y outt ob ei -lklnowtnr u-tvhal,u aesis nducbeyd
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single-vvaarliuatebhdlde ee ,g raetet acthoae v da luet hlei ngusiusbttilocef tt hiweeo sr d i'nttr huneea 't ural
expretshsee slo efpv oesls itbhitalhtivi tasyl iusien deedl anguIangdeef.eu dz,tz ryu- tvhalrueepsr esbeyfun ztzeyd
thvea loufte h vea rlieTa.hb feu zszeyt s t Fheiinne trpretseudb soeftt hsue n iitn tearnvmdao ld elulnicnegr toani nty
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prefereonntc hepeso ssibloeft hvieal llu-ekvsna orbwilnae exepsrsiionnn ast ulraanlg uHaogweesv.ae ttr h,te i moef
X. Ntohtadeti stvianlcumtea sys imaunletouhsalvaye Haakc'csr itpioqsusei,tb hieloirtyty h deai nmde nosfi on
degreoefp ossiebqiultaio1lt . y incompilnfoertmea htaindoo bnte elna id bare in a striking
In ctahsoeef i ncompilnefotrem awteci aocnno mputfaes hi(oanl thtohuewgyeh r ael rebardoyio ndignZ adeh,
tow haetx ttehnietn forma"tXii Fso" ni sco nsisten1t79 5w)i".tF hu ztzryu- tvhalumeigsh"tt h eanp peaasr a
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ofµF o veAr.M oreowvees rh,ab leal l tlh meo re cerotfta hienrs eea gdsiS.nmi)i latrhl'eyl ocalfiutztyzr'yu tohf
thaXt t akietsvs a liunes ome sAu baasslet lth vea luevsa lueemsp hasbiyzB eedl lmaannd Za(9d17e7hw) a s
outsAi hdaeva es maldleegrro efpe o ssibtihcliaisbnt e y ;s ometiimlnelds-e urstoogde,n ekarisan lod fac ontext
estiemdba ymt eanosf d aua mle asoufrn ee cesNs(iAt)y depeenndcwyh,i ilrtee l almye atnhsia ntf uzlzoyg wihca,t
1- Il(A()A i st hceo mpleomfeA n)t. Tdhuia=sl itiys ctarluliteeshdv aluwaittrehed s pteoac d te scriopft ion
ana vailabolf(e v asgtiuanetc,peo l mektneo)w leadngde ,
betwepeons siabnidnl eicteyys m seiatsuirsae g sr aded
nowti trhe spteotc htae c t,uo abjlectsitvaoetft e h weo rld.
versoifto hnoe n eex isitnmi ondga l wlhoigecixhcp ,r esses
Lalsytf,uz zlyo goircs ,u bcatlhceurlaeiron efo wb eing
ar elabteitownte henene cesasnatdrh ype o ssiabllreea,d y
