M 34
Ma~ewaruwaceroniig (C~OPHIIK CTa-
~ e i i nepe~on . c anm.).M., U ~ H ~ H U ~1974. B , 64 C. (Hoeoe B XHSHH, HayK...
13 downloads
346 Views
2MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
M 34
Ma~ewaruwaceroniig (C~OPHIIK CTa-
~ e i i nepe~on . c anm.).M., U ~ H ~ H U ~1974. B , 64 C. (Hoeoe B XHSHH, HayKe, TeXHWKe. Cep~fl %MaeMOTwa, rr~fieptre~a~aa, 7. kf3AaeTcfl exeMecasHo c 1d7r.) B nepsofi c r a m e6opnn~aonncan ueron @ ~ ~ M H ~ OHBnpudnn~HHR XeHHOrO O C T H R I p a 3 ~ ~ 6 $ q a n n~ xBKTHPeCKHX aanaP SKOHOMnKn. ncnxonorp * ~ ~ T B W $ $ ~ I $ e gdnacrei?, a ~ompblxo c n o ~ ~ y w ponb nrph5 hoBi?fieIi~e, xapdtM?ptoe nnr rrrns~x cyqecrs. BT0paq crarbrr nocssqe~ia npaKTsPecKolay npsuenennm reopstr arp 06J?aCTH MBTeMaTHKH. WCUlenYK)lI(efi CHTYBUHA, B KOTOPUX CTanKneamrcr unrepecbl pa3nn~nblxnmnefi, oprann3aqnR n T. a.
u@if?
-
Coc~aea~enb UIMJ'IEFfKO A. B. n e p e s o n s ~ ~ wTOPEJIMK B. A., OPJlOBCKHFf C. A.. PMHrO H. M., CTPMrAJIEB A. A.
IlPEAKJlOBHE
nore. A. 3 a A e .
.
OC'HO~~IHoiorb 6 0 ~ x 0 :
AA K AHAnU3Y CnOWlMX CUCTEM M flPOUECCOB flPHHRMR PEUlEHMFl 5 Maprnn Ul y 6 w n. FEFlWHr 'I4 'HrP
TEoP'G~R
.
3
49
Pedrmop 0. D. WBAHHUKMA. OSnomlca Jl, fl. POMACEHKO. X y ~ o m penalcrop 8. H. KOHKIXO8. Texnnq. peaswop A. M. KPACABHHA Koppanop $I LI. . BACMb€&3L
OCHOBbl HOBOrO IlOaXOAA K AHAnM3Y CJlOXHblX CMCTEM M IlP04ECCOB IlPMHATMA PEUlEHMW
~ ~ , nena, IIpeACTaBJIflB 3 ~ 0 kCTaTbe OIIHCbIBaeTCIt TIOnXOA, K O T O ~IIOH CyTU eT c&k OTKa3 OT O ~ W ~ ~ D W H ~ ~ ~ * ~ O S H ~ M ~ eC TOTAOBB~ aHiLnH3a H H ~ ~ XCH-
L. A. Z a d e h. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes.- IEEE Trans.-Syst., Man, Cybern., vol. SMC-3. 1973, Jan., pp. 28-44.
HUH E O H H M ~ ~ RBJXeHHEl H~ O T ~ ~ ~ T B J I CS ~B03MOlKHOCTbm K ~ eIW KOJIIiWCTBeHHOrO a H a J I W a . -MY IIOABepFfiyTq COMHeHHlO llPaBOMepHOCTb p a ~ ~ y ~ zTeHAeHIIUU ~efi aHanU3HPQBaTb ryMaHHCTHYeCKUe CUCTeMbI T a K , K a K eCJlU 6b1 OHW ~ ~ U I MeH XaHHCTH9eCKUMU CUCTCMIMN, O I I H C q a e M b i h 4 H B T q M H H a X pasHOCTH~IX, ~ H W p e ~ u e a n bunn ~ ~ xu H T e r p a n b H H x ypameH U ~ ,0 3 H a 9 a e T B3RTb AHCCOHUPYIOUYIO HOTY. pa3 T a K a R H T ~ U 3BYqUT B &0fi p a h e .
K~K
Ham OCHOBHOB~e3gcs a ~ ~ ~ i o s Ba eTOM, ~ c ~rn no c~oeji
H a c ~ y n J I e H U e 3nOXU @bIqUCJIUTeJIhHbIX MaLUUH BbI3BaJlO CTpOe PaCLUHpeHHe c @ p b I HCROJIb3OBaHHR KOJIHYWTBeHHbIX M~TOAOB a ~ a n u s a3a c s e ~wx n p a M e H e H u R AJIR a ~ a ~ u 3 ~K aOHOMMSeCKHX, ~ P ~ ~ H W C T N ~ ~ C K COUUaJIbHMK, NX, 6ii0.~10ru4e. CKUX U APyX'HX CUCTeM, B KOTOPblX OCHOBHYH) P O J I ~ U r p a e T noseaeme, ~ a n o ~ u ~ a r o r rRl oesee A e H u e rr
m o ~ no3swr~arn . PBCRPHT~ himPne ~ a f npnponbl i ~ ~ u e03aaB a T b BCe 60JIee & donee i C ~ l I I ~ H M MaIIIHHbI. e HO 9TH Xe
YCIleXU BCWIAJIU KUHPOKO M a H W H O e Y ~ ~ X A ~B HTOM, U ~ t%MH HM MOXHO CPaBHHT~JI~HO HHCTHQeCKUe CHeTec n o M o w b i o ~eopda MM. Tan, ~ a n p u ~ e p , Y ~ P ~ B J ~ ~ HBH KOHC R eCKHX HaBHlX&HOHHMX CHWM B ~ I C O K OTO'IHOCTH, ~~ m r u y J I n p o B a n n npHMeHeHwe ~ H AJJRH a H a J I H 3 a 3KOHOMHYeCKUX U ~ A O J I O ~ H Y ~ ~ K U X c u m . Ycnexu ~ a ~ p o c ~ o n n s e c ~ao~ raon u 3 a @ U ~ H ~ ~ C K H X CHCTeM C IlOMOwEH) MOaeJtHpOBaHHR H a 4 R M IIpKBeJifi K TOMY, ¶TO 3KOHOMeTPHrleCKOe MOAeJIUPOBaHRe C nOhlOL4bM EBM CTa-
W~THBHO
CYTU 06b19~b1eKOJIHWCTBeHHbIe M e T O w a H a J I U 3 a CHCTeM Hen p U r O A H H AJIR r y M a H n c T n r e c K n n LnLtcrn n d 6 u e J I I ~ ~ N X CHCTeM, CPaBHUMbIX n0 CJIOXHOCTH C rYMaHHCTK'IeCKHMU CBCTeMaMH. B OCHOBe 9 T O r 0 Te3HCa J I e K U T TO, YTO MOXHO h J I 0 6b1 H a 3 B a T b ( I P U t f t Q U W MCOBMeCmUMOCmU. C y ~ b9TOX'O IIPHH4 ~ n aMOXHO B M P ~ ~ Un pTH~q e p H O TaK: YeM C J I O m e e c H c T e y a , l TeM ' M ~ H @ &fW C ~ O C O ~ H JAAa T b TOqHbIe U B TO Xe BPeMR B M m U H e n p a K T H Y W K O e 3 H a q e H H e CYXAeHHR 0 ee I I O B a e H U H . ,&iR CHCTeM, CJIOXHOCTb KOTOPYX npeBOeXOAHT H e ~ o T O p ~ fn iQ p 0 ~ O B H BYpOBeHb, TOqHOCTb fi ~ T ~ ~ K T U ~ I CMHCJI ~ C K U CTIHOBRT~ ~ CR I I O Y ~ UUCKJIIOWXQUHMH A p yr apyra XapaKTepHCTHKaMH l. MM~HHO B 3TOM CMbICJIe T O ~ H MK ~O J I H ~ W T B ~ H H a H~aIJ ~I H~3 noBeAeHWl I'YMaHBCTWYeCKHX CUCTeM H e HMeeT, n o - B m U M O M y , banbu10I'~ npaKTUqeCKOP0 3 H a W H H R B PeaAbHEJX C@tJ&aJIbH W , 3KOHOMHqeCKUX U A P y r H X 3 W a 9 a X , CBII3aHBb;lX C y Y a C T H ~ MWHWO s e J I o s e K a sinH rpynnu aroaeii. M~oiirn a r l x o A , p a 3 ~ u ~ a e ~Bu i i p a h ~ e orrupae~cs , Ha I l p w I l Q C b I h ~ y 0 TOM, W O 3JIt?MeHTaMU .WllIJIeHE$R qf%!IOF€K ta RBARWrCR H e YHCJIa, a 9JIeMeHTJd HIU(OT43PblX He¶WltH& MHOX e C T B UJIn KJIaCCOB O~WKTOB, AJfR fr@fWPbIX IEp&XQ& OT UnpUH~JI@XHOCTH K KJIaCCyU IE Z#elI~)IHa$neXHOCTH% B e C K a q ~oa6pase~, a H e n p e p m e H . B c a M o u w e , H ~ Y ~ K W npx~ , C y U a R IIpOU@&Cy MbILLlReHHR ~ & J o B ~ K P , HaBOAHT H a WblCJIb 0 TOM, YTO B OCHOBe 3 T O r 0 npO$@%% JI-T He Tpa&fnZHOHHaR g B y 3 H a S H a R HAH &atf<e MHOr03H@VHaR JIOrUKB, JJOr@Ca C ~ e w c a f iU C T H H H O G T ~ ~ , CSq39MH 4 H ~ ¶ ~ % B M , N npemar(s BblBoAs. x G t r K H jpwm B M e m o raran eesgricaa, me H q a c T a T o q H o u 3 y a e ~ ~ anorsxa a arpam oc-
mi
M
a
c
HOBHYIo POJlb B TOM, YTO MOXeT OKa38TbCR 0 ~ ~ 0Hf3 i~ a H 6 0 J I e e Ba)KHbIX CTOPOH YeJfOBeYeCKOrO M W J I e H H R C~OCO~HOCTU oqmuearnb n~@op~auum T., e. B M ~ W P ~143 T ~n a B m u e r o H a ~ 0 3 pr a 3 ~ 0 0 6 p a 3 H Rc ~ e n e ~ nTfei H T O ~ ~ KTOe , K m o p M e m e w m H o w e H w e K a ~ a n n 3 u p y e ~ onpo6ne~e. fi
-
n o CBO& npspofle OUeHKa RBJIReTCR ~ ~ H ~ J I M x ~ H U BO ~M. MHOrHX C n y s a R X AOCTaTOYHa BeCbMa ~ ~ U ~ J I H X ~ XHa pHa K~ - R T e p H 3 a U H R ~ a 6 o p aAaHHbIX, nOCKOJIbKy B ~ o J I ~ L U H H C T BOC~ &Z~=ra R L I P ~ K ~ R HOBHMX s a ~ a s ,p e w a e M b I x T O ~ H O C T ~ .Y e n o ~ e q e c ~ ~MOW f i wcnonasye?. A O ~ ~ C T U M B C T ~ ~ a ~ 0HeTOYHOCTH, fi KOAHPYR UH@PM~YUH), UAOCTaTOYHYd AJIR 3aAa'-lW) (HJIH UAOCTITOYHYIO AJIR peI.Ue~liSf))) 3JIeMeHTaMH H e rIeTKUX MHOXeCTB, KOTOPbIe JIHJIIb ~ P N ~ J I U X ~ H HOnHCbIRaWT O HCXOAHbIe AaHHbIe. ~ O T O KM H @ P M ~ I ~ HIIIIo, c T ~ I I ~ I O I UB~ M03F ~~ y e p e s o p r a H b 1 B P ~ H I I R , cnyxa, O C R ~ ~ H E I Ru ~ p . , c y x n B a eTCR, TaKUM 06pa30~,B TOHKYIO C T P Y ~ ~ K HH@PMBIJIIII, Y ~eo6x o n ~ l ~ o AJIR f i p e m e H y n o c ~ a s n e ~ ~ sanasn oii c MuHuManb~ 0 f iCTeneHbKl T04HOCTU. C ~ O C O ~ H O C O T n~ e P l l P O B a T b HeYeTKUMH MHOXeCTBaMU H BbITeKaIOIQaR 113 H e e C ~ O C O ~ OUeH ~ T ~ HMBaTb HH@PMI~IIK) RBJIReTCR OAHHM U 3 ~ a H 6 0 J I e eUeHHbIX KaqeCTB seJIOBe4eCKOrO p a 3 y M a , KOTOpOe @ Y H A ~ M ~ H T ~ ~ ~ H H M 06paso~ oTJIHYaeT Y ~ J I o B ~ Y ~ C K pHa ~3 y~M OT T a K Ha3bIBae M o r o M a m n H H o r o p a s y ~ a ,n p u n n c b I s a e M o r o c y ~ . q e c ~ ~ y l o r r l ~ ~ BMYHCJIHTenbHblM MawUH8M.
_w-nzny=
T ~ ~ A H ~ H o H MeTOAbI H ~ I ~ aHaJIll3a CUCTeM HenOCTaTOsHO nPMrOAHbI AJIR aHaJIkI38 ryMaHUCTH9eCKUX CNCTeM HMeHHO IIOTOMY, YTO OHR H e B COCTORHMH OXBaTUTb HeseTKOCTb YeJIOBeYeCKOm MbIwJIeHUR U IIOBmeHHR. ~ O ~ T O MAJIR Y A~~CTB~HHOrO a H a n H 3 a ryMaHBCTUqeCKHX CHCTeM HYXHbI nOAXOAbI, AJIR KOTOPbIX TOsHOCTb, CTPOrOCTb U M ~ T ~ M ~ T N ~@ ~p C ~K aH- ~ ~ n H 3 M H e RBJIRIoTCR YeM-TO ~ ~ C O J I H I T H O H ~ O ~ X O A U M ~U I MB KOTOPbIX HCnOJlb3YeTCR MeTOAOAOrHYeCKaR CXeMa, AOnyCKaIOa a c l HeYeTKOCTH H 9aCTHYHbIe UCTIIHbI. ~ O A X O A , OnNCblBae~ b l f iH U X e , IlpeACTaBJIReT ~0608H ~ K O T O P ~ In~y~C,T b H e pewsIOUHB, war B STOM ~anpaWlentIn.
% nOffXOfl UMeeT T P H OTJIRYNTeJlbHMe YepTbl: 1) B HeM HCllOJlb3YI4YlCR T a K HaSbIBBBILbie ((JIMHrBHCTHYeCKUe)> IIepeMeHHMe, BMeCTO qHCJIOBbIX n e p e M HJIU B AOIIOJIHeHNe K HHM;
2) n p o c T M e o T H o w e H n r i M e w y n e p e M e H H b u l n o n n c N s a m c R C nOMOUbIO HeWTKHX B ~ I C K ~ ~ M B ~3) H CJIOXHbIe U~~; OTHOIUeHUR O n H C b I B a ~ C RHeYWKNMH aJIPOPNTMaMH. n p e X ~ eYeM n e p e f i ~ k l K ~ O A ~ O ~ H O~ M ~ C~ ~ X A ~ H UHaLUerO H ) nOAXOAa, 6 ~ n o6~ nonesao n p m e c T u q H o B H b r e coo6paxe~u2,nexaurne B ero
X H O B e . H ~ Y H ~CMKPaTKOrO ~ ~ ' ~ R C H ~ CMblCJIa H M R JIUHI'BHCTUseCKUX IIepeMeHHbIX. 1) Ji'u~aucmuwc~ueu wwmw n e p e N e w m e . K ~ Kyxe OTMeqaJIOCb, C ~ O C O ~ H O C T OUeHHBaTb ~ H H @ O ~ M ~ U H IUrpa€!T ~ c y u e c T s e H H y m ponb B x a p a ~ ~ e p n 3 a s uc sn o x H s r x ~ s ~ l e ~ w i i . C ~ O C O ~ H O C TYeJIOBeKa ~ OQeHUBaTb H H @ ~ M ~ I ~ U K~, a u 6 O J I e e RPKO ~ P O R B J I R e T C R B HCllOJIb30BaHHH eCTeCTBeHHblX R3bIKOB. KaX~0eCJIOBO X eCTeCTBeHHOr0 R3bIKa MOXHO PaCCMaTpMBaTb K a K C X a T O e OIIHCaHHe HeYeTKOrO IIOAMHOXeCTBa M (x) nOJIHOrO MHOKeCTBa o ~ J I ~ c T Up a c c y X A e H f f f i U, r A e M (x) e C T b 3 H a W H H e X. B 3TOM CMbICJIe BeCb R3bIK, K a K UeJIOe, MOXHO P a C CMaTPHBaTb K a K CMCTeMy, B COOTBeTCTBHU C K O T O P O ~ ~HeqeTKHM IIOAMHOXeCTBaM M H O W T B a U nPHIIHCbIBalOTCR bJleMeHT a P H b I e UJIH COCTaBHbIe CNMBOJIM (T. e. CJIOBa, I'pyIIIIbI CJIOB H I I ~ ~ A J I O X ~ H U R(60JIee ). n o ~ p o 6 ~3 Toa TOYKa 3peHEIR -06cyW a e T c R B p a 6 o T a x [4 1 n [5 T ~ KH,a n p u M e p , ecnu s ~ a s e ~ u e CylueCTBHTeJlbHOrO .!@emOK eCTb HeWTKOe IIOAMHOXeCTBO M (ysemotc), a s ~ a s e ~ Uu pen n a r a T e n b H o r o ~ p a c r c b l d . - H e s e T n o e IIOAMHOXeCTBO M (fCpWHblG), TO 3HaYeHUe COqeTaHUR K p W m d tpemox RBJIR~TCR n e p e c e s e H H e M M (yeefio~)u M (fcpacflbld). Ecny PaCCMaTpHBaTb QBeT 0 6 % e ~ ~ KaK a H~KOTOPYI~ p e M e H H y I o , TO s ~ a s e ~ uwofi r r n e p e ~ e ~ ~ o~ ipi a: c ~ b l dCUHUIZ, , ~ e f l m b l d ,3eneuud H T. A. MOXHO HHTepIIpeTMpOBaTb K a K CHMBOJIbI HeYeTKUX I'XOAMHOXeCTB IIOJIHOrO MHOXeCTBa BCeX 06%eKT0B. B 3TOM CMbICJIe QBeT RBJIReTCB ~ e w m l c o dn e p e ~ i l H 0 ~ ; T. e. n e p e ~ e ~ ~ o~fHi ~, Y ~ H U ~ M N - K O _ T O _~ O R ~B J I R G R CHMBOJIM H e g e T K P X MHOXeCTB. ~ X H OOTMWHTb, YTO 3HaYeHIIe nepeM~HHO%- -seT?~bIpaXe~~~e IIOHRTMeM ecTeCTBeHHOr0 k 3 M ~ a TIKIIM, K a K ~ p a ~ ~ br O~p af3iA,O M e H e e TOYHO, 9 e M 9UCJI0, 060s~asamuteeAJIHHY BOJIHM, COOTB~TCTB~IOLU~IO AaxiHoMy m e T y . B n p e A m y q e M n p k i M e p e ~ H ~ Y ~ H H R Mn He p e ~ e ~ ~ uos ie iT 6b1na T a K H e 3JreMeHTapHbIe IIOHRTHR, K a K ICpWHbld, C U H U ~ , mnmud w T. A. B Qnee 0 6 I U e ~cnysae 3 ~ a q e n u ~T a~K u x n e p e M e H H b I x M o r y T 6 ~ n p~e A nbo x e H u a B H e K o T o p o M cnerrw a s a H p M 33-55,H B wnx c n y s a f i x C O O T B ~ T C T @ I O ~n e~p~e M e a H M MM ~ ~ Y A ~HaSbIBaTb M AUH28UCmUWCKUfiU. T ~ KH,a n p H M e p , H e q e T K a R n e p e M e H H a R w o m a M o r n a 6b1 n p n H n M a T b cnenymOWHb U H e 8HaPeHWR: BMCOKU~,~ ~ ~ B M C O P Cd060nbH0 U~, 8b1!&0fGUd, ~WOKU f&?~ ,M H b B W o K U d , W H b - M H b BMCOKUS, ~~~COICU~, NO ~e w u b , 8 t w n w ~ 6 6 1 ~ o ~ u l6onee j, MU & e w e s b ~ o ~ u d3ru . 3HaYeHHR I I ~ ~ + I ~ C T ~ ~0606 B ~ R I npeAJIoXeHHB, ~T 06pa30~aH~Me nOHRTHeM B~~COKHB, OTPllQaHHeM He, COIOSIMR U W NO, a T a m e HeqeTKUMU CJIOBaMW T k i n a OWHb, d 0 6 0 ~ b H 0 , 6&/u(e H 6onee
I.)
-
-
-
-
9
UAU Mf@d!. DnpeaeneHm
srehc CMHCJIe ~ O ~ & ~ C nPHB=E?flfiOMY H O BMWe n e p e M e H H a a mmm a~nsercd n u i i r e u c T u s e -
CKOB.
K ~ 8Ky ~ mBHAHO nhxe, B pa3nwe 111, nnnrsm~tis&~ue nepehe~ean p e n ~ a 3 ~ a w 6B-t ~ R O B H O Mnna c u c T e M a T u q e c ~ o lxapa~wpu3a~wn C J I O ~ M X &nu nnoxo O n p e n w e H H b i x nsne~ni!. B c y a H m ~ ruitOPa, , @+~aamaacb CYP ncnotlwomHUH K O J ~ U ~ I ~ ~ ?e~er.ie~~sijr ~ ~ H ~ M X H o n n p a f i i j C H a cnmsiwe opucasua ~ u i i ae x , ~ m p i. m bner~j$er w o s e r t , MH npn.~ o 6 p a a e ~cir&oZkioe~16 . arTb CKCTeMbl H ~ C T O ~ B K O c h b ~ ~ b i WO e , OliH fIkfi0eTynfibl: U ~ ~ I ~ H O M aYT e M ~ T U W K O M Y
-
a~dna3y. C~&M
x
Hy
3 a f i # k U ~ 0 c ' k b Me)KAY fiBYid5l ~ R J ~ , ~ ~ B M M ' f IHe f 3 e ~ e H H b S ~ h
0 6 ~ 4 o~n0u c ~ b a mc n o ~ o u b m~ a d n u u ~mopym ~, CJIO-
BeCfiO MOJfrHb npC?&CTWHTb
B B U a e Hd&3pa
61wcka3~saHU8,
tianpa~ep,eenu x p a B u b 5, ~ 0 . ypasilo 10; ecnu x pamo 6, " $ p a a ~14~H T. A.
e t ~ o i fl i?c i r o c o 6 a n n c a H b a n p a l s i e ~ ! H a e ~ cHs B H a m e M ~ O A XOAe, TOJIbKO IIepeMeHHbIe X U y SBJIRlOTCR HeWTKUMH. % sacrnoeTw, C e n N x u g JiunrBucTuniecKEte n e p t ? M e ~ e b I e , TO s b r e ~ a s b i B a n u f l , onukbmarduue ~ ~ B H C H M U C T y ~ OT k, M O ~ J I N 6bI B b I i ' J f t ~ q e ~ Tb a K ( c ~ o BH~ ~, ~ B H H~ yHp c~n B U k ,dpemzi~nafOT ~06UjDk 3 H a q e H U B HetlWKUX I I e P e ~ k h H b l ~ ) : ecne x maao, TO g OWHB o t t e n b mum eenti x ne o w 6 M W , ~d y we,mum eegn x Fie wmo u nd iznutco, TO y jCe ~ A U ~ ~ DT.' A. U H e s m r ~ u eB u c K a s M s a H u a T u n a ads A cneayer Br, rde A n 3 aaiem H e a n p e A w I e H H o e ssatteene, H a n u ~ e p ,~ R H b o i r *A C TO&&, TO 'hi A b J i ~ t e H 6 M ~ b # k H W ~ ) , 0 6 b 1 9 ~ MB ~ ~ B C ~ A H ~ PesIi. B H OO ~ ~ H ~B K p a 3O fOBOpe 3 d a q e ~ n ~ T a K u x ~ M e k w b l ~ a n aofni p e n e J r e n M wleris nnoxo. B pasnefle V 6 y w n o n a b a H o , s ~ Bo L I C K ~ ~ H B ~ H (113 ~ I O A cnenym Bs IMONHO IIpHAaTb *n~oe 3 H a s e m e naxe T o r n a , aorna A n B H e s e T K u e M a e x e c m a , can 3kiarfChnR A u B o n p w e ~ b riaK i H e K a f o p H e nO&iHO]KeCTBa o&racTH ~ ~ K C Y ~ A ~ H U ~ . B npeasrpimm n p u l w e p e mtibuiekne M e a y H ~ ~ ~ K H M U nepe~e~~Mltin x u 4 R B J I R ~ T C ~n~ p m B TOM C M W ~ , 4m er0 M0)KHO OllHCaTEi RaK M H O W ~ ~ T B OB M C K ~ ~ ~ ~ B Lhli&& LHU~~ *U3 A c j l e y e ~Bs, r&e A H B c n ~ B o nh ~e q e ~ ~hi~t3h ~ n e c ~n ~ pM , c T a s n n m u e co&l s ~ a s e ~ n nde p e ~ e t f f l k x x H C O O T ~ ~ H H O . OhUCBHV,9 6onee CJI6XHblX 3dilenk10c ~ e ay OT x IdOryT i ~ b ~ p e 6 ~ H~ e qme T~K fu ei anrapmu: Raft
-
$6
-
-
+!
6 y m no~a3awnonpod~oB pa3ne~leIV, n 9 H R T H g ffBqqfCOM)
aaropnma u r p q ~OCHOBH~IQP O J I ~ B n o c T p O e n u n C ~ ~ G & B U P W ~ A H ~ @ H H OOnHCaHHfl ~O H e O l l p w e H H b l X q 0 ~ a ~ t i f€3i EX B ~ ~ I ~ ~ H o I L ~ ~ H H ~ ~ .
3) Onucatiw t e m u x @ y ~ ~ y uut oJ m t i o ~ ~ ucs r iwwwrl~ 3ananne ~eseT~aii ( ~ ~ Y H K U HcU noMoilLbIo
rrewm~lurm z o p u m k l o s .
HeMIIeTKHX B b i C ~ a 3 b t ~ a H UaHBnOI'H4HO fi 3aAaHUIO o ~ H ¶ H Q B @YHP UHU aaBn~uefinap B u n a (x, f (x)), x s ~ a s t t ~ uaprye MeHTa, f (x) C o o T B e T C T B m e e 3HaYeHHe @ ~ H K U U U . BMWTQ ~ a 6 . nO ~~~ ~ I ~ H Y@KYIH K L I N ~ MOWO OnpeAeJImb aamp~waWCKU (T. e. C nOMOl4bIO I I p o r p a ~ ~ b IB) TOqHO T a K lfCB C Q@ HerIeTKylC M O u b I o H e q W K O r O aJIrOpUTMa MOXHO OJlp@eJrUTk @~HKUUK).TOx e c a M o e OTHOCHTCR u K O n p e n e n e H u x o MHOXWTB, ~ e s g r f u xm~orrre~uB H npyrax a h e ~ m s . no C B MCyTU ~ H e q e ~ K U f iBJIIDPUTM 161 n p e A ~ a B A I f e TCO@% ynopqoreasym n o c n e A o B a T e n b p o c T k UHCT Y K Q H ~ (no~ Q ~ ~ HnpoQaHM!2 CI AJIa B ~ ~ H C J I U T ~M~a ~w UHblf,' H O ~ HeKWphl. N3 QQTQPbIX M O r P C O A e P X a T b CUMBOJIH q e S q K u X M H O X ~ T P , H$IIpaM@p: ecnti y eenqm, TP WMMW y m e ~ b w ~ mx b ecnu y He O y e n b eenum u tie OWN^ m o , mo o w ~ pi? b IWM N W YBeAUYUmb X ~ C J I U y MMO, TO cmn; WJIU tiem, mo yMnuuumb x H a 2.
-
rae
-
nw4-
To, ao B a n r O p w r M e A o n y c K a m R BHCTPYKUHB H O ~ O T u n a , ~ O ~ B O J I H npu6JInxe~no ~T O n u c m a T b c ero noM O U ~ W came pa3H006pa3nb1e c~oxuiwR B A ~ H H R . Baqno $YAY(IU HeqeTKHMU n0 C B O ~ %RPHP@4et T a K B e Q p w a g U f l TO, MOrYT 6 ~ nWHOCTbJ0 b W e K B a T H b I UarlSM ~ Q C T ~ W ~ 3aH O ~ ~ nasn. Hesff~uea n r o p u ~ ~ TaKQg'o bl w r y T aaTb S ~ K TuBHare cnaco6rJ npn6naxe~~oro onsawin u e ~ e q g g@YHKNEB, O I ' ~ ~ B U S ~ H H~ ~ H~ ,K U H O H N ~ O B ~ HCHCTeMbf, IIR CTP~T~SH~ w T. A. B nanb~elrrrenrMIA oCTaHeBwMcn H a H e K o m p w x n3 OCHOBHHX CB~Z~CTBJ I U H ~ B U C T H ~ ~ C B H nepenreaawx, X HeveTKwn BMC K ~ S ~ ~ B U~ He4WKUX H U ~ aJifopUTheoB. QH@KO Mbi H e 6y.W nwraTMI-s n p w a B w T b H a m nonxaq ero npwwxesua B KaKOM-TO OKOHsaTeJl bHOM BUAe. %y CTaTbrQ CJI6?&yeT PflCCMaPkfe a ~ bn p w e B c e r o K a K p p e m a p w T e J r b n o e o614ee o n H c a H w e w m a , senammema mxo40~OT TP~IJU~FUTO?HYTU H.c~po~ % T H B HaYqHoM a~anuse,41ew~a;n p u & u x e ~ ~ anpwpma n KOTOpOrO o'rpaXae'C HeOnpeAeJleHHOCTb n O B g e H k S ~ ~ 0 5 , ~ s e ? y n 0 3 ~ a ~MyO X ~ Tc-raTb O C H O B O ~h~ ~ e pee a n H c T f i s w K o r a m a ~ q s sr y M a n s c T u q e c K n x cHcTeM.
pwa
u
a
M3 n O c n e A y I O m A x pa3neno~~ Y A ~B HT ~ H O , s ~ oT e o p m u s e c K w e o C H o s a H m H a w e r o nonxona H a c a M o M Awe s n o n H e ~ o s HbI A MMaTeMaTAqHbI f I O AYXY. fieJl0 B TOM, ¶TO UCTOgHHKOM H e o n p e n e n e H H o c T u B H a w e M nonxone n s n R e T c R H e n e x a u l a f l B a-0 OCHOBe T e O p A R , a cnoco6~HCnOJIb3OBaHUR JIJraHrBACTAW?CKUX IIepeMeHHbIX H H ~ ~ ~ KaJIrOpUTMOB U X B @OPMYJINPOB~HHU H P e U e H H A P e a J I b H b I X 3aAas. , ~ ~ ~ ~ c T B H T ~ J I ~ H OB C TKAI X , AOM cnysae c T e n e H b T O ~ H W T H p e t l I e H u R ~ o x m6b1~bc o r n a c o B a H a C T ~ ~ ~ O B ~ H N F 3aAaWi IMM U T O s H o C T b I o A M e I o ~ U X C R AIHHbIX. n o n o 6 ~ a f i~ H ~ K O CCOCTaBJIReT T ~ OAHY U 3 B a X H b I X W P T P a C CMaTpHBaeMOIW MeTOAa.
B
F A e CUMBOA U H f e r P A P O B a H A R 0 6 0 3 ~ a ~ aOeI I~ e P aUBK) 0 b a e ~ U HeHHR OfiHOTOqegHbIX H e W T K H X M H O X W T B PA (Y)/Y. Ecnu HOCATeJIb d COCTOAT A 3 K O H e s H O r O WiCJIa 3JIeMeHTOB, TO HHT e r p H p O B a H H e B (2.2) MOlKHO 3 a M e H U T b CYMMUPOBaHUeM:
+ +
A = PIIYI unu
n
A=
II. H E K ~ T O P ~CBOBCTBA IE HEllETKMX MHOXECTB A n r l T o r 0 s~06b1 CAeJIaTb H a W e w 3 n o ~ e ~ B n~o neH e CaMOCTORTeJlbHbIM, MbI A3JIOXNM T e C B O ~ C T BH~e s e T K U X MHOXeCTB, KOT O p b l e ~ O H ~ A O ~ H T CBR 8 a J I b ~ e f i ~ ~(60d'Iee e ~ . n o ~ p o 6 ~ o06e c y x n e H t i e n o n o x e ~ ~ iT ie o p A u s e s e T K u x MHOXWTB, memW A X OTHOUIeHHe K A ~ H H O TeMe, ~ COfiepXHTCR B pa6o~ax
(2.3)
k I ~ n
2
(2.4)
R/Yi,
i-1
,' . . .,
-
r A e sucno pi ( i =r 1 n) c T e n e a b npuHaAJIemocTu 3 J I e M e H T a yi MHOXeCTBY A. ~ ~ M W U Mq ,T 0 3 H a K IIJIIOc B (2.3) 0 6 0 3 ~ a s aO~~ % ~ A U H ~ H aH ~ H, e a p s @ ~ e ~ u s e c ~CYMMUPOoe BaHAe. nOJIHOe MHOXeCTBO = ljn) MOlKHO n p e A C T a B A T I i n p O C T 0 B BAA€! CYMMbI
KoH%?~Ho~
(Y1,. . .,
U
[I-171.)
XOTR, C T P O r O rOBOpH, B b I P a X e H U R 3aIiACaTb B BAAe
.
(2.5) li (2.6)
CJIenOBanO
6b1
.- .
MHOX~CTBOM H ~ ~ ~ I B ~ ~MHOX~CTBO, T C R H O C H T ~ J ~KOTOPO~O ~ CoCTOAT A 3 ~ A H H C T B ~ H H OT ~0 9~K H . Ecnu d OAHOTouesHOe H e 9 e T K O e MHOXeCTBO, HOCUTWeM KOTOPOPO RBJlReTCR T O P K a Y, TO M H ~ Y A ~ n M HCaTb
-
A
-
ply,
(2.1)
T o r ~ aHerIeTKOe
IIOAMHOXWTBO
MHOXeCTBa
U,~ O n H C b I B a e MAO e
nOHRTAeM UeCK0AblC0, MOXHO 3 a I I A C a T b B B A A e ( C W M B O ~= ~ 0 6 0 3 ~ a s a ep~a B e H c T B o no onpe~ejre~uro)
a ~npmepa l ~ npeanonoxm,
wo
X = {Toi, AUK), Y = {LIxoH, AXUM), TorAa 6 u ~ a p ~ oHeYeTKOf2 e OTHOuIeHUe C X O ~ C ~ @Me>Kny U 3JIe MeHTaMIhMHOXeCTB X U Y MOXHO 3anllCaTb B B U A e C X ~ C ~ S= O
-
TOM, AxoH)+O,~/(TC)M, AXAM) I+~,?/(AHK, AxoH)+O.~/(AHK, AXUM).
~ O M H M O 3TOr0, JaHHOe
OTHOlueHHe MOXHO
hp&!~$t)d~b
B Bli&3 MU?lpU@l O~OuLeilWr
U
A - H ~ W K OM ~ HOXeCT@Onp&?Qp&&dii,TO MOXHO HanHCaTb nposop~1~~" =cpell~eflo~ m a ~ o / A x u ~ cun~uo/b6
+
+
+ ~ o / , h ~ .
H e v e ~ ~ ncTeneHu e npunamexamn
MMO,
epedue
+
N ~ZUA~UO
R&RRICYCCR UpH 3TOM HeqeTKHMM RqBMHQXeCTBaMU IIOJIHOrO MHoxecTsa V, onpeAensreMoro cneAyiounM o6pasork
V = O + 0 , 1 + 0 , 2 + . . - + 0,9+1.
h
ROS=
J
Xx.2
(9.221 W y . ( P ~ ( X . Y ) A I ? ~ ( ~ , ~ ) ~ ~$),
(2.19) 1 Bblpallte~ne (2.22) onpenenner MaxcnMnnHoe apaa3~cnenneR H 8. Anano~qno OnpeAenReTcR H r+iaKcamanbHoe npomsenenne c TOR pasHHU~R, 9TO /\ 3aMeHReTTR apH MeTHVeCKHM npOH3BeAeBHeM. f i a ~ e e uonpo6~omi nponraene~" pacc$orpes. B pa6ore [2].
aVb = max.(a, b) =
a, n p u - a > b b, npu a 4 b,
(2.23)
Ilepeceqe~ueA
M
B 0 6 0 3 ~ a s a e ~Acn~ B u
onpeAenReTcR
pa-
BeHCTBOM
A n B &S((pA (P)A U
C h p E i ~ a ~ HHe, e COlo3bI U H WlU, YKJIOHYliBbIe nOHRTHR O w l i b , BeCbM, 6 0 / 1 b ~ , ~ e l i b u l eH R p y r U e TePMHHbl, KOTOPbIe BXOART B Onp-eHue s ~ a s e ~ u iniu H r B k i c T u s e c K u x n e p e M e H H b I x , M o r Y T PaCCMaTPHBaTbCR K a K CkiMBOJIbI P a 3 J I U q H b I X ~ I I e p a u H f i , O n p e A e J r e H H b I X H a H e q e T K H X nOAMHOXeCTBaX I/. Haubnee CyIQeCTBeHHbIe H 3 3THX 0nepaJlkifi 6 y f l y ~OTMeqeHEd H U X e . ~ o m m e ~Au e0 6 0 3 ~ a s a msepes ~ A H onpeneJIReTcR.KaK
1
AOnOJIHeHUR COOTBeTcTByeT OTpHUaHHiO. T ~ K H M X CUMBOn H e q e T K O r O MHOXeCTBa, TO f&? X CJIayeT U H T e p n p e T I l p O B a T b K a K ( ~ 0 u H e er O B O P R , AefiCTBYeT H a H e q e T K H e MHOXeCTBa, T O r A a K a K H e m A ~ ~ ~ C T B Y ~ T H a HX CHMBOiIbI; IIOHUMaR 9 T 0 , Mbl 6 y R e M HCnOJIb3OBaTb CHMBWH ki fit? B ~ ~ N M O ~ ~ M ~ H N M O ) . 0 6 ' b e A H ~ e ~ N HeqeTKMX e MHOXeCTB A U B 0 6 0 3 ~ a q a e ~ ~ ~ A $- B H OnPeAeJIReTCR PaBeHCTBOM
OnepmEiR
06pa30~,€!CJIH
1
-
1~
1
PB
WIY.
(2.29)
+ + +
(2.34) u unu v = 0,813 + 114 115 0,616 (2.35) u u v 0,713 0,516. n p o u 3 ~ e d e t l u eA N B 0 6 0 3 ~ a s a e ~ AB c ~ki o n p e A e J I R e T c R K a K
-
A
AB
=Ju PA (Y) PB ( Y ~ / Y -
(2.36)
kropoe r r p w a w a m co0oB xifner~oe ~ ~ o ~ ~ e c m aenaloro,
K W M ~OCHOBKMX
TOJIbKO ¶TO OrIPeAeJIeHHbIX ~ I E p a i t H f i , H M ~ A~Apyrue R onepaitmi, ~ o ~ o ncnanwywrcx p ~ e B npenCTaBJIeHWU JIHHrBKCTN¶eCKHX H W I X ~ ~ , ~ ~ J ~ ~ H HHOe C~ Tm~ p~ b~ I. e ff3 HEX 6 y f i y ~KPaTKO OnpeAeJIeHH (&met3 n o ~ p 0 06cy~fie6 ~ ~ H u e whx onepau~iiMOXHO ah^ B [151). OIXepauA5I KotlyeNmpUgWZHUR O l ' I p w 8 a R PaBeHCTBOM A
CON (A) =Aa.
(2.44)
46eca p c 3 y f i b T a W SlgHEaRHeHHR
B
F K
OBH09JIeMl2HTHOMY YHO-
TepMHHaX f( p e 3 y J I b T a T IIpHMeHeHEIR A A a m R paeexcrBoM
F
K HeqeTKOhrlY MHO-
fig
TeJIbHO BeJIHKO.
Onepauws pacmmwua
o n p e n e n n e T c R KaK C,
DIL (A) = A''=. Aefic~~ae ~ 0 f iOn$pa&HM p a w l 4 KOHUCHTPHPOBBHUR.
CJIeAyeT h H W p n p e ' f W p 6 ~ t n b K a K O & ~ U H ~ H U ~ ?c e % e R e r s a qeTKUX MHOXeCTB (9)K (Y), Y e U. T ~ K U06pa30~, M (2,48) a H a n o r n s H o UHTerpaJrbHOMy n p e n c T a 6 l n e H u m n u ~ e f i ~ o roneo p F p a C (y), UrpaK)uH?4 POJIb k i ~ l l ~ J I b C HXapaKTePHCTMKW. 0~ K a q e c T B e u n f i l o c T p a u m i (2.48) n p e A n o n o x u M , YTO U,A w K (II)O n o e A e m m g . TaK:
B
K
~pOTAB0IIQJIO)KIiO A ~ ~ ~ C T B A HO)n e -
one pa nu^ rcompacmrjo~u~rne~cu~urcayuu onpeaeJrcteTcR KaK
*a
O n e p a U U R oTJrU¶aWCR OT KOHUeHTPUPOBaHHR TeM, 9TO O H a y B M A ¶ H B a e T 3 H a W H H l I PA @), K 0 7 0 p b I e 6 0 J I b I U e 0,5, t4 y M e H b u r a e T Te, KOTOpbIe MeHbIUe 0,5. T ~ K H06paso~, M KOHT p a C T H a R N H T ~ H C H @ A K ~ I ~ AYMeHblllaeT R H W e T K W T b A (=pa Heqt?TKOCTH MHOXeCTBa, n o a o 6 ~ a ~ 3HTpOnHH, O n p W e J l e H a
116 1). Onepaws y e e ~ u m u f itmmnkmnu B r J p a m a e T c a B rrpespam e H H H o6moro (sw~aro) m i o x m a B H e q m o e HJIH B yse-
B
JIkI9eHHH C T e n e H A H e T K O C T H H e W K O N ) MHOXeCTBa. P a y f i b T a T IIpHMeHeHHR ~ o fOin e p a a H H K A 6 y o 6 ~0 3 ~ ~a ¶ a ~ b F~ (c At ) HJIH T ~ XK 3 0 3 H ¶aeT (( X I I P H ~ J I H ~ H T ~ J I ~PH;o~ B3>, H~ I3 TCl B p e M R K a K X. =!k@H@'JkI4 <X e C T b HeW?TKoe MHOxecmo qncen, n e x a u ~ xB O K ~ ~ C T H O C T Uwcna 3)). Onepam~
2.
-
-
T o r ~ aP€!3YJIbT%T ~ P H M ~ ? H ~ H WFR K' A ktMe&F BHA F (A; K) 0,8fl/l.+ 0,412) 0,6 (112 0,411 0,413) = 0,811 + 0,3212 + 0,612 0,2411 0,2413 * (2.52) = 0,811 0,612 0,2413.
+
+
+ +
+
+
+
AJIR
MaJIbHOM tf3MKe. HalIlMX QeJIefi R3MK L MOXHO PaCCMaTpHB a T b K a K COOTBeTCTBHe M e X A Y MHOXeCrBOM TePMNHOB W 06JIac~bmP a C C y W e H M R (&a TO9Ka 3peHBR O n H C a H a 60~1ee A e T a n b H o B I4 1 H [5 AJIR n p o c T o T b I M ~ npennonaraew, I ~FTO T o n p e A e n e H H o e MHOX~CTBO). M H O ~ O C w i T a T b , TO TO COOTBeTCTBHe X a p a K T e p H 3 y ~ T C R He9eTKMM Ha3MBaIoWHM O m HOuleHlleN N U3 T B U, KOTOPOe CBR3bIBaeT C KaXAMM TepMMHOM X B H K ~ X A ~ I M / ~ ~ ' ~ ~ KY TBO M C T e n e H b PN (x, Y) IIpMMeHMMOCTH X K .u. H a n p M ~ e p ,eCJIH ~ = M o n o d O i i M y =23 rOAa, TO PN ( A O A ~ ~ O23) ~ , MOXeT 6b1Tb 0,9. T ~ P M HMOXH 6b1Tb BJIeMeHTapHbIM, H a n p B M e p , X = BMCOKU~, MJIM COCTaBHbIM, KOrAa OH RBJIReTCR CG9JIeHeHMeM 3JIeMeHTapHMX TePMHHOB, H a n p m e p , x = o w ~ bsblcorcub klyxuutla. @EIKCEIPOB~HHO~O X @YHKUNR nPMHaAJIeXHOCTM P ~ ( XY) , OlTpeAeJIReT HeXTKOe IIOAMHOXeCTBO M (x) MHOXeCTBB U, @YHKUUR lTpMHa&AeXHOCTU KOTOpOrO 3 a A a e T c H KaK
T
U
I;
-
u
T
-
AJIR
n
PM
(x)
(Y)
xET,
= P N (x, Y), (2.53)
YEU.
3TO HeqeTKOe nOAMHOXeCTB0 RBJIReTCR no OIIpeAeJIeHHH, 3HUWHUe&L X. T ~ K H M 06pa30~, 3HaqeHEle T e MHHa 2 eCTb HeqeTKOe nOAMHOXeCTB0 M (x) M3 JIR KOTO O r 0 X CJIYXMT CHMBOJIQM. XOTR X H h f (x) HBJIRIOTCR pa3JIM9HbIMM 0 6 3 e ~ ~ a MW (X eCTb BJIeMeHT B TO BpeMR K a K (x) HeseTKOe IIOAMHOXeCTBO U), MbI ~ Y A ~ IIHCaTb M X BMeCTO M (x), 38 MCKJIIoqeHMeM TeX C J I y s a e B , KOrAa MMeeTCR H ~ ~ ~ X O A N M O C T ~ NX Pa3JIMYaTb. MJIJIlOCTpaUHU IIpeAIIOJIOXHM, 9TO 3 H a W H u e T e p M H H a A l 0 ~ o d O d OllpeAeJIeHO nOCpeACTBOM
d
T,
M
-
AJIR
I1,
ecnw y <25
K ~ yCTaHOBJIeH0 K
B p a 3 A e J I e 11, 3 H a q e H H R J I M H ~ B H C T M ~ € C K O ~ ~ CHMBOJIaMN HeWTKWX IIOAMHOXeCTB U , KOTOPbIe llpeACTaBJIRIQT ~060fi @ p a 3 b I HJIH IIpeAJIOXeHHR B eCTeCTBeHHOM MJIM @ ~ M ~ J I ~ H o M R3bIKe. Hanpu~ep,eCJIH U e C T b ~ a 6 o pUeJIbIX W C e J I
I i e p e ~ e ~RBJIRKITCR ~~fi
H 803pUCf)Z eCTb JIMHrBMCTH9eCKaR IIepeMeHHaR, 0 6 0 3 ~ a s e H H a g X, TO 3Ha9eHHRMM X M O r y T 6b1Tb &0JZod0d, N e M O ~ o d O i i , o w b wondod, H e ouem wondo2i, cmapab, w c m a p b i i i , H e o w u b cmapud H T. A.
B o 6 u e ~cnysae s ~ a s e n~ a~~er ~ u c ~ ~ q ence~poe i~i e ~ ~ o i i
...
e C T b C W T ~ B H OTePMWH ~~ X = X1 X2 X,, K O T O P ~ Il'If3eACTaB~~ JlReT ~0608 COYeTaHMe 3JIeMeHTapHMX TePMHHOB XI, X2 X,. 3 T H 3JIeMeHTaPHMe TePMNHbI MQXHO p a 3 6 M T b H a Y e T M p e K a Teropm: 1) p e p B H 9 H M e Te-I, K O T O P W IIBnRIOTCfI CNMBOJIaMN CneUWaJIbHbIX He9eTKNX nOAMHOXeCTB O ~ J I ~ C T ~H ~ c ~ ~ X A ~ H U R ( ~ a n p ~ ~ wondoii ep, u c m a p b l d B n p e A M A y m M npw~epe); M COIo3bI U, UAU; 2) OTpHUaHHe 3) I C e o n D e d e n e H H o c m u T M n a O W H ~ , MHOZO, cna60, 6onee unu ,ueNee (XOTR 6onee unu wewe c o A e p x u T B ce6e T p a cnosa, OH0 ~ ~ c c M ~ T ~ H K aB K ~3 J~I eT~ ~e ~R~ a p H b lTf~iP M N H ) H T. A.; 4) MUpKef?_bl, TaKHe, K a K BBOAHUe CJIOBa. & H O B H ~ H np06JIe~a PI, KOTOPaR B03HMKaeT B CBR3H C UCnOJIb30BaHBeM JIUHrBBCTB9eCKHX IlePeMeHHbIX, 3 a K J I K N a e T c R B cne,aymryeM: nywb ~ a 2 0 - 3 ~ a ~Ke ~~ ~ O e ~3 nOe ~ e ~ TSLPHOM) ' TepMWHa X i , i = 1, n, B CoCTaBHOM TepMWHe x = x, x,, K O T O P M ~ n p e A c T a B a R e T co608 s ~ a s e ~ w n ueH ~BWCTH¶~CKOM-~~~~M~T H ~HPO~~V ,C T C RBbIqHCJlHTb 3 H a q e H H e X B c M M c n e (2.53). %a s a ~ a s aR s n a e T c R q a c T H m c n y g a e M ocH O B H O ~ 3aAarIIi B K o J I K ¶ ~ C T B ~ H H O H ~ ~~ ~ I I ~ ~ A W I CeMaH~ H H O ~ ~ TWKe [4], a MMeHHO, 3 a A a q H BM4BCJIeHUR 3Ha9eHMR COCTBBHOrO TePMHHa. PI eCTb W C T H ~ c~~yqafi I ~ ~ n p e ~ b ~ q y 3Z4Wni, ~ e 8
. ..
. . .,
. . .,
MK, r A e h = o w r t o , a u = e b l c o ~ u l iw n 0 6 e K . ~ @ U H N M ~ RTOqKY 3PeHUR, OnUCaHHyfO B p a 6 O T e 1151, H e o n eAWIeHHOCTb h MOW30 PaCCMaTpUBaTb KaK O I I e p a T O e , KOTOPb! nepeBOAliT HeYeTKOe MHOXeCTBa M npeftCTaBnflmuee 3 ~ a s e ~ uu,e B H e s e T K o e M H O X ~ B DM (hu). yxe rosopumoca BbIrue, H e o n p e A e n e H H o c T u B M n o n H a w r + Y H K U ~ K ) r e H e p a s s H 6 o n b m o r o M H o x e c m a s ~ a v e ~ u AJIR f i - nuHrBucTusec~ofin e p e ~ e ~ ~u3 o i i~e6onbmro nePBuqHMx TepMUHOB. Hanpu~ep,u c n o n b s o B a H u e r + HeonpeAeJTeHHaGTu o w i l b B C o w r a H u u c r t e m , u u nepaugsbul TepMnHohi & m ~ u t i M ~ I MOXeM r e H e p U p O B a T b H e W T K U e MHOXeCTBa OWMb B M C O K U ~ , w own6 s w o 1 c u l i u T. A. AJIR o n p e A e J I e H u x ~ e o n p e d e ~ z e i c m mhu KaK O I I e p a T O p a ynof5~0 UCIYOJIb30BaTb H e K O p b l e OCHOBHbIe o n e p a r f s k , o n p e A e J I e H H b I e B pa3~e~1e 11, UCO&HHO oneparlnu K o H s e H a p a u u u , p a m a m e H m u yaenuqeaaa w e t l e l r a m u . B n o c n e A y a u e ~MM y K a m e M , MK a o MOXHO caena~bAJIH ecT ~ C T B ~ H HHeOnpeAeJIeHHOCTH O~~ OYertb U MCKYCCTBeHHbIX H e o n P C A W ~ H H W T tlA/OC ~ ~ ~ If .UUiiyC. X ~ ~ ~ K T ~ ~ H TaK#X CTUK HeOIIpeM A ~ J I ~ H H O C TKaK ~ ~ ~6 0, / l b t M , M H b U , Y N W , c#%, 8p&, &tlO/t-, if8 MOXHO ~ a f i ~Bl ip a 6 O T e [15 1. XOTR B IIOBCeAHeBHOM EICIIOJrb3OBaHUU HWl'lpefteJIeHHOCTb W e H b H e HMeeT qc?TKO OIIpefteJIeHHOrO 3HBqeHHff, B C P H O C T N OHa A e f i C ~ ~ y KaK e ~ yCUJIUT@JIb, r e H e p U p y R nOAMHOIKeCTBo T o r 0 MHOXeCTBP, K KOTOPOMY O H a I I P N M e H R m R . ~ P O C T ~ R onepaqua, K o T o p a a u M e a m CBO~~CTBO, O n e p a q H R : KOHQeffTpaQUti (CM. (2.44). %IHaBOBUT H a MbICAb 0 TOM, YTO OWHb X, X TePMNH, AOJfXHO 6bRb O n p e A e J R H O KaK K B a A p a T X, T. e.
19K
(US,
p pa
K~K
T ~ K Uo6paso~, M ecnu
c T e n e H b n p u ~ a q n e x ~ o : ~A u x o ~ aK K n a c c y cmapax n l o d e d e c T b 0,8, TO ero c r e n e H b npuaannexHOCTN K Kn.accy o q e i t b c m a p b l x ntoded e c T b 0,64.Hpyrofi npo: CTO# V U M e p :
U=1+2+3+4+5
-
-
o u e n b W e f f b M a / l e i r b l ~ u l i = 1/1
+ 0,412 + 0,113.
x = oreub ice m n o , I - I a n p ~ ~ ~ ecnu ep,
(CM.
puc. 2)
(3.6)
U
(3.10)
(3.11)
TeJrbHO n p O C ~ 0 f i3 a ~ a ~ e fCOBepIIJeHHO i, C X O A H O ~C~ 3 a ~ a Y e f iBbIs u c J I e H u R 3HaYeHUR ~ ~ J I ~ B C K O I B ' OM p a X e H U R . B KaqeCTBe np0C T O ~ u n n I o c T p a u u N p a c c M o T p a M B b I s u c n e a u e 3~ase~ui-i coCTaBHOrO T e p M U H a
~ ~ M ~ T U YTO M ,
He ouelzb morlzo = 1(ouelzb moulzo) = 1( m o v l z ~ )(3.1 ~ 4)
rAe
x = tie orelzb manenbtcudi, n e p ~ u s u ~ Ti ei p M u H ~anelzbtculiO n p e A e a e H
(4.1 ) KaK
1a/tt?lzb~~d = 1\11 $0,812 $0,6/3 + 0,414 + 0,215 (4.2) C 06JIacTbm paccyme~~fi U=1+2+3+4+5. (4.3) B ~ ~ A C T(3.8) B H IIpUMeHeHUe ~ 0 n e p a ~ ~O 2W H b K MHOXeCTBY iUa&?lzbtc~dA a e T ouelzb mnelzb~usi= 111 + 0,6412 + 0,3613 0,1614 0,0415 (4.4) N, YqHTbIBaR (2.26), IIOJIyqaeM ue ouelzb manelzbrcuG = 1(oclelzb manelzbtcudi) = = 0,3612 + 0,64/3 0,8414 + 0,9615 0,412 + 0,613 0,814 115. (4.5) B KaqeCTBe HWKOJIbKO donee CJIOlKHOrO n p U M e p a P a C -
+
BCJ'I~ACTBH~(3.15) U AeCTBO
(3.16) MbI
nnmc nnmc x
UMeeM ~ P U ~ ~ I U ~ E I T ~T JO IX~- H O ~
= mulzyc
olcelzb
X.
(3.17)
-
+
-
+
+
+
CMOTPUM C O C T ~ B H O ~TePMUH ~ 13
ebiculedi cmenelzu = ~ u l z y colcelzb ouelzb, e sbiclued cmenelzu = n n m n n m ouelzb.
(3.18) (3.19)
oueub ~&eubtcu~i u He oueub 6onbluo1Z. B TOM cnyqae oueub 60/2buoZi= (6onb~10G)~ = = 0,0411 0,1612 0,3613 0,6414 115 owlzb OYeub 6onbluoG = ( 6 0 n b w l i ~ ) ~ 0,113 + 0,414 + 115 . h..menb owlzb60nbfuod 111 1/2+ 0,9/3+0,6/1 x
= tie
+
- -
IV. BblYMCnEHME 3HAqEHMFf IIMHrBMCTMLIECKOFl IlEPEMEHHOFl
E c n ~MbI
3HaeM, K a K BbIYUCJIRTb 3 H a q e H U e COCTaBHOrO TepMUH a BUAa hu, BMqHCJleHUe 3Ha¶eHUR 60~1eeCJlOXHOrO COCTaBHOrO T e P h l P H a , K O T O P ~ IM ~O ~ X W BKJIIOqaTb TePMUHbI He, UAU, U B AOnOdlHeHUe K TePMUHaM BUAa hu, CTaHOBUTCR CPaBHN-
24
-
+
+
+
+
+
(4.7)
(4.8) (4.9) (4.10)
cnedoeamenbiro, o w fie OUelzb M A ~ N ~ K 'U ~H e O W7 Hb 6) 0 ~ b ~ d = (0,412 0,613 0,814 1/51n (111 112 0,913 (4.11) + 0,614) 0,412 0,613 0,614. ~ H ~ ¶ ~ H ~U UR H ~ B H ~ T H ~ ~~ C~ K P ~O M~ ~~ H H O0 6A 0, 3 ~ a q e ~ ~ o i i ~xdcmtw,A ~ I ~~ TP H M ~AP P Y ~ Op o A a . B 3TOM c ~ ~ y q aMU e n p e A n o n a r a e M , %TO 06nac~bp a c c y ~ ~ q e ~ ecrb uii U,
+
-
+
+
+
+
+
+
re
U
3JIeMeHTbI npefiCTaBJIRlOT BepORTHOCTH. n p e A n o ~ r o m U M , ~ITO~ bXOTUM l B ~ I ~ U C J I U3T ~ ~ a ~ e ~ n e
rAe
x = 8 s w w d cmeneuu tie noxoxe, (4.13) s eucu(eG cmeneuu onpeneneuo K a K '(cM. (3.18)) s s b l c u r e d cmeneuu =muu yc o v e u b o w u b (4.14)
T~XHHK KOTOPYIO ~, MM WCIIOJIb3QBaJIW AJIR BMqWCJieHHR 3 H a q e I i W 6 COCTaBHOI'O TepMWHa, eCTb s a ~ ~ ~c b n y~ q aff ii 6 O J I e e 06uero nO&XOfia, ~ o ~ o p bOfIWCaH ~ f i B [4 H [5 P ~ C C M ~ ~ T P W B ~ @ M M ~IIOAXOfi MOXHO IIPHMeHRTb K BbIVHCJIeHUIO ~ H ~ ¶ ~ H H B J I U H ~ B I ~ C T H ~ W KnOe~ p ~ e ~ e ~ ~ oIIpU f i , YCJIOBAW, q T 0 COCTaBHHe TePMHHM, IlpenCTaBJIRIOlUUe X U 3 H a q e H H R , MOrYT 6 b l ~ breH(?PNPOBaHbI J I U I ~ I ~ H H O KOHTeKCTa ~~ ~ ~ ~ M M ~ T U K O &K . asCfBe U J I J I K I C T p a ~ U PaCCMoTpUM JIuHI'BUCTIlYeCKyIO H e p e M e H H y H X, s ~ a s e ~~mopoil u~ n p e A c T a s n e H N c n u c K o M : ~ e u w u d ,ue Y a ~ e t i b ~ ~ t 6. iO, A b ~ u , d , Ne 6 0 ~ b ~ t . iOWHb , M O X e f l b K ~ 8 , Ize W U b & a / l e ~ b K ~ d ,~ e f t b UAU ~ ~ Ned W t l b OWHb 60nbtuoG, MCUeNbK U U~ (60~bUU)t.i i&lU H e Y c u t e ~ b K u G ) , OiieHb OWUb Y O X e l t b K ~ d u ue W N ~ w u b 6 0 ~ b m du T. A. P a c c ~ a ~ p u s a e3 ~H ~ a see H w M o r y r G H T ~ reaepnpoeisar J I u I I I ~ H H o ~KOHTeKCTa ~ ~ P ~ M M ~ T U 6 K O=~ ~ S, P), B K O T O P O ~MHOXeCTBO ~ KOHesHbIX CJIOB BKJIIOqaeT 3JIeMeHT a p H b I e TePMUHbI N U l e ~ b ~ U f i60dbUU)d, , He, U, U R a - O W H b Ii 'J'. &.; Ha! OKOHqaTeJIbHbIe CJIOBa ~ ~ O ~ H ~ Y ~S,W A, T CB, R C, E; p E 4 y J I b T U p y I O U a R CUCTeMa WMeeT BNA
1
I.
B
VT
w e u b oveub
tie noxoxe = (ue noxo~~ce)~ *
a~1/0+1/0,1+1/0,2+0,4/03+0,2/0,4.
s sucused cmeneuu ue noxoxe = muuyc
ouenb
(VT, vN,
D,
(4.18)
S-tA
C-tD
B-tC
D -+ M J ~ ~ N E +6 0 n b ~ t . i
ouenb ne no-
CJ'IeAyC!T 3aMeTBTb, qTf) IIpU BM¶HCJIeHWU 3 H a W H H R COCTaBHOrO T e p M u H a B n p e A m y w x npmepax MH ucnonmoaanw 0 6 ~ s HbIe n p a U J I a IIpeAmeCTBOBaHWR, A ~ ~ ~ c T B Y I O UnH pW ~ npw6pa~ O B ~ H H6Uy n e ~ c ~ u s ~xp a x e H u f i C . ~ o 6 a a n e ~H aeeo n~p e a e J r e H ~ O c ~ e f 3TW i n e a B W J I a npeAIIIeCTBOBaHkfR MOXHO BblPaBUTb CJIeAyIolUUM o6pa30~:
B-ti~e
c
C
~ K U ~
(S). Kaw~oe npasuno sisona 3
B (4.20) nopoxaae-r o T H o r u e H u e M e m y HeqeTKWMU MHOXWTBBMU, 0 6 0 3 ~ a 9 e ~ ~ b I COOTBeThf~ CTBeHHO TePMBHajIbHhIM W HeTePMHHaJIbHbIM CUMBOJI~MW. C a y sae (4.20) r r n oTHorueHwR T a K o B u (MU O n y c K a e M npaanna BblBOAa, KOTOPbie H e OKa3bIBaH)T BJIHRHU R H a COOTBeTCTBYIOLUWe MHOXC~CTB~):
B
S+S u/lu A * S L = S R + A R A+A u B*AL=ARnBR
B TOM CMbICJIe, ¶TO BbICKa3bIBaHIIR A 3 B (A BJIe¶eT B) II A \;lB(rie A UAU B) HMeIOT IIAeHTUsHbIe ~ a 6 J I H l i b UCTUHHOCTH. l
1
H U X H HIIHAeKCpi ~ L
H
R
U C n O J I b 3 y I o T c R 3 A e C b AJIR TOrO, g~06b1
pasnusa~b CHMBOJI~I, C T o R L q u e B ne~ofi u npa~ofi Y a c T R x . Y~06b1BbI¶HCJIHTb 3 H a q e H H R COCTaBHOrO T e p M U H a X, H e 0 6 x 0 ~ ~n p~O B0e C T H C H H T ~ K C H Y ~ C K Ha H~a~J I U 3 X B T e p M H H a X 0 I I p e ~ e ~ r e ~ I'PaMMaTAKH ~ofi G. T o r ~ a ,3 H a R CHHTaKCH¶eCKOe A e p e B O X , M O X H O IICIIOdIb30BaTb COOTHOIUeHUR (4.21) AJlR BbIBOAa CUCTeMM y p a B H e H I I f i (B ~peyr0JIb~0fi @ p ~ e ) , PeIIIeHMeM KOTOPOB RBJIReTCR 3 H a W H H e X . H a n p u ~ e pB, C J l y W l e , K O r A a C O C T ~ B H OT~e~P M H H
TO
eCJIU 6 0 ~ b t U 0 l i , T O r A a AlCUbl2i, W J I H Cic0Ab3KUd,
T O r A a 0nGZHblb;
OHM RBJIRKTCR COKPaLqeHHRMU ~ p e ~ J I 0 X e ~ U f i l
ecnw x - ~ O J I ~ I U O T~ o~r,A a y - ~ a n ~ f i , ecna A o p o r a C K O ~ ~ ~ KT ~o rRA,a e s ~ aonmria.
B CYlIlHOCTU, I l p e A J I O X e H H R W O r 0 B H A a OnHCbIBaIoT OTHOIUeHUH M e X A Y ABYMR HeOnpeAeJIeHHbIMU IIepeMeHHbIMH. 30 03HasaeT, TO H e o n p e A e a e H H o e B ~ I C K ~ ~ M B c~ nHe AHy ~e T c K o p e e OnpeAeJlRTb K a K H e s e T K O e OTHOIUeHHe B CMbICJIe (2.19), a H e K a K CBR3KY B CMbICJIe ' (5.1). 3 ~ e c b uenecoo6pa3~0 onpenenmb c ~ a s a n a dempmoso
cornacymca c (4.11).
B O ~ M O X H O C T ~OnpeAeJIRTb CMbICJI 3 H a ¶ e H U f i , n p U H H M a e M b I X J I I I H ~ B U C T M ~ ~ C K IOI~e~ p e ~ e ~ ~ o f H i ,~ O ~ X O A U M HJIR ~ aHaJIU3a H e s e T K H X B ~ I c K ~ ~ ~BIH B A a ~((ecJrH H u ~A~ T O r A a Bw, H a n p H M e p , <(eCJIU X H e O W H b iuCUbl6, T O r A a l j O W H b O W H b 6onbluoli)). 0 6 TOM r o B o p m c R B C n e A y m u e M pasnene.
-
60JIee o~LUNM, Ba)KHMM B H a I U e M ITOAXOAe RBJIReTcrR ~0npedefieHHoe ~ b ~ c ~ a 3 b ~ K e ae c~ mu eA , m r A a Bw, K O P ~ K O A 3 B, B KOTOPOM A ( ~ H T ~ U ~ A ~ U H TB ) ( K O H C ~ K B ~ H T) He¶eTKHe M H o x e c T B a , a H e n p o n o 3 u q ~ o ~ a ~ r b ~ bn1e pe e M e H H b I e . BOT TNnH¶HbIe IIPIlMePbI TaKHX B ~ I C K ~ ~ ~ I B ~ H U ~ ~ :
-
n p o u 3 6 e d e ~ f U ? A B y X H e s e T K H X MHOXeCTB. ~ Y C A T ~ He'IeTKOe IlOAMHOXeCTBO 06nac.r~P a C C y X A e H H R U n y C T b B - HePeTKOe IlOAMHOXeCTBO ~pyrofi,~ o o 6 u erOBOP R, O ~ J I ~ C T PHa C C y X A e H u c l V. T o r ~ aA e K a p T o B o n p o ~ 3 s e ~ A e ~M ~B, e 0603~asaeMoe A B, o n p e n e n n e T c s l c n e A y m L q u M o6pa30~:
u
x
V. HEYETKME YCJlOBHblE IlPEAJlOXEHMA M COCTABHOE IlPABMnO BblBOAA
r e U x V o 3 ~ a s a e A~e K a p T o B o n p o u s ~ e ~ e ~Hsees e T K u x MHOXWTB U H V, T. e.:
-
~ ~ M W U Mq ,T 0 K O r A a d H B H e H e s e T K H e , (5.2) npeo6pasoB b I s a e T C R B 06b19~0eO n p e A e J I e H H e A e K a p T O B a FIpOU3BeAeHHR MHOXeCTB. M H ~ I M HCJIOBIMH, (5.2) OLlHaqaeT, ¶TO A X B HerIeTKOe MHOXeCTBO YnOPRAO¶eHHbIX nap (u,o), 24 (I CO C T e n e H b H ) ITpUHaAJIeXHOCTH (u, V) II ( A X B), 3 a a B a e P d o f i @ p ~ y J I o f i PA (u) pB (v). B 3TOM CMbICJe A X B e C T b He¶eTKOe OTHOIlIeHUe U K
E
v,
6U,
A
V.
Ecna BblCKa3HEaHHe U W J I H A, TOrLla BB paCCMaTpHBaTb mcKmL3bleaHHe cresnu A , Torna 8 , mase CB c Heonpew neeam C, mrna noJryumR pa~nus~haemiTegnpeTawH TOM) npeftJIomeHHa B sasucu~oc~w OT n p e m o x e ~ ~ fm i ~oCK~WWKO C. B qacTHocTu, ecnH M ~ Inpennoqomtn, sn, C t.. V, Torfta uecnu A, Torna B (snu A *B)P nepexonmrT B Kate
ecna A, TorAa B, maue
c
A
=
A x B ' + ( l AX.^), (5.9)
.
L7
Boo6qe, ecnu A . ., A, - HeqeTKue no,qMHoxecTsa U, B1, , . ., Bn - HWeTKUe IIOnMHOXeCTBa H 3 V, TOrAa ecnu A,, TorAa B,, uaaue, emu A,, TorAa B, A
. ..
+
wiase, ecau A,, TorAa 8,=A, x B, A,x Ba+ *.. A,xB,. (5.10) ~ ~ M ~ T TO H I(5.10) V I , nepexofiw B (5.9), ecna n p w o w w a e CeCJlW A TOrAa B, UHaW CB NHTepnpeTHpOBBTb KaK a H X H A, TorAa B, mrase ecnu 7A, TorAa CB.Cne~ywTame OTM~THTL, sT0, IIPHMeHRR (5.9) IIOBTOPHO, MM JlOJIYWiM
+
+
ecnu A, Torna (ecnil B, Toraa C, mase D) Lmase E = A X B X C + A X ~ B X D + ~ A X(6.11) E,
ecnH A, Torna B, ,mase C = (emn A, Torna B) n (5.1 4) n ( ~ W Hi A, m r ~ ac), KOTOpW AJIR He'IeTKUX MHOXC?CTB A, B EI C CnpaBeflJIHBU nHWb I I ~ u ~ J I H X ~ H H%O 3 . RIBOpHT 0 TOM, rIT0 B COOTBeTCTBHH C (5.15) OIIpeAWHHR BbICKa3MBaHHR UeCJIH A, TOrAa B, HHaqe Ch) H e m s A, m a BB c noMoqfrm (5.9) H (5.12) He COBC~M nonX O AJIR ~ HeqeTKHX A, B H C. CJIenyeT TaKXeOTMeTHTb, qT0 y H 3) A 3 B CnpaBeAJIUBbI AJIR ~ C f i H 1) U = V, 2) X Bcex ~ J I ~ M ~ H T OU, B mma u3 (5.12) HMeeM, TO
KOHKPeTHO, THnHYHaR npo6~1e~a, C ~ O T O p o f i CTaJIKUBaKXCR npu pa3pa6oT~eT a m x a n r o p w T M o B , COCTONT B cne~yro~tte~, M M ~ ~ T c ,He¶eTKOe R OTHOIlIeHNe, C K a X e M , : U -+ V, KOTOpOe OnpeaeJrReTCR HerIeTKAMH BbICKa3bIBaHHRMA. npo6Jre~a COCTONT B TOM, 9 ~ 0 AJIR 6 ~ JI1060r0 HeYeTKOrO IIOAMHOXeCTBa X f U OnpeneJINTb HeYeTKOe l I O ~ M H O X e C T B 0Y V, KOTOPOe X NHAyUHpyeT B V. H a n p u ~ e p ,lIyCTb MMeWrCR CJleAYIOLUUe A B a npeAaoxeHuR :
R
6
1) x - oilem wan~u', 2) eCJIH X - &$ MUJblu',
TOrAa
y - 60/lb~10u',
NHarIe
y
tie o w ~ b6 0 n b ~ l o d i , ~3 KOTOPIJX B T o p o e onpenenxw c o r n a c H o
(5.9) H e o n p e A e n e H H o e OTHOUeHlle R. B O ~ H H K BOnpOC: ~ ~ T KaKOBa 6 y ~ mBeJIUsNH a y, &JIN X OrIeHb M ~ J I ?& B ~ TH a 3TOT BOnpOC AaeTCR CJleAyIoU A M nPaBAJIOM BbIBOAa, KOTOPOe MOIKHO P a C C M a T p A B a T b K a K 0 6 0 6 u e ~ ~N e~ B ~ C T H O n~pOa B I f J I a modus ponens. c o c m ~ o enpasuno s b ~ o d a : e c n A - HeonpeAeneHHoe OTHOUeHHe ++ V A X - HeOnpeAeJIeHHOe nO,U,MHOXeCTBO U, T o r A a H e o n p e A e n e H H o e n o A M H o x e c T B o y c V, K o T o p o e AHAYUNpyeTCR nOAMHOXeCTBOM X, AaeTCR K O M ~ O ~ A U(CM. A ~ ~(2.22)) ~ A X, T. e.
U
R
R
Y = [0,36 0,4 0,6 0,811 (5.19) C ~ e n a e H~e c K o n b K o s a ~ e s a ~ ~OTHOCHT~JI~HO fi (5.16). B o - ~ ~ P B ~CJIeAyeT IX, OTMeTATb, YTO KOrAa R = A B a X = A , MbI nOJIyqElM y = Ao(A+B) = B, (5.20) YTO CTPOrO BMnOJIHReTCB, KOrAa A, B N C - 0 6 b 1 ~ ~ b 1 e MHOX e C T B a , H ~ ~ H ~ J I A x ~ H HKOrAa o, A , B N C - H e s e T K K e MHOXe-
CTBa. MM~HHO B 3TOM CMbICJIe COCTaBHOe n p a B N J I 0 BbIBOAa M O X HO PaCCMaTpRBaTb K a K n p k i 6 ~ 1 A X e 0 ~ ~6 ~0 e6 u e ~ n~p e a B H A a modus P O n e n S ( ~ ~ M ~ T K YTO M , BCJIeACTBNe TOrO, KaKIlM o6pa30~ A 3 B o n p e A e J r e H o B (5.1&),rIeM 6 0 a b m e x crmusawcn OT A , TeM M e H e e ~ ~ T Ko nOp e A e n e H y). Bo-BTOPIJX,B b I P a X e H N e (5.16) aHaJIC$rNYHO ~ a p r t i ~ a J I b ~ 0 f i BePORTHoCTH B TepMllHaX (PYHKUHHY C J I O B H O ~BePORTHOCTU, ~ T.e.
(5.21) rAe
9s = B ~ { P X-xi} r j = Bep { Y = y,]
-
X
N
P f j Bep {Y = yjlX = x,}, Y - c n y s a f i ~ ~n eep e M e H H b r e co ~ H ~ Y ~ H N R xl, M N x2,
...
li Y1, Yz, 0 3 H a Y a e T , rIT0
me .ua/rMu' N 6 0 n b u o u ' OnpeAeJIeHhI no (4.2) M (4.7) COOTB~TCTBeHHO. T o r ~ anOACTaBJlRR , B (5.9) ~ a f l b l dBMeCTO A, 6 0 ~ 6 ~ 1 0 6 BMeCTO B H N e OW3fb ~ O R ~ U CBMeCTO O ~ MbI nOJIYqAM MaTp ~ u yOTHOW~HMR R A J I ~ H e o n p e A e n e H H o r o B ~ I C K ~ ~ I J B ~ H U ~ ((eCJIll Ma/rblli, TOrAa ~ O R ~ U L O ~HHaYe ', IZe OWN6 6 0 . f l b ~ ~ ) b . P e 3 y J I b ~ aKOMnO3HuHN ~ R C X = O W 6 &Ulbllf: eCTb
C,
.. .
COOTBeTCTBeHHO. OAH~KO 3 T a aHaJI0rUR H e (5.16) e C T b OTHOIlIeHAe M e X A y BepORTHOCTRMH. B - T P ~ T ~ MCJIeAyeT X, OTMeTUTb, YTO H3-3a HCnOJIb30BaHHR MaKCHMNHHOrO npOH3BeAeHAR M a T p H q . B (5.16) OTHOlueHHe MeH
R
R
33
PaHee,
HeS€!TKHe BblCKi%lblBaHHH H r P W OCHOBHYiO POJIb B OnUCaHHU W p e a J I U 3 a u U He¶eTKUX aJIrODUTMOB. 06 3TOM n o f i p l m pesb B c n e A y l o u e M p a s A e a e .
VI. HEYETKME AJlfOPMTMbl
Hanpumep, ecnu x - w w d mu cpea~ua,u R = A 3 B 0 3 ~ a s a eecnu ~ x H e YM u tte 6 0 n b t u o l i , TOrAa y - w t i b Yadblli, TO MOXHO
nUCaTb:
o
nwtbul) =
(rce wanwb u rce
6 o ~ b w o i b o w r c bma~ud)
unu cped~ud(He mmwd u rce ~ O A ~ U L O ~ J O W ? Hm~ a d ) . b c n ~ ~ sea ~e e s a ~ u es :a m o O C O ~ H ~ B ~m T ~ B, n p a K T U 9eCKUX npUMeHeHURX HeseTKUX B M C K ~ ~ M B ~ AJIB H H ~ OIIUCI~ HUSI CJIOXHUX NJIH nnoxo o n p e A u e H H b t x O T H O I J ~ ~ H H B ~M~~ I ~ C JIeHurr (5.91, (5.10) U (5.16) ~ Y A Y T ,B a d B U e N B O P R , BbInOJIH e m B 60nbuoii CTenLtHu I ~ P H ~ J I U ~ -~BH o aH e eOTOM, . AononH U T ~ J I ~ HUCTOgHBK ~I~~ HeT04HM3TU CBSI3aH C n p e ~ h a ~ n e He9eTKOI'O MHOXeCTBa KaK 3HaYeHUH JIWH~BEICTB~~WKOR nepe~ e H 4 5 0 f i . ~ ~ ~ ~ ~ ~ o J I oHX a nU p UM M e, p , lIT0 OTHOtlreHHe M e X A y HeseTKUMU IIepeMeHHbIMU X U lj O t I U C M B a W l I HeOnpeAeJIeHHUM B b f C & a s m a H u e M awns Manbffi, m r A a bonbruoi& mase, e c n f i c p e a z l u l i , T o r A a cpedtiu21, U H a s e , ecna bo/lbllcoti, T o r A a o w b ~mafi&. 0 6 ~ 4 MM ~ 0n p u n u c m a e M n e p e ~ e ~ ~xopf ai 3 n u s ~ s enuarBUCTUWCKUe 3 H a W H H R U. BbI'fUCJIReM COOTBeTCTBYIOIIlUe 3 H a 9 e HHR y, ucnonb3y~(5.16). T o r ~ a n, p u 6 J I u x a f I 3 ~ a s e ~ unepek M ~ H H O JIUHrBHCTUrIeCKUMU ~ ~ CWMBOJIIMU, MbI IIPNXOAAM K
cne~ymwefi ~a6nuye:
A
I3 ,
m~n&
cpcanud 60nbutd
.
BMBOA
&AH0
-
X
d o d b ~ d ~e m d W H ~ marlMa cpea~ud W H b JULtbLd OWHb p l e H b
-u He W e H b 60~bUOfi
~~e~
rpy60 rOBOPR, H ~ W K U ~aJIMPUTM eCTb YnOPRAO'IeHHOe MHOXeCTBO HeseTKUX U H C T ~ ~ K U U B KOTOPbIe , IIpU UX peaJIH3aUUH nawr npu6rruxe~~oe D e w e H u e n p o 6 n e ~ ~B. ~ o i iunu u ~ o i i @ p ~ eH e Y m A e aJIrOpUTMU IIgUCYTCTgYroT BO MHOrHX Y@UIHX PaCCMOTpeHURX. T ~ K MbI , UCnOJIb3YeM H e g e T K U e aJIWPHTM6I C03HaTeJIbHO UJIU ~ W C O ~ H ~ T ~ ~KOrAa ~ H O ,UAeM ffeWKOM, BOAUM MILUNHY, U U e M npeAMeT, 3aBR3MBaeM y3en, FOTOBUM oben, N m e M HOMep B T~JI€!@HHo~ K H W e U T. A. E0JIee T O N , no C y U e C T B y , 3TU aJlrOPUTMM IIIUPOKO UCnOJIb3)WTCR B np0rpltMMHPOBaHWU, UCCneAOBaHHH ~ I I e p a U ~ f i nCUXOJIOI'UU, , Hay K e y n p a B J I e H U H U M ~ A U U U H C K O ~AUarHWTUKe. ~ ~OHRTUR HQseTKOrO MHOXeCTBa U, B YBCTHOCTU, HeqeTKOrO BhU3Ka3biBaHUR CO3AaeT 6asuc AJIR HCnOJIb3OBaHHR HeUeTKHX aJIrOPUTMOB 6 0 J I e e CUCTeMaTUseCKUM U, CJreAOBaTejrbHO, 6onee ~ H T H B H M Motipaso~,s e M STO 6mo BO~MOXHO pasee. T ~ K , HeqeTKHe aJIrOpMTMM MOrYT CTaTb BaXHbIM UHCTPYMeHTOhA AJIR ~~PH~JIHHS~HU aHaJIU3a O~O CUCTeM U npOUeCCOB nPHHRTHII peUIeHU8, KOTOPble CJIUIIIKOM C W X H W &JIR npHMeHeHUR 0 6 ~ s ~ 0 f i M ~ T ~ M ~ T H ~ TeXHHKH. ~ C K O ~ ~ Q > ~ ~ M ~ JXapaKTepUCTHKy I ~ H ~ w IIOHRTUR HeYeTKOfO aJIr0PUTMa MOXHO A a T b C nOMOwbK) IIOHRTUR Ht?¶eTKHX MaIIIMH T b i o p U ~ r aHJIU H€?WTKOI'O MaPKOBCKOI'O aJITOpHTMa 16 1- 18 I. B TOM pasame r n a B H a R ymb oBeyme~uaCOCTOUT B TOM, Y T Q ~ MCBR3aTb IIOHRTUe HeqLTKOI'O a J I M p N T M a C nOHffTURMU, BBeAeHHbIMU B npeAMAYUUX pa3AeJIaX, U llpOUJIJIK>cTpUpOBaTb nPWTbIMU n p U M e p a M U HeKOTQpMe npHMeHeHUR TaKHX a J I r 0 P UTMOB M H C T ~ ~ K U UBU HeYeTKUX aJIrOpUTMaX MOXHO pa3AeJIHTb Ha ~ p K unacca: 1) Hamawo4ue n p e d ~ o x e w ~H, a n p u M e p ,
I He W H b 6 0 ~ b U l d p l e ~ bw e n b 6 0 ~ b t u o d W e H b OqeHb d 0 n w t 0 d hi& UAU cpedHulS
x w 5 = ,uamli x = 60AbuloGi x = 6 0 ~ X
b ~ Ul itit? oqefib ~ a l i 2) Hewmrcue 861cKaau3aHux, H a n p u M e p , aecqu x - wanwli, T o r n a y - 6 o n b t ~ 0 f i , 60JIb~ofi8,
uHaqe
y - He
-
WJIH X I ' I O J I O X H T ~ J I ~ H ~TI O ~ r~A, a YMeHbIIIHTb Y ile3HaI1Uml?/lbHOB, 6(eCJIH X Mi1020 6 0 / l b ~5, TOrAa CTOnB, <WJIH X OWHb Maflbla, TOrAa UATM K 7)). ~ ~ M ~ T H9TO M , B TaKHX IIPeAJIOXeHHRX a U 6 0 l l p e ~ ~ y YJIeH O T H O I I I ~ H A ~nu60 ~, I I ~ ~ A I I I w T B ~ I O I ~ JHI H~ 6~0, 06a MOrJ'T 6 b I ~ bCHMBOJIaMU He9eTKHX MHOXeCTB. 3) B e 3 y c n m ~ b l e a r c m u s i l b l e npedno%ce~u%, H a n p u M e p , YMHOXHTb X H a X YMeHbIIIHTb X CAeZKa C T e p e T b HeCKORbKO n e p B b I X IIORBUBIIIHXCR eAHHHQ HATH K 7 nerIaTb x CTOn OTMWMM,9TO HeKOTOPbIe U 3 3THX IIHCTPYKUH~~ RBJIRKlTCR HeYeTKRMH, a HeKcYrOpbIe - H W . K O M ~ M H M P O B ~ Ha3HaYaIOLUee T~ A HeqeTKOe BbICKa3blBaHHR HYXHO B COOTBeTCTBHH C KOMnO~HUUOHHbIM npaBHJIOM (5.16). HanpFi~ep,eCJIU B H ~ K O T O P ~MOMeHT I~~ BbInOJIHeHUR He9eTKOrO anropuma M ~ IB c T p e g a e M M H C T ~ ~ K U H U 1) x = O W H ~u a / l e ~ b r c u C 2) (ecnu x u a n e n b ~ u l i , T o r g a y 60nbwoa, m a Y e y H e OWHb ~ O R ~ ~ U O & > , r A e ~ a n e ~ b r c u ZHi 6 0 n b w o C o n p e A e n R r o T c R c o r n a c H o (4.2) N (4.7), TOrAa pe3YJlbTaTOM BbIIlOJIHeHHR M H C T P Y K U M ~1) ~ H 2) 6 y n e ~s ~ a s e ~ y, s eA a H H o e c o r n a c H o (5.19), T. e.
-
.
~ ~ f i
TO p e 3 y J I b T a T BbInOnHeHHR AOJIXeH 6mb eAHHCTBeHHbIhi 9HCn o M B H H T e p B a n e M e m y 3 11 8. Ha ~ a ~ oO cf Hio B e ~ b r 6 a p a e ~ c ~ T a K O e ~HcJIo? K ~ K y K a 3 a H O B I6 1, Pa3YMHO AOnYCTHTb, YTO pe3yJlbTaTOM BbInOJIHeHHR 6 y ~ 3JIeMeHT e ~ HeYeTKOrO MHOXeCTBa, E i ~ e I 0 U H f iH a H B b I C I U ~CTeIIeHb npHHaAJIeXHOCTH 3 T m y MHOXWTBY. ECJIH~ a ~ 03fleMeHT fi H e enHHCTBeH, K a K B (6.5), T O r A a MOXHO CAeJIaTb ~ J I y s a f i ~ b I fMJIH i n ~ 0 ~ 3 ~ 0 J I b ~ ~bbI1f 6i 0 p CpeAH 3JIeMeHTOB, HMeIOmHX HIHBMCLUYH) C T e n e H b IIpHHaAJIeXHOCTH MHOXeCTBY. MOXHO T a K X e BBeCTH H ~ K H~ p~H ~ e p U f i , COrJIaCHO KoTOPOMY J I H H ~ ~ ~ Y HnoO P ~ O Y M B a I O T C R3JIeMeHTbI HeW T K O r O MHOXeCTBa, HMemIIJ,He HaHBbICIUyIo C T e n e H b IIpUHliAJIeXHOCTH 3TOMy MHOXeCTBY, H, TaKHM o6pa30~,0 6 p a 3 y e ~ c R ~ A N H C T B ~ H H ~~aIH~6~0 J I b L t I H f i 3JIeMeHT. Hanpa~ep, B cnysae (6.5), eCJIH BBeCTH K P U T ~ P I I ~MHHHMH3aQHH ~ 4HCJIa LUarOB, TO H 3 BCeX 3JIeMeHTOB C ~ a k f ~ b I ~ I U CTeneHbIO efi npHHaAJIeXHOCTU MHOXeCTBY 6 y ~ m~ b 1 6 p a ~ H0 a H M e H b I l r e e YHCnO 5. A ~ a J I o r H q ~ b I BOnpOC fi B 0 3 H H K a e T B CBTYaQHU, K O r n a KCI I b I ~ y e ~ b AOJIXeH ~fi oTBeTHTb ((AaP HJIH ((HeTP H a . ~ e 9 e ~ ~ BOllfi npoc H a n p H ~ e p , npe~nono%u~, YTO ~ c n b I T y e ~ onpenno~y x e H a IIHCTP YKQHR
.
-
y = 0,3611
+ 0,412 + 0,6413 + 0,814 + 115.
(6.1)
B K O T O P O ~&an0 ~ o n p e A e n n e T c R no (4.2). T e n e p b npwnonoxm, YTO x = 3, n p u Y e M TO sacno u M e e T c T e n e H b n p u H a n J r e x H o CTH MHOXeCTBY MCUbLd, P a B H y I O 0,6. ~ o J I x ~ H JIH 9eJIOBeK BbInOJIHUTb KCTOIIB HJIH UHATH H a h? Mu ~ Y A ~AOnyCKaTb, M YTO B ~ O A O ~ H ~CHTYIQHRX IX 9eJIOBeK CAeJIaeT ~ b 1 6 0 p ((60JIee H C T A H H ~ I ~ ~H B a, l l p H M e p , ((X l)taROP IIpeAnOYTHTeJrbHee UX H e MCUO)), T a K K a K B H ~ I & M C J I y Y a e C T e n e H b HCTHHHOCTU n p e A n o x e H m g3 M~JIOB pama 0,6, YTO 60~1bmeCTeneHH HCTHHHOCTH YTBepXAeHHR ((3 H e MGXO)). Ecnu 06e aJIbTepHaTUBbI u M e m donee s n H M e H e e p a B H b I e ~ H ~ Y ~ HHCTHHHOCTH, H R ~1,160~ M O X e T 6 b l ~ bCAeJIaH npOU3BOJIbHO. Y A O ~ C T B hlbI ~ 6 y ~ H a 3 b I B a T b 3TO l I p a B H J I 0 ~bI60paO A H O ~U~ 3 AByX aJrbTepHaTHB npasuno~n x l e o 6 n a a a t o w C m b m e v i z a m u s b l . O W H ~B a X H O IIOHRTb, 9TO TOJIbKO 'lTO PaCCMOTPeHHbIe BOnPOCbI B03HIPKaIOT JlHLUb B TCX CHTYaUNRX, B KOTOPbIX T ~ ~ ~ J ~ TmC 0R 6, ~ P e 3 Y B b T a T l3bInOJIHeHHR H ~ ~ ~ T K MHCTPYKo R QHH RBJIRJICR eAHHCTBeHHbIM 3neMeHTOM ( ~ a n p ~ ~ YucJIoM), ep, a H e HeqeTKHM MHOXeCTBOh!. T ~ K U 06pa30~, M ecnu pa3peILIa€!TCfl, 4~06bfp e 3 y J I b T a T BbInOJIHeHMR (6.6) HeYeTKUM, T O r A a AJIR X = 3 MbI nOJIYYUM He9eTKOe MHOXWTBO BHAa O,~/CTOII f ~ , ~ / u & T uK 7,
-
-
-
AJIR
B a x ~ oOTMeTHTb,
YTO K a K B (6.1), T a K H B (6.4) Pe3YJIbTaTOM BbInOJIHeHAR HHCTPYKUHU RBJIReTCR H e 9 e T K O e MHOXeCTBO, a H e f?,QHHCTBeHHOe qHCJI0. O A H ~ KKOrAa O 9eJIOBeK A a e T H e 9 e T KyIO HHCTPYKUHIO, TaKyIO, K a K ((CAeJIaTb HeCKORbicO IUarOBP, rne Hecrconbuo o n p e f i e n e a o TaK:
e ~
omasam, m
Kmpoe
onepaquH
A o n m U BH~O~HHTT~CR ~ ~ ~ ~ J I J I ~ J HI eUm~H M o ~ npUCYTCTBye'l' 0 COCTaBHOM IIpaBHJIt? BbIBOAa H Hrpal?T =HOBHYiO POJIb B IlOHHMaHBW IleYeTKHX BdlrOpWMOB B HX BHIICUtHeHHR JIIOAbMH H MaIIIHHaMU. Aaaee MH n o K a x e M H ~ C K O J I ~ K On p w e p o B H e g e T K u x anwPUTMoB B CBeTe K O H U ~ I I ~ HPaCCMOTPeHHbIX ~~, B IjPefiMJlyI4HX naparpaaax. C n e ~ y ne o~n x e p r c H y T b , YTO mu n p a M e p w unnmCTPHP)a(YF J I U U b OCHWHble aCIIeKTH HeWTKNX 8JIrOPUTMOB u H e A e M o H c r p u p y I o T HX -KTUBHOCT~ B p e m e H u u nparcTs~ ~ C K Hnpo&ne~. X HeseT~ue WIrOpNTMbI ~ ~ 0 6K J~I ~0~ C C U @ H ~ COOTU~OB~T~ BeTCTBeHHO o ~ J I ~ c T R M NX IIpNMeHeHUR: WIrOPHTMU Onp,l@JIeMUR U UA~HTH$BKBIJ.UN; ~ U X ~ B N O P B C T U ~ ~ C K 8flIWPHTMbl; H@ a n r o p u T m np UHRTNR p e m e ~ fi. n ( G e ~ y wO T M ~ T U T ~ , r ~ ~ o aJIlVpUTM OIIpeAeJreHHOrO T u n a MOWeT BKJriOWTb B ce6a aJXr0PHTMH A p Y r N X THIIOB K I K IIOAaJII'OpBTMbl, H a n p ~ w p ,anr0PUTM OnpeAejIeHHR MOXeT B K J I I O ' ~ ~ TB ~ c e 6 ~IIOAaJII'OPHTMbl OTHorUeHUR U nPHHRTUR ~ ~ U ~ H U RMU . ) HaqHeM C I I p H M e p a a n r o p n T M a onpeAeJIeHaR.
napannenbao. Aonylue~ue T a K o r o
O A H H~3
OCHOBHMX 06JIaCTefi IIPUMeHeHUR HeYf?TKUX #!U(rOPUTMOB o n p e A e n m w e C ~ O X H ~ I X nnom , o n p e a e f i e n w x nna HeYeTKHX I I o H R T U ~ ~B TepMUHaX %flee IlpOCTMX HJIH MeHee HelIeTKUX ~ O H R T W BOT ~ ~ . nPElMk?PH TaKHX HeqeTKBX ~ O H R T H ~ ~ : x a p a K T e p r J n o s e p K a ; M e p H CJIOXHOCTH; M e p b I ~ O X Q X ~ H ; HWffpeAeJIeHHbIe 60JIe3~ii(IPTPHT, ~ P T ~ P H O C K J I & P ~N~ ) T. 4. ~ O C K O J I ~ KHeYeTKOe Y IIOHHTHe MOXHO PaCCMaTPUBaTb KaK CWMBOJI HeYeTKOrO MHOXeCTBa, i t e ~ m r ~a/ppUm& u~ QfZpf2&A~H#E RBJIRWCR B A ~ ~ ~ C T B W T W ~ H O KOHeYHbIM CTN MHOXWTBOM B03MOXHO HeYeTKHX HHCTPYKUH~~,KOTOPbIe O I I P W R I O T He. W T K O e MHOXeCTBO B TePMUHaX APYrHX HWeTKHX MHOX€?CTB H O )A a w F (u, B03MOXH0, CaMOrO C&R, T. e. ~ ~ K ~ ~ C H B UJIH npouenypy A n s B H s u c n e H u R c T e n e H u ~ ~ U H ~ A J I ~ X H O C KT WUA o r o s n e M e H T a O ~ J I ~ C T Hpaccyxae~uiio n p e m s e M o M y MHCB nOcneAHeM cnysae a n r o p u T M onpeAeneutisr urpam ponb ampurnma udeurnu@wyuu, T. e. a n r o p H T M a , KOTOPM~~ J'CTaHaBJIUBaeT, IlPHHaAJIeXUT UnU HeT 3JIeMeHT MHOXeCTBY, HJIH, donee e e ; - YCTaHaBJIHBaeT er0 CTeIIeHb IIpHHWXJIeNHOCTU. l l p u ~ e p T a K o r o a n r o p u T M a A a e T c s npouenypofi (CM. 15 I) B m n c n e H u R c T e n e H u n p u H a A n e m m T u pana ( n p e ~ -
-
XWLTBY.
J I O X ~ H U H ) B HeYeTKOM R3bIKe, IIQPOlKJ(eHH0M A N L ~ ~ ~ H K BW O -~ TeKcTa r p a k l ~ a T H ~ 0 f i . B KatIeCTBe OYeHb IIpOCTorO I I p U M e p a HeWTKOrO W Q p H T M a O n W W I e H U R PaCCMeTpUM HeWTKOt? IlOHRTUe W. BHOB~ c n e a y e T n o m e p K H y T b , YTO ceepxnpwme o n p w e a e H H e nplrrB e A e a o H w x e numb A ~ Ru n n r o c T p a y H H u H e n p e T e H A y e T urr ToYH4E OIIpeAeJIeHUe IIOHRTUR 06U.4. ~ & ~ C T P Y K ~ H H COCTBBJIRIQ, wue anropum OBAJI, 3qecb n e p e s u c J r e H M . CHMBOJIT B s ~ u x H H C T P ~ K L W ~ 06031iasae~ X u c c n e n y e ~ b ~ 0f 6i ' b e K ~ . Tepmu~61HrntWIb1ff u t n m b s y m f i o6parueuarr K n o a a r r r o p u T a s y ~btm KfibItf, KQTOP& iIpeAHa3H51YeH AJIR O n P W d l B H R , 5 i s n R e q - i nu T B ~ ~ K R Huna M HW. MHCTPYKWK)BHAR WJIH A, TO BI CAeAyeT UHTepIIpeTUpOBaTb, KaK at!CJIH A, TQ B, a H a s e n e p e i i ~K~ c n e ~ y ~ ~ uUeHf Ci T ~ ~ K U H U I .
ma
AJI~OPHTMCTBAJl:
1) W n U T H e 3aMKHyT0, TO T H e W; CTOII. 2) ecan T ca~onepece-iica, TO T H e o a p ~ ;m n . 3) ecnw T H e BbInYKJIO, TO T H e m;CTOII. 4) WJIA T He H M ABYX ~ &nee ktnw MeHee o p T o r o H a n b H w x oceB cu~~iSTpm, TO T ge own; c T o n . 5) ecnu donbrrra~O C ~T H e RBJIII~TCR ropa3~0bee n n u H H O ~ , W M MeHbILlaR OCb, TO W ; CTOn.
6 T -O d-pumu
T
H e OBa/l; C T m .
B ~ I ~ ~ Y K J I B~ IOCHOBHOM R: m noAanrnPHTM BKJXIOqaeT B ~ e 6 RnPOBePKY T O N , COXpaHReT J'IU KptiB v 3 H a 3 H a K I l p H &BUXeHUU BAOJIb T B n e p B O H a W M b H 0 BH~ ~ ~ H H HaIIpWAeHHH. O M 1) x = a ( ~ e ~ o ~ Ho aps aan b~H a R Tosmta T). 2) ~ b 1 6 p a ~Hba i l PaBJIeHMe ABUXeHNR BAOJIb T. 3) t ..r H a n p a B n e x u e ~aca-renbHofi K T B x. 4) X' = X 1 ( A B H X ~ H U ~ U 3 X B COCeAHmK) TOYKY). 5) t' H a n p a s n e H u e ~ a c a ~ e n b ~Ko iT i B xr. 6 ) awyron my t1 H t. 7) x
-- +
--
xr.
H a n p a m e H u e ~ a c a w b ~ oKf i T B X . 9) x' x +l. 10) t' w H a n p a a n e H w e ~ a c a ~ e ~ r bK~ oTk B x'. 11) fi yrm ~ e m q y ti w t. 12) eWH $ H e UMeeT T ~ K OXe~ 3HaK, YTO H a, TO T
8) 1
-
He 8trUlYMIIO; BO3BpaT. 13) e C n U X' a, T o 6bMYICllO; B03BPaT. 14) nepeRTu K 7). I f p ~C n e ~n y e T. OTM~TUTL, TO n e p B H e T ~ HHCTPYKH LLUH B a n r O p H T M e OBAJI o n p e A e n e H H u e . rIn, we K a c a e r c x
.-
T
KOMaHA 4) 11 5), TO OHA BKJIIOqalOT O l l p e A e J I e H U R T a K H X nOHRK a K a6o~teeUJIH fieflet? O p T O r O H a J I b H b D H 3Na%UfTleRbiu, A J I H H H W , KOTOpbIe XOTR U RBJlRlOTCR H e s e T K H M U , B C e Xe MeH e e CJIOXHM u 6onee ~ O H R T H M , q e M n o H m e man.% HJIJM)C T p H p y e T OCHOBHYH) (PYHK~UIOHeYeTKHX aJIM)PHTMOB O n p e AeJreHUR, a UMeHHO, C B e A e H U e HOBbIX HJIH CJIOXHbIX HeYeTKUX I I O H R T W ~ ~K 60~1een P o C T b I M UJIU 60JIee nOHRTHbIM HeYeTKHM IIOHFITUHM. B 6 0 J I e e p a 3 p a 6 0 T a ~ ~ B0a ~p H a H T e a J r r O p U T M a OBAJI OTBeTaMH H a 4) H 5) MOrJIH 6b1 6 b l ~ bC T e n e H H BbInOJIHeHUH Y c J I o B H ~ ~ B 3TUX UHCTPYKUEIRX. K o H ~ Y H ~ I Mp e 3 y J I b T a T O M a J I r 0 p H T M a T O r A a 6 ~ n a6bl C T e n e H b IIpUHllAJIeXHOCTH HeYeTKOMy M H O X W T B Y OBaJIOB. B 3~0fiCBR3H CJIeAOBaJIO 6b1 OTMeTHTb, YTO B CHJIY (5.15) ZUIrOpFiTM OBAJI, K a K yCTaHOBJIeH0, n p k i 6 J I H 3 U ~ e J I b ~ 3KBEI0 BaJIeHTeH BbIPaXeHKH)
TUG,
T
man = sanz~tiymatln tie ca~onepecetcatoquZicRn s b ~ n y r c n b l d n donee unu v e H e e o p m o z o i l a n b t i b l e mu cunznzempuu (6.7) n 6 o n b l u a x O C ~~ u a ~ m e n b uanuwuee o mu, KOTOpOe O n p e A e J I R e T H e s e T K O e MHOXeCTBO 08UR K ~ IKI e p e C e Y e H U e 0 6 b 1 4 ~ b 1U~ HeYeTKUX MHOXeCTB, CUMBOJIH KOTOPbIX CTORT B n p a ~ 0 f i W C T H (6.7). O A H ~ KOAHO O CYIILeCTBeHHOe o T n k i w e C ~ C T O H TB TOM, TO WOT a n r o p m M H e T O J I ~ K O onpeA e J I R e T I I p a B y I O W C T b (6.7), HO T a K X e YCTaHaBJIHBaeT n o p H &OK, B KOTOPOM C J i e A y e T COBepIUUTb 3 T U Bbl9HCJIeHUR.
K ~ BUAHO K
U 3 H a 3 B a H U R , H e 4 e T K U e a3IrOPUTMbI n O p O X A e H U R C J I y X a T A J I S n O p O X A e H U R , a H e AJIR O n p e A e J r e H H R HeYeTKUX MHOX~CTB. B O ~ M O X H n pHH ~ J I o X e H U R 3THX aJIrOgUTMOB: IlOJrym H a e o6pa3vo~nosepea H A p y r o r o p o A a obpa340~;pesenw IIpllrOTOBJIeHHR IIUUki; COYHHeHHe MY3bIKH, n p e ~ J I 0 X e ~ H k B eCTeCTBeHHOM R3bIKe, p e 9 H . B K a s e C T B e n p O C ~ 0 f iH J I J I l o c T p a Q H U aJIrOpHTMOB ITOpOXAeHUB p a c c M o T p a M H a n H c a H H e ~ Y K B MP, r A e ' s b I c o T a h H WHOs a m e b n p e A c T a B n r r m co6ofi n a p a M e T p M a n r o p H T M a . nPOCTOTbI P 6 y BOCnpOH3BOAMTbCR ~ ~ KPK ~ Y H K T N P H ~ I ~ ~ o6paseu C BOCeMbH) TOYKaMH n0 ~ e p T E i ~ a J I b ~ JIUHHH. 0fi A J I ~ o ~ u T M P (h, b): 1) i = I . 2) (i) = b ( n e p ~ a f i T O q K a H a OCHOBIHUH).
X
K
5) Ecnu 57. 6) 7) 8)
i'=
7, m0
CAeJIaTb IlOBOpOT B n p a B O U
I l e p e f i ~ ~ Kl 3). ~ P O A B N H Y T ~ C RH a ~ O B ~ P H YHTa ~ 45';
nepefi~~
h/6;
IIOCTaBHTb TOYKY. IlPOABElHYTbCR Ha hl6: KIOCTaBUTb
TOYKY.
9) To x e c a M o e . 10) To x e c a M o e . 11) To x e c a M o e ; c T o n . TO a J I r O p U T M p a 3 0 M K H Y T O r O T H n a B TOM CMbICJIe, YTO OH H e C O A e p X U T o 6 p a ~ ~ o iCBR3U. i 4 ~ 0 6 ~C A1e J I a T b er0 M e H e e qYBCTBNTeJIbHbIM K O I U H ~ K ~ MB, 0 3 H U K a I O U A M n p U er0 BbIIIOJIHeHUU, MOXHO 6b1~06b1 BBeCTW HeYeTKyIO O ~ ~ ~ T H YCHB R) 3 b I I y T e M BBeAeHUX YCJIOBUR OKOHYaHUR BbIIIOJIHeHUR aJIrOpElTMa npll 60JIee HJIU M e H e e y ~ O B J I e T B O p U T e J I b H O M BMIIOJIHeHUU s a ~ a s ~H. a n p ~ ~ e pecm , n o c n e A H F i r r T o s K a H a mare 11) H e IIOIIaAaeT H a Bep\TUKaJIbHyIO W C T b MOXHO BePHYTbCR K LLIary 8) U YMeHbLUBTb UJIM Y B e J I U W T b YrOJI n O B O p O T a H a marax 8)-1 I), q~06b1U C I I p a B U T b OKOHqaTeJIbHYH) o I I I M ~ K Y . ki3noxe~ue P e u e n T a U3rOTOBJIeHNFI IIIOKOJlaAHbIX KOH* B pa6o~e [ 19 1 A a e T X O ~ O I I I UI I~p U M e p TDrO, YTO n p e A C T a B J I R e T co6oii B A ~ ~ ~ C T B H T ~ J I ~ H O ~C Te H9 e ~ ~ Ea iJ IfriO p H T M n O p O X A e H U R C O ~ P ~ T HCBR3bIO. O ~
P,
Hetlemicue Hewmrcutl
onucamenbmle
u 6uxesuopucmurecrcue
anzopumwbl
o n u c a m e n b m t i anzopumfi c n y x w T A J ~ R o n M c a H m OTHOrUeHNR UJIH O T H O L U ~ H HM~e~X A Y HeYeTKMMU n e p e M e H H b I M U . n0~06~blfi a J I r O p H T M , l l c n o J I b 3 y e ~ b 1 f i AJIR ~ ~ H ~ J I H X ~ H H O ~ O OlIllCaHHR nOB€!AeHkiR CHCTeMbI, ~ Y A ~H aT3 b I B a T b C R N e W M K U Y
6uxesuopucmuw~1~u~ anzopumnzow. Huwe ITpkiBeAeH n p 0 ~ T O f i I I p U M e p
OnUCaTeJlbHOI'O a J I r 0 PUTMa, 0 6 0 3 ~ a Y e ~ ~ 0 r 0~ O T 0 p b 1 f iBKJIIOqaeT B c e 6 ~ TPN HapaM e T p a x, y, z. 3Tm a n r o p M T M onpenemeT H e s e T K o e T e p H a p H o e O T H O ~ ~ H HB~ O ~ J I ~ C TPUa C C Y X A e H U R = 1$2 3 f 4 f 5 C TePMUHaMM ~ a / l f ? t i b l C ~ d U ~ O R ~ U U )O~n ,p e A e J l e H HHMH (4.2) a (4.7).
R,
R
U
+ +
Amopum R (x, g, z): 1) e c J r H x m o H y eenurco, TO z o v e f i b m o , maqe z H e vano; 2) ecnn x senurn, TO (,,ecna g M a n o , TO z o v e u b eenurco, maqe z ~ a n o " ) m a q e z u y o q e r t b m a n b l .
f l p U ~ & 3 6 ~ 0 ~ U M o c l . 3HarleHUH u 3TUX ~ b I C ~ a 3 b U 3 a H U fMOXHO i B E J s u c n u T b c ~ O M O ~ A(5.9) O u (5.11). B TOM cnyqae WHOweaue 6 y y n e ~ n e p e c e s e H l r e M m~orue~uii, onpeAweHHHx HHCTPYKUUHMW 1) U 2). Apyrok n p u M e p H e s e T K o r o anr0pm.rhl.ao T H o m e H u r r F (x, y), ~ o ~ o pu n~n il oic T p u p y e T npyroii a c n e K T n o a o 6 ~ ~anropmx MOB, COCTOUT B C n e A y u m e M . A ~ z o p u m F (x, y): yem1) ecnw x M a n o a x c~a60y s e n u s w b , TO y 9HTCR. 2) t?CJIU X MfUO U X 3HaclUtTERbHO YBeJrUrlHTb, TO dl yI3eJrH9UTCR 3 ) E ~ U t n e R b H O . 3) emu x wnmo H x c n e r K a y e e n u c l u m b , TO y yB@JIH¶HTCP
R
cpedue. 4) ecna x MUICO u x Y B W I H ~ N T3~i c a r u m b i t 0 ,
TO y yemaW i t b 3HaYUt?WRbNO. H B n p e n u A m e M cnyrlae, s ~ a s e ~ n H eas e T K u x yc.rio~HHX , n p e ~ ~ ~ o ~ Be ~TOM u f i anropume MOXHO B ~ U C J I H T ~ , ~ c n o n a 3 yM~~ T O A ~wI3 pa3neno~IV u V, ecns AaHM o n p e A e n e HUH IIePBUqHbIX TepMUHOB 6~?Abu10d W MZMttbtC~d, a T a K X e HeqeTKHX TePMHHOB CRU60, 3HUclUllzeRbN0, Cpedile. K a s e c m e n p o c T o r o n p u M e p a 6 ~ x e ~ u o p u c ~ u r l e c anro~oro pwma n p e n n o n o x u M , m U M ~ CRu e T e M a S c ABYMR onpeEWX?HHbIMH COCTORHURMU (CM. [3 0 6 0 3 ~ a q e ~ ~ bgl I ~U Hg8, AByMX HeYeTKUMH BXII)AHbIMU BeJIHqUHaMH N U ~ K UH~ BWCOKUG ki A B ~ M R HerleTKHMW BbIXOnHbIMH BenNqWHaMU 6 o n b w i i U Af&WG. 0 6 I a c ~ b I C ) P a C C Y m @ H H H 3 H a q e ~ t i i BXOAa t H BblxoAa cIsnrreTcR neficmmenb~a~ ocb, I I p e a n a n o x ~Ranee, ~ WO nOBeAeMUe S Maw0 I I ~ H ~ J I H X ~ H H OX Oa p a K T e p H 3 O B a T b n p w s e n e H n u M H w w e a n r o p u T M o M . OAH~KO n n R O u t i c a H H x OTHOW H N R M e X A y BXOAOM, BblXOAOM U COCTORHHeM CUCTeMhI BMeCTO B ~ I C K ~ ~ ~ I MbI B ~ HCnOJIb3YeM H U ~ ~ 06~9~ ~861Iliky 0 nepeXOAOB. 9HTCII
K ~ K
Ha n e p ~ ~Bf~i ~ J I R KAa x e T C H , ~ITOma ~ a 6 n u OnpeAeJiReT ~a O ~ ~ I ~ H YAmepMHHHpOBaHHYIO K) CWCTeMY C KOHePHbIM q u c n o h l COCTORHW~~. OAH~KO B a X H O OTMeTWTb, 9TO B P a C C ~ a ~ p U ~ e M o f i CUCTeMe BXOAEJ N BbIXOAbI RBJISKYXH HWeTKHMU IIOAMHDXeCTsaMU ~ ~ ~ ~ C T B U T ~OCU. J I ~T H ~OK ~U ~ o(ipa30~, M MM MO~JIN' 6b1 IIOCTaBHTb BOnpOC: KaKOB 6 y . 4 ~ BblXOA CUCTeMbI S, KJXU OHa H a x o n u m a B COCTORHUW gl H BXOA ouetib m a d B cnyqae nan~ 0 f iCUCTeMM S H a 3TOT BOnpOC MOXHO OTBeTUTb, npUMeHHB comamoe npssuno Brasofla (5.16). C npyrok CTOPOHH, m . x e BOnpCX norepm 6~ CMEJCJI, eCJIN abb S 6b1~1a AeTepMUHHpOBaHHOB C H C T ~ M OC~ ~KOHeqHbIM 9HCJIOM COCTOBHU~~,OnUCbBaeMofi
n p e m ~ e i i~a6mueii.
Hcser~ufi
6 u x e ~ u o p a c ~ u s e c ~ au nf ir o p m ~~ o m No C ~ O J I ~ 3OBaTb AAR OnHCaHHR. U 60Jlee CJIOXHbIX nOBmWHfl, CBH3aHHblX C HaJIUqUeM c n y ~ a f i ~ b3JfeMeHTOB ~x B CHCTt?Me. Hanpti~ep,H a n u s w c ~ J I y r l a f i ~ b I 9JIeMeHTOB x B S MoI'Jro 6t1 A a T b C J i ~ y l o r u W e HeseTKOBePORTHOCTHbIe X ~ P ~ K T ~ P H & H K @e I~
WPM
nmwmurr:
B
I),
Anzopum IIOBEAEHMfl:
rAf?
& lJt Xt
- BXO& B MOMeHT t, - BblXOA B MOMeHT t,
- COCTOHHUe
B MOMeHT
f.
,
, ,
g tiepORmti0 g eeporrmtio g eeporrmno%g mano8epomnnoB
,
W&b YMOBePOfimNO eeporrmoa YMOOYetib mmb~ e p o x r n ~ d ~w p a ~ m ~ o ~
B 9 ~ 0 8T ~ ~ J I UTU~ P~M U H & p o s m f i o w ero M O ~ H @ ~ K ~ U H H W H ~ u MUO c n y x a T AJIR n p ~ & n m e ~ ~oon urcoa i i H H eepomHOCTHbIX XapaKTf?pUCTHK. Hanpu~ep,aecnu BXOA M U A TeKYCOCTORHHe eCTb gl,TO C J I e A y m e e COCTOSIHHe 6f?pORmHO 6ynm g,,. A ~ a n o r u s ~ aecnu o, BXOA &?AUK u T e K y m e e COCTORH H e eCTb g p , . T O W H b MUCMf?pOIUtlMO, qTO B b l X M 6 y ~ w eeAlU€. ECJIH3 ~ a q e ~ uTee p M u H a sepomm o n D e a e n e H o c r r e n y m w M 0 6 ~ 0 1 3 0 (CM. ~ (4.16)):
5) ECAU Bbl HaXOAHTeCb OWHb f?ZO OCTaHOBNTeCb; H e p e f i ~ H K 7).
6 ~ ~ 3 1K ~ n0e p K p e C T K y ,
6) n p o n o ~ ~ x a i iocleiib ~ e ~ e d ~ e f npu6nmambc~; t~o nepeii. 5). 7 ) Ecnu H a n e p e K p e c T K e H n H 8 6 1 ~ 3H ~e r o HeT M a w H H , rno npoe3xafi~e. 8) ~ O A O X A H T ~HeCKORbKO CeKyHA; n e p e f i ~ H K 7). B p ~ nJIH CJIeAyeT rOBOpMTb, 9TO p e a J I b ~ b 1 g BapMaHT 3TOrO a n r o p H T M a ~ M J I6b1 HaMHOrO CdIOXHee. B ~ X H ~BI M 3TOM n p H -
TH K
Hewmtcud mzopumfi npuHRmuR peuteicua - s o
~eseT~Hii a n r o p u T M , K O T O P M ~ CJIYXIIT ~ AJIR n o f i y q e H H R ~ P W ~ J I B X ~ H H O ~ O o n H c a H m c T p a T e r m u n H pemamuero npasma. O ~ ~ I ~ H M M U n p H M e p a M H TaKHX aJIrOpHTMOB, KOTOPbIe MbI HCllOJIb3yeM 6OJIbIIIefi 9 a C T b I o nOAC03HaTeJIbH0, RBJIRIoTCR aJIrOpHTMbI noCTaHOBKH aBTOMaLLlHHbI H a CTORHKe, n O K y n K H AOMa, nepec e s e H a R n e p e K p e c T K a a T. A. &R UJIJIIOCTP aIJ,HH TaKQrO aJIrOpHTMa PaCCMOTpH M A B a npOCTbIX n p H M e p a , B3RTbIX E13 nOBCeAHeBHOr0 OnbITa. l 7 p u ~ e p . l7epee3d nepeicpecmrca: ~ ~ 0 6p a 3~6 W0~ b pacc ~ a T p l l B a e ~ b 1 af Ji I r 0 p H T M H a HeCKOJIbKO llOAadIrOpHTMOB, K a X 143 KOTOP~IX n p u M e H m K o n p e A e n e H H o M y T u n y n e p e K p e c T KOB. ,QJIR HaUIHX ~eJIefiAOCTaTO9HO OnHCaTb TOJIbKO OAHH H 3 3THX nOAaJIrOPHTMOB, a HMeHHO, nOAaJIrOPHTM, KOTOP~IW ~ c n o n b 3 y e ~ cK~o r, A a H a n e p e K p e c T K e e c T b S H ~ KCTOII. H B k p y r ~ xnpmepax 3 ~ 0 r opas~eaa,MM c A e n a e M ~ R ynpoA uamwtix n p e ~ n o n o x e ~ ~9 b~, 0 C6o K~p a T H T b O n H c a H M e a f i r e PMTMa.
M e p e HBJIReTCR TO, 9TO ~ a ~ 0aJIrOpUTM fi MOr 6 b 1 6 b 1 ~ bnOCTpOeH aHaJIOrU9HO OIIHCaHHOMy yIIpOUeHHOMy B a p H a H T y . Eonee TOrO, BHAHO, 9TO T a ~ 0 f iH e 9 e T ~ H f i aJIrOpHTM MOr 6b1 CJIyXtfT'b BC~X@KTWBH~IMCPeACTBOM PaCnpOCTpitHeHNR OnbITa.
n~fi
K~K
Anzopumirr IIEPERPECTOS: e c n H e C T b C B ~ T O , @ O ~T, o 0 6 p a ~ H T b C RK aJIrOpHTEdy CBET W O P , H H a q e , e C n H eCTb 3 H a K CTOn, TO 0 6 ~ a T t i T b C RK a J I r O PMTMY 3HAK, N H a s e , e c n H e c T b ~ a r a m ~ uxa~b~ii ii CHrHaJI, TO O ~ ~ P ~ T E I T ~KC aJIrOpWTMY R MMTAJIKA, H H a v e 0 6 p a ~ H ~ b ~ R K a n r o p H T M y HEI(OHTPOJIMPYEMb1n.
1)
li'odan~opumu 3HAK: 1) Ecnu H e T s ~ a cccTonB ~ a H a sameii c T o p o a e , mo ecnu H ~ TM a m u H ~a n e p e K p e c T K e , mo n e p e c e K a T b H a ~ o p ~ b n o P CKOPOCTH, UHaW )KAaTb, n O K a aBTOMaiUHHbI H e OCBO~OARTnepeKPFTOK, H 3 a ~ e n e~ p e c e K a T b ero. 2) Ecnu B a a a B T o M a m H H a H e npu6nu3unacb K nepeepeCTKY, mO IIPOAOJIXaTb A B I l X e H H e C ~ 0 p ~ a J I b H 0 fCKOPOCTbK. i B T e q e H H e necmbtcux ceKyHA; n e p e i i ~K~ 2). 3) 3 a ~ d n u m bd s u ~ e ~ u e . 4 ) Ecnu BM O W H ~cnemme A H e BHAHO nonauebc~axMarum, k~ H ~ TM a m m H a n e p e K p e c T K e u n H tz06nu3ocm~OT H e r o , mo iuedne~tio npoesmaik-re n e p e K p e c T o K .
B K a s e c T s e n o c n e n H e r o npmepa p a c c M o T p w M a n r o p m M n p H H R T m p e r u e H m A n R n e p e B o A a cnenoro M c n b I T y e M o r o H I13 H ~ W J I ~ Hn03E19kIH O~~ Cmapm B K O H ~ ~ H ~ll03MLlUK) K) pnb (CM. PHC. 3) ( 0 9 e ~ bCJIOXHbIe q e T K I l e ~ J I I ' o P ~ T M ~TaKOrO I Tuna AJIR HCllOJIb3OBaHHR p 0 6 0 T a ~ W n p H M e H e H b 1 B Shakey p06OTe, IIOCTpOeHHOM r p y n I I 0 b M C K ~ C C T B ~ H H MO H ~TO ~ J I J I ~ K TB~ C T ~ H @PACKOM M C C J I ~ A O B ~ T ~ J I ~ C K OMHCTATYT~. M O n H ~ a H l i e 3TOlW po60Ta npHse.qeHo B pa6o~e1201). A n r o p F i T ~ , ~ a 3 ~ a H ~ b IOBSTACLE fi ( n p e n ~ ~ c ~ s ano e), IIpeAnOJIOXeHHlO EICnOJIb3YeTCR 9eJIOBeKOM-KOHTPOJIePOM K O T O P ~ IMOXeT ~~ H ~ ~ J I I o A ~ TK~a K , H BbIllOJIHReT eI'0 HHCTPYKUHa. 3 T a H e q e T K a R 0 6 p a ~ ~ a CBR3b R W r p a e T B a X H y I o POJIb B C03AaHHH BOSMOXHOCTM AJIR C H a n p a B H T b H K l+?AU He; CMOTpR H a HeqeTKoCTb U H C T P Y K I ~ M U ~ ~ H a O I I I H ~ K U WX BMnOJIHeHHR. A J I ~ P H T M COCTOUT k13 T p e X n0aanropu.rMOB ALIGN ( B ~ I P ~ B H U B ~ T HUG ~), (npHfiepxW~a~bcR)H STRAIGHT (npa~o). 3anasa a n r o p u T M a STRAIGHT n e p e B o & H CO C T a p T a B ~ ~ O M ~ X Y T OnYHKT ~ H ~ I1,~ 3~a T e M H 3
-
C,
OBSTACLE
n p e n m B H f f AO T e x nop, noxa H e o T K p o e T c a npsuo% nym K UWIH. BM~CTO OnHCaHUR 3TNX nOAaJII'OpUTMOB B TePMUHaX H e W2TKHX YCJIOBHbiX ' ~ o J I o x ~ H H ~ ~KaK , 3TO AeJIaJIOCb B npeAJ&QyU U X n p U M e p a X , y ~ 0 6 ~ eORUCaTb fi HX B BNAe ~JIOK-CXW, KaK n o ~ a 3 a ~Hoa puc. 4-6. B 6 n o ~ - c x e ~a ner o p u T M a ALIGN E 0 6 0 3 ~ a q a e To m a 6 ~ yBbIpaBHHBaHHSl, I4 MbI AJIX nPWTOTbI npeAlIOJrO%NM, q T 0 E H e MeHReT 3HaK. TepMHHaX HeWTKAX BHCK~~MB~H ~ JHI~o ~K - c x ~aM n r~o p m M a STRAIGHT, H a n p u M e p , IIepeBOAkiTCR B C J ' I ~ y I O l Q U e HHCTpyKSHH.
B
l 7 0 a w o p u m ~ STRAIGHT: 1) Ecnu H e 6 ~ ~ 3 1 mo ~ 0 ,c n e n a T b mar; n e p e i i ~K~1). 2) Ecnu H e o w ~ 6.0~3~0, b mo c n e n a T b ~ l a ~ b l mar; li nepefi~~ K 2). 3) ECM H e OWHb OWHb 6 . 0 ~ 3 ~ m0 0 , CAeJIaTb OWilb &a;llblfi war; n e p e i i ~ K~ 3). 4) Cmn.
VII. 3AKJlK)~MTEJlbHblE 3AMEqAHMFI
crapr
c r u a b mr
B WOM H n p e A m y u H x pame~laxn a ~ ~ ociTia T b U MM cnenanw I I O n b R K y p a 3 B A T b IIOAXOA K a H a J I H 3 y CNCTeM, KOTOPbfe H a CTOJILKO CJIOXHM HJIN nnoxo onpenme~br,s ~ Hoe n o m a m c R TOqHOMY KOJIHWCTBeHHOMy a H a J i H 3 y . I(oH~~H IIOJIyqeHHbIe o, HaMH p e 3 y n b T a T b I C n e A y e T P a C CMtYrPUBaTb ANLUb KaK I I e p ~ b i f in p 0 6 ~ b 1 f i U l a r B 9 M M H a n p a B JIWHU. ~ C H O ,rITO MHOrNe B M b I e U BTOPOCTeneHHbIe aCneKTbI H a r u e r o n o A x o A a paccMoTpeHar 3 ~ e c bH e n o c T a T a s H o n o n H o H J H BOBCe H e PaCCMOTPeHbI. CiOAa OTHOCRTCR BOnPOCbIO POJIN H ~ Y ~ T K0O6 p ~ a~ ~ ~ oCBR3U fi B p e a J l N 3 a ~ N H HeWTKHX aJfrOpNTMOB, peaJIU3aUHU HeWTKHX aJIrOPNTMOB B qeJIQBegeCKOM M 0 3 r e , B3aWMOCBR3U HeqeTKHX WHCTPYKUW~~,B QUeHKe $ ~ K T H B H ~ C T A HeWTKHX aJIrOPUTMOB, B IIpEiMt?HeHHN COCTaB~ o r onpamna BbIBoAa H n p a s u f i a npeo8n&amaefi anbrepHaTNBbl, a T a m e BO B3aHMOCBR3U HeOnpeA~JIeHHOCTH H B e PORTHoCTN B IiOBeAeHNH ryMaHHCTHqeCKUX C H m M . I(~K 6b1 TO HU 6 ~ ~O0I X W , C ~ H H M3 ~n e~C b MeTOA Aa>Ke B C y Q e c T s y m a e M ero COCTORHMH MOXHO +@~KTHBHO HCIIOJIL3 0 B a T b nJIR @PMYJIUPOB~HWR U IIPN~JIHx~HHoM) PeILleHHR
e-
Pnc. 6.
lloaa~~rop~~r anpsM0,.
c a m x p a 3 ~ 0 0 6 p a 3 ~n~p xa K T r i q e c K u x
s a ~ a s ,oco6eaao B T a KBX ~ ~ J I ~ C T R KaK X , 3KOHOMBKa, H a y K a 06 YllPaBJIeHHB, nCHXOJIOTHR, JIUHrBkICTHKa, ~ ~ H o o ~ ~ ~ ~H C oKB Y C~C TH B ~IH HI ~ ~ I~ , p a 3 y M , nOHCK k i ~ @ o p ~ a q B BMeAHUkiHa , H ~ H O J I O ~ H RB . 60JIbulefi CTeneHM 3TO OTHOCHTCR K TaKHM 3 a A a q a M B 3THX ~ ~ J I ~ c T R x , AJIFl KOTOpblX MOXHO H B ~ ~ T THHe q e T K I l e aJIrOpHTMb1, IIO3BOJIRIoW H e OnHCblBaTb IIJIOXO OIIpeAeJIeHHbIe ~ O H R T H H , OTHOIIIeHLlR w n p a B M n a n p s H R T m perue~afi.
JIUTEPATYPA 1. L. A. pp. 338-3s. 2. L. A. Inform. Sci., 3. k. A.
Z a d e h.
Fuzzy sets.- Inform. Contr., vol. 8, 1965,
Z a d e h.
Similarity relation and fuzzy ordering.vol. 3. 1971, pp. 177-200. Z a d e h. Towards a theory of fuzzy sy&ems.- B c6.: Aspects of Network and System Theory. N. Y., Holt, Rinehart and Winston, 1971. 4. L. A. Z a d e h. Quantitative fuzzv semantics.- Inform. Scl., vol. 3. 1971, pp. 159-176. 5. L. A. Z a d e h. Fuzzy Languages and their relations to human and machine intelligence.- B c6.: Proc. Conf. Man and Computer, 1970. 6. L. A. Z a d e h. Fuzzv. a1eorithms.- inform. Contr., vol. 12, 1968, pp. 94-102. 7. E. S a n t o s. Fuzzy Algorithms.- inform. Contr., vol. 17, 19, 1970, pp. 326-339. 8. L. A. Z a d e h. On fuzzy algorithms. Electron. Res. Lab., Univ. California, Berkeley, Memo. M-325, 1971. 9. S.-K. C h a n g. On the execution of fuzzy programs using finitestate machines.- IEEE Trans. Comput., vol. C-21. 1972, Mar., pp. 241-253. 10. S. S. L. C h a n g and L. A. Z a d e h. Fuzzy mapping and control.- IEEE Trans. Sust.. Man, Cybern., vol. SMC-2. 1962, Jan., pp. 30-34. 11. R. E. B e 1 1 m a n and L. A. Z a d e h. Decision-making in a fuzzy environment.- Management Sci., vol. 17. 1970. 12. J . A. G o g u e n. The logic of inexact concepts.- Syn., V O ~ . 19. 1969, pp. 325-373. 13. G. L a k o f f. Hedges: a study in meaning criteria and the logic of fuzzy concepts.-- Proc. 8 th Reg. Meet. Chicago Linguist. Soc., 1972 -. 14. L. A. Z a d e h. A system-theoretic view of behavior modification. Electron. Res. Lab., Univ. California, Berkeley, Mema. M-320, 1972.
-
I . L. A. Z a d e h. A fuzz -set-theoretic interpretation of hedges. El&tr%n Res. Lab., Univ. ~ a l i k i a .Berkeley. Memo. M-335, 1972. D e L u c a and S. T e r m i n i. A definition of mn16. probabil tic entropy in the setting of fuzzy sets theory.- Info)m. Contr., VOI. 20, l972, p . 301-412. T. e e. F u n y logic and resolution principle.- .J. Ass. h., vol. 19, 1972, pp. 109-119. H u g h e s and M. J. C r e s s w e 11, An Introductitm ic. London, Methuen. 1968. L e d 1 e y. Fortran IV Programming. New York, McGraw Hill. 1% - - ---, ----. 20. B. R a p h a e l , 5. D u d a , R.E. F i k e s , P . E . H a r t , N. N i l s o n , P.W.T h o r n d y k e and B.M. W i l b u r . Research and a plications - artificial intelligence Stanford Rps. Inst., Menlo Park, &if., Final Rep., 1971. Olt.
e.
!
