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Ïðåäëîæåíû íîâûå ïîäõîäû, àëãîðèòìû è èõ ïðîãðàììíàÿ ðåàëèçàöèÿ â îáëàñòè àâòîìàòè÷åñêîãî óïðàâëåíèÿ ñëîæíûìè ñèñòåìàìè, îðèãèíàëüíûå èíôîðìàöèîííûå òåõíîëîãèè â íàóêå, îáðàçîâàíèè, ìåäèöèíå. Äëÿ ïðåïîäàâàòåëåé óíèâåðñèòåòîâ, íàó÷íûõ ðàáîòíèêîâ, ñïåöèàëèñòîâ, àñïè- ðàíòîâ. Ó çá³ðíèêó íàâåäåíî ðåçóëüòàòè äîñë³äæåíü, ùî ñòîñóþòüñÿ êîìï ’ þòåðíî¿ ³íæåíåð³¿, óïðàâë³ííÿ, òåõí³÷íî¿ ä³àãíîñòèêè, àâòîìàòèçàö³¿ ïðîåêòóâàííÿ, îïòè- ì³çîâàíîãî âèêîðèñòàííÿ êîìï ’ þòåðíèõ ìåðåæ ³ ñòâîðåííÿ ³íòåëåêòóàëüíèõ åêñ- ïåðòíèõ ñèñòåì. Çàïðîïîíîâàíî íîâ³ ï³äõîäè, àëãîðèòìè òà ¿õ ïðîãðàìíà ðåàë³çà- ö³ÿ â îáëàñò³ àâòîìàòè÷íîãî óïðàâë³ííÿ ñêëàäíèìè ñèñòåìàìè, îðèã³íàëüí³ ³íôîð- ìàö³éí³ òåõíîëî㳿 â íàóö³, îñâ³ò³, ìåäèöèí³. Äëÿ âèêëàäà÷³â óí³âåðñèòåò³â, íàóêîâö³â, ôàõ³âö³â, àñï³ðàíò³â. Ðåäàêöèîííàÿ êîëëåãèÿ: Â.Â. Ñåìåíåö, ä-ð òåõí. íàóê, ïðîô. (ãë. ðåä.), Ì.Ô. Áîíäàðåíêî, ä-ð òåõí. íàóê, ïðîô., È.Ä. Ãîðáåíêî, ä-ð òåõí. íàóê, ïðîô., Å.Ï. Ïóòÿòèí, ä-ð òåõí. íàóê, ïðîô., Â.Ï. Òàðàñåíêî, ä-ð òåõí. íàóê, ïðîô., Ã.È. Çàãàðèé, ä-ð òåõí. íàóê, ïðîô., À.Øòåôàí, äîêòîð-èíæåíåð, Ã.Ô. Êðèâóëÿ, ä-ð òåõí. íàóê, ïðîô., Î.Ã. Ðóäåíêî, ä-ð òåõí. íàóê, ïðîô., Í.Â. Àëèïîâ, ä-ð òåõí. íàóê, ïðîô., Å.Â. Áîäÿíñêèé, ä-ð òåõí. íàóê, ïðîô., Ý.Ã. Ïåòðîâ, ä-ð òåõí. íàóê, ïðîô., Â.Ô. Øîñòàê, ä-ð òåõí. íàóê, ïðîô., Â.Ì. Ëåâûêèí, ä-ð òåõí. íàóê, ïðîô., Â.È. Õàõàíîâ, ä-ð òåõí. íàóê, ïðîô. (îòâ. ðåä.). Ñâèäåòåëüñòâî î ãîñóäàðñòâåííîé ðåãèñòðàöèè ïå÷àòíîãî ñðåäñòâà ìàññîâîé èíôîðìàöèè Ê ¹ 4619 îò 18.10.2000 ã. Àäðåñ ðåäàêöèîííîé êîëëåãèè: Óêðàèíà, 61166, Õàðüêîâ, ïðîñï. Ëåíèíà, 14, Õàðü- êîâñêèé íàöèîíàëüíûé óíèâåðñèòåò ðàäèîýëåêòðîíèêè, êîìí. 321, òåë. 40-93-26 © Õàðê³âñüêèé íàö³îíàëüíèé óí³âåðñèòåò ðàä³îåëåêòðîí³êè, 2001 }xoTU3.m͇Z0p#U  5U#@r /E->Wt(`+AL V$d);;s˰3;җ{ys31"Z#2""G"\+DՐUԏ✬|QJ/Z^+LΛu˛79UXdwNSKc&™l߲wVf=FS!q9"^GL79&F =eqpEzp_`'p sq~P8pv쎬 \.$K{㾺Os o53S8c` 5_Wq nuzj:G9N$Gy\w6evIJip'3p$.)M~~ ߄xKx;n L?wܴ 3 RI_Y Fhrwgyg3-=`q|K_Cg[g! ӆo? j%a4֨(V`u4fJ+T38ôLmN_> %:vF@tF>TKz{B!$[{k>^Z);[)-.W&A>ߝRߵ)]zqJbyJ PJn:gQOs̛tm*O)uҊHM!Mu*=rt7|f: P8V? ! h+ODVL}l=݆c|٫>r< |g;53OF}H0ON}tȞWb^Z?n2]˄m[vJLն7o,ⰳCϹFoka_9o(Kkﺠm.wU.z^y{k}ů$~z\u٥oǖƎ?^=rO%lԗ"D<5 ICOn1pǎ _-Wҥe)Ic}zpq^:/.Hu?O/M'kޤw]8nߨw5+mK[ڴ.mM9.nG TPNh~/;ǝ|}wMבJ+?Tc qG}ŝOk\Ô9>иIwqVa'u_z鵾1?/9fmk_ġG5o΍u>o{p|ެy;oyS߽#|Z \8>_#{ 4e6l#z?+8lG8Oھ),䘾~_o OE6wMu{IsÆF=pKvϻ⛲d +Z};ٳ ]l~Miz4[2/SRn^.IoKoOHl|nQ߮c--]v` Y p `zh@kaK1ӣ  vm\'Tuog5⛾Ѿg&pNѣo߁6M} ^'[_LrFD v[;Ьv;WRqĸk: /8SMKSwQGA>mE΀u~ieFO?FC3CIwsSy#jf~u7%3GKRkd]S`+u q'C_i˜(QV[SGGRN =,'Voz{ݼ1|NdaMlҴ>-m+|)b:tncKs>D\ܼWZZp{ A[pO\3Y_.~@i^ 0 ѳ?<.^|679׬_r_kry / x^gߦ$LNkgeFltg)A?}(qp8>s}MϦ{"]HCvҹrOF cDМ&q_y^{ k)z3OnE'=o,vO[ }@vfu;Dqb[@WE?Cnc~o7T<}oSfz ˗sGuѮ覕-=-e).S<8؆ssg܂^ VBk2 lC=PygG9Ch0ك%z t7s6m94|*4Ι<紾׫|=K{ownO'7Ƭ{i[MkuJ8Tⲏ7^vwy_փ݈@<]yV% V}ڧ- ڱy~_ AW.MG9WE[k6Qe'γPgF'=~7!NwQ7:l~_[J%Os$3"IwW! 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VK8|%>CͳN%wKGǷ;{֚HIJ{-+nG%A74 (K+gE1 4d|t |ڙV>ΡLIJbtCǴ5IKUSw\<{\йjYM Հ67\UIkR8k^*P{|-3O7~{C+x}dmR%l~S{2Hlgk_~x~RF`'ex9"tC&N{8^qGhSdl*L_'﴿ex?4 rexW-NjSXnoJiۤooޕ+E5'ƥڙ9[|P-3W5[Ob@%)Û{RkM=x6 /Ogod#;"_̗BO4.PN^zgB#z\#1r=.扗cCqC?W[ψ7QwȜ_9x4Kw^Иy+]r\u{^lZիϜFZk1gNzߘ/{r3hrR󧽥K#&%=04{V^aGWd2{G ]d ٽm>;) J\ҷ;,,4 ÓÄÊ 519.71 Å.È. ÊÓ×ÅÐÅÍÊÎ ÎÁ ÎÄÍÎÌ ÌÅÒÎÄÅ ÀÍÀËÈÇÀ ÂÇÀÈÌÎÄÅÉÑÒÂÓÞÙÈÕ ÏÐÎÖÅÑÑΠÍÀ ÍÅ×ÅÒÊÈÕ ÑÅÒÅÂÛÕ ÌÎÄÅËßÕ Ïðåäëàãàþòñÿ ïðèíöèïû ïîñòðîåíèÿ, àíàëèçà è ìîäåëèðîâàíèÿ äèíàìèêè âçàèìîäåéñòâóþùèõ ñóùåñòâåííî íå÷åòêèõ ïðîöåññîâ, ïðåäñòàâëåííûõ â âèäå îòíîøåíèÿ “ óñëîâèå-äåéñòâèå ” , â ïðîñòðàíñòâå ñîñòîÿíèé íå÷åòêîé ñåòåâîé ìîäåëè, ïîñòðîåííîé íà îñíîâå íå÷åòêèõ èíòåðïðåòèðîâàííûõ ñåòåé Ïåòðè. 1. Ââåäåíèå Ìîäåëèðîâàíèå, àíàëèç è ðåàëèçàöèÿ âçàèìîäåéñòâóþùèõ ïðîöåññîâ âêëþ÷à- þò â ñåáÿ ðåøåíèå ðÿäà ïðîáëåì: âûÿâëåíèå ñâîéñòâ àäåêâàòíîñòè ìîäåëè îïèñûâàåìûì ïðîöåññàì ðåàëüíûõ îáúåêòîâ; ñòðóêòóðíûõ è ïîâåäåí÷åñêèõ ñâîéñòâ ðåàëüíûõ îáúåêòîâ; ïðèíÿòèå ðåøåíèÿ î íåîáõîäèìîñòè è ïóòÿõ ìîäèôèêàöèè ìîäåëè è ïðîöåññîâ â ðåàëüíûõ îáúåêòàõ ñ öåëüþ îáåñïå÷èòü òðåáóåìûå ñâîé- ñòâà è ïîêàçàòåëè êà÷åñòâà îáúåêòà àíàëèçà. Ýôôåêòèâíûì àïïàðàòîì ðåøåíèÿ çàäà÷ ìîäåëèðîâàíèÿ è àíàëèçà âçàèìîäåé- ñòâóþùèõ íå÷åòêèõ ïðîöåññîâ ÿâëÿåòñÿ àïïàðàò ðàñøèðåííûõ èíòåðïðåòèðîâàí- íûõ íå÷åòêèõ ñåòåé Ïåòðè [1-4]. Èçâåñòíî íåñêîëüêî ìåòîäîâ àíàëèçà ñâîéñòâ îáúåêòîâ ìîäåëèðîâàíèÿ ñåòÿìè Ïåòðè [4]: ìåòîä, îñíîâàííûé íà ïîñòðîåíèè è àíàëèçå äåðåâà äîñòèæèìîñòè (ïîêðûòèÿ); ìåòîä Ñèôàêèña [5], îñíîâàí íà èñïîëü- çîâàíèè ýëåìåíòîâ ìàòåìàòè÷åñêîé ëîãèêè; ìåòîä, îñíîâàííûé íà ìàòðè÷íîì ïðåäñòàâëåíèè ñåòåé Ïåòðè â ïðîñòðàíñòâå ñîñòîÿíèé è àïïàðàòà ëèíåéíîé àë- ãåáðû; ìåòîä äåêîìïîçèöèè, îí ïîçâîëÿåò áîëåå óäîáíûì ñïîñîáîì èñïîëüçîâàòü äðóãèå ìåòîäû è ïîäõîäû, íîñèò ïðåèìóùåñòâåííî âñïîìîãàòåëüíûé õàðàêòåð. Ïîäõîäû, íàðÿäó ñ ðÿäîì äîñòîèíñòâ, èìåþò ñóùåñòâåííûå îãðàíè÷åíèÿ: îðèåíòèðîâàíû íà ðåøåíèå çàäà÷, êîòîðûå ïðåäïîëàãàþò, ÷òî âñå ïðîöåññû è èõ âçàèìîäåéñòâèå ÿâëÿþòñÿ ÷åòêèìè ïîíÿòèÿìè è ìîãóò áûòü îïèñàíû ÷åòêèìè ìíîæåñòâàìè è ÷åòêèìè (îáû÷íûìè) îòíîøåíèÿìè.  ðàáîòå ïðåäëàãàåòñÿ ìåòîä ìîäåëèðîâàíèÿ è àíàëèçà íå÷åòêèõ âçàèìîäåé- ñòâóþùèõ ïðîöåññîâ, îñíîâàííûé íà àíàëèçå äèíàìèêè ðàçâèòèÿ ïðîöåññîâ â ïðîñòðàíñòâå ñîñòîÿíèé íå÷åòêîé ñåòåâîé ìîäåëè. Ìåòîä îðèåíòèðîâàí íà åãî ðåàëèçàöèþ ñ èñïîëüçîâàíèåì ñîâðåìåííûõ êîìïüþòåðíûõ òåõíîëîãèé. 2. Ïîñòàíîâêà çàäà÷è Íå÷åòêàÿ ñåòåâàÿ ìîäåëü (ÍÑÌ) ) ( ~ f S ïðåäñòàâëåíà ìíîæåñòâîì ãðàôè÷åñêèõ îáðàçîâ íå÷åòêîé ðàñøèðåííîé èíòåðïðåòèðîâàííîé ñåòè Ïåòðè [1]. Îïðåäåëåíèå 1. 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Óòî÷íèì ïîíÿòèå íå÷åòêèõ äèíàìè÷åñêèõ îáúåêòîâ â ÍÑÌ. Îïðåäåëåíèå 2. Íå÷åòêèìè äèíàìè÷åñêèìè îáúåêòàìè (ÍÄÎ) 1 1 }, ) ( { 1 S s f DO s  áóäåì íàçûâàòü òàêèå âçàèìîäåéñòâóþùèå îáúåêòû ÍÑÌ, êîòîðûå ñîçäàþòñÿ â ïðîöåññå ìîäåëèðîâàíèÿ, õàðàêòåðèçóþòñÿ óñòîé÷èâîé ñòðóêòóðîé, ïî êðàéíåé ìåðå îäèí àòðèáóò ÿâëÿåòñÿ íå÷åòêèì, à ñîäåðæàíèå àòðèáóòîâ è ñâîéñòâ èçìåíÿåòñÿ ñîãëàñíî äèíàìèêå ðàçâèòèÿ ìîäåëèðóåìûõ ïðîöåññîâ. Òîãäà ñïðàâåäëèâî ñëåäóþùåå óòâåðæäåíèå. Óòâåðæäåíèå 1. Åñëè îïðåäåëåíà ÍÑÌ ) ( ~ f S , òîãäà ìíîæåñòâî ãðàôè÷åñêèõ îáðàçîâ ÍÑÌ ìîæåò áûòü ïðåäñòàâëåíî ìíîæåñòâîì íå÷åòêèõ äèíàìè÷åñêèõ îáúåêòîâ . }, ) ( { 1 1 1 S s f DO s  Ñëåäñòâèå óòâåðæäåíèÿ 1.  ñîîòâåòñòâèè ñ óòâåðæäåíèåì 1, ìíîæåñòâà T P ~ , ~ , èõ âçàèìîäåéñòâèå, êîòîðîå îïðåäåëåíî ôóíêöèåé ) ( ~ f F , ìíîæåñòâà ìàðêèðîâà- íèÿ ïîçèöèé P p j ~ ~  – )} ~ ( ~ { j p M , îïðåäåëÿþùèõ ìíîæåñòâà âåêòîðîâ ; }, ) ( ~ { 0 W w f M w  S s f M V v f M s k v l   }, ) ( ~ { ; }, ) ( ~ { , ãäå )} ( ~ { f M l – ïîäìíîæåñòâî ïðîìåæóòî÷íûõ âåêòîðîâ ìàðêèðîâàíèÿ ñåòè ) ( ~ f S ; )} ( ~ { f M k – ïîäìíîæåñòâî êîíå÷íûõ âåêòîðîâ ìàðêèðîâàíèÿ ñåòè ) ( ~ f S , ïðåäñòàâèì íå÷åòêèìè äèíàìè÷åñ- êèìè îáúåêòàìè S s f DO s  1 }, ) ( { 1 . ÍÅÎÁÕÎÄÈÌÎ: 1.Èñïîëüçóÿ ìîäåëü ) ( ~ f S , ïðåäñòàâëåííóþ ìíîæåñòâàìè, ðàçðàáîòàòü ïðèí- öèïû è ìåõàíèçìû ìîäåëèðîâàíèÿ è àíàëèçà äèíàìèêè âçàèìîäåéñòâèÿ è ðàçâè- òèÿ ïðîöåññîâ { П ~ i }, i  I â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ, ïîçâîëÿþùèõ ðåàëèçî- âàòü ñëåäóþùóþ ñõåìó: )} ( ~ { )} ( ~ { ) ( ~ { 0 f M f M f M k l   . (3) 2. Èñïîëüçóÿ ÍÑÌ ) ( ~ f S (2), ïðåäñòàâëåííóþ ìíîæåñòâàìè ÍÄÎ S s f DO s  1 }, ) ( { 1 , ðàçðàáîòàòü ïðèíöèïû è ìåõàíèçìû ìîäåëèðîâàíèÿ è àíàëèçà äèíàìèêè âçàèìîäåéñòâèÿ è ðàçâèòèÿ ïðîöåññîâ { П ~ i }, i  I â ïðîñòðàíñòâå ñîñòîÿ- íèé ÍÑÌ, ïîçâîëÿþùèõ ðåàëèçîâàòü îáðàòíóþ ïðîöåäóðó ìîäåëèðîâàíèÿ ïî ñëåäóþùåé ñõåìå: )} ( ~ { )} ( ~ { ) ( ~ { 0 f M f M f M l k   . (4) 3. 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Ìåòîä ðåàëèçîâàòü ñ èñïîëüçîâàíèåì ñîâðåìåííûõ èíôîðìàöèîííûõ òåõíî- ëîãèé. Ñëîæíîñòü ìåòîäà ïî êðèòåðèþ çàòðàò âû÷èñëèòåëüíûõ ðåñóðñîâ â åãî ðåàëèçàöèè äîëæíà áûòü íåçíà÷èòåëüíà ïðè ðåøåíèè êîìïëåêñà ïðèâåäåííûõ âûøå çàäà÷ íà ðåàëüíûõ îáúåêòàõ. 3. Ïðåäïîñûëêè è ïîäõîäû ê ðàçðàáîòêå ìåòîäà Ïîñòðîåíèå ÍÑÌ ñ èñïîëüçîâàíèåì íå÷åòêèõ ðàñøèðåííûõ èíòåðïðåòèðîâàí- íûõ ñåòåé Ïåòðè ñâÿçàíî ñî ñëåäóþùèì: 1. Ìîäåëèðóåìûå ïðîöåññû (ÿâëåíèÿ), ñîâåðøàþùèåñÿ ía îáúåêòå ìîäåëèðî- âàíèÿ è àíàëèçà, îïèñûâàþòñÿ ìíîæåñòâîì ñîáûòèé è óñëîâèé, êîòîðûìè ýòè ñîáûòèÿ îïðåäåëÿþòñÿ, à òàêæå ïðè÷èííî-ñëåäñòâåííûìè îòíîøåíèÿìè, óñòà- íàâëèâàåìûìè íà ìíîæåñòâå “ óñëîâèÿ-äåéñòâèÿ ” . 2. Îïðåäåëÿþòñÿ óñëîâèÿ-äåéñòâèÿ. Ïîñëåäîâàòåëüíîñòü èõ íàñòóïëåíèÿ óï- ðàâëÿåòñÿ â ïðîñòðàíñòâå ñîñòîÿíèÿ îáúåêòà àíàëèçà, êîòîðîå çàäàåòñÿ ìíîæå- ñòâîì óñëîâèé. Óñëîâèÿ ôîðìóëèðóþòñÿ â âèäå ïðåäèêàòîâ. 3. Óñëîâèÿ (ïðåäèêàòû) ìîãóò âûïîëíÿòüñÿ è íå âûïîëíÿòüñÿ. Òîëüêî âûïîë- íåíèå óñëîâèé îáåñïå÷èâàåò âîçìîæíîñòü íàñòóïëåíèÿ ñîáûòèé. Óñëîâèÿ, ñ ôàêòîì âûïîëíåíèÿ êîòîðûõ ñâÿçûâàåòñÿ âîçìîæíîñòü ðåàëèçàöèè ñîáûòèé, áóäåì íàçûâàòü “ in-óñëîâèÿìè ” . 4. Ïîñëå òîãî êàê ñîáûòèå íàñòóïèëî, áóäåò îáåñïå÷åíî âûïîëíåíèå äðóãèõ óñëîâèé, íàõîäÿùèõñÿ ñ in-óñëîâèÿìè è ðàññìàòðèâàåìûìè ñîáûòèÿìè â ïðè- ÷èííî-ñëåäñòâåííîé ñâÿçè. Ýòè óñëîâèÿ áóäåì íàçûâàòü “ out-óñëîâèÿìè ” . 5.  íå÷åòêèõ ñåòÿõ Ïåòðè ïðèíèìàåì ñëåäóþùóþ èíòåðïðåòàöèþ [1]: ìíîæå- ñòâî âõîäíûõ óñëîâèé (àíòåöåäåíòîâ) è âûõîäíûõ óñëîâèé (êîíñåêâåíòîâ) îïèñû- âàåòñÿ ìíîæåñòâîì ïîçèöèé J j p j  }, ~ { , à ìíîæåñòâî ñîáûòèé (äåéñòâèé) – ìíîæåñòâîì ïåðåõîäîâ I i t i  }, ~ { ; ïîñëåäîâàòåëüíîñòè ñîáûòèé îòîáðàæàþòñÿ ñðàáàòûâàíèåì ïåðåõîäîâ; âûïîëíåíèå êàêîãî-ëèáî óñëîâèÿ ñâÿçàíî ñ ïîÿâëåíè- åì ìåòêè 1 ) ~ ( ~  j p M â ñîîòâåòñòâóþùåé ýòîìó óñëîâèþ ïîçèöèè; ñîãëàøåíèÿ î ïðàâèëàõ ñðàáàòûâàíèÿ ïåðåõîäîâ ÿâëÿþòñÿ ñïîñîáîì âûðàæåíèÿ ïðè÷èííî- ñëåäñòâåííûõ ñâÿçåé ìåæäó óñëîâèÿìè è ñîáûòèÿìè â ñèñòåìå; òîëüêî ïîñëå âûïîëíåíèÿ in-óñëîâèé ìîãóò íàñòóïèòü ñîáûòèÿ; ìîìåíò ôàêòè÷åñêîé ðåàëèçà- öèè ñîáûòèÿ îáû÷íî íåèçâåñòåí, ïîñêîëüêó èíîãäà áûâàåò òðóäíî âîññòàíîâèòü ïîëíûå öåïè íåïîñðåäñòâåííûõ ïðè÷èí è ñëåäñòâèé, îïðåäåëÿþùèõ ôàêò è âðåìÿ íàñòóïëåíèÿ (èëè ïðîäîëæèòåëüíîñòü) ñîáûòèÿ, âûÿâëåíèÿ ñâîéñòâ ÷åòêî- ñòè è ò.ï.; ïîñëå òîãî êàê ñîáûòèå èìåëî ìåñòî, ðåàëèçóþòñÿ out-óñëîâèÿ, êîòîðûå, â ñâîþ î÷åðåäü, ÿâëÿþòñÿ in-óñëîâèÿìè íåêîòîðûõ äðóãèõ èíöèäåíò- íûõ ñîáûòèé è ò. ä. Ïðè ýòîì ïåðâîïðè÷èíû ìîãóò êàê èñ÷åçíóòü, òàê è ïðîäîëæàòü äåéñòâîâàòü. Ýòî ñâÿçàíî ñ òåì, ÷òî â ÍÑÌ èìååòñÿ ðåñóðñ ìåòîê èëè æå îáåñïå÷èâàåòñÿ èõ ðåãåíåðàöèÿ. 6. Äèíàìèêà ìîäåëèðîâàíèÿ íà ÍÑÌ ñâÿçàíà ñ ìåõàíèçìîì èçìåíåíèÿ ìàðêè- ðîâîê ïîçèöèé è ñîãëàøåíèÿìè î ïðàâèëàõ ñðàáàòûâàíèÿ ïåðåõîäîâ. 7. 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(6) 8. Ïðè îáðàòíîé ïðîöåäóðå (4) ñðàáàòûâàåò òîëüêî âîçáóæäåííûé ïåðåõîä, ò. å. òàêîé ïåðåõîä i t ~ , äëÿ êîòîðîãî ) 7 ( 0 ) ~ ( ~ | )} ( ~ { ~    j i j p M out p p (7) ÷òî ñïðàâåäëèâî, òàê êàê ïî îïðåäåëåíèþ ñïðàâåäëèâî (6). 9. Êðîìå èçëîæåííîãî âûøå (ï. 7, 8), òàêæå äîëæíû âûïîëíÿòüñÿ ñëåäóþùèå óñëîâèÿ: èìååò ìåñòî ñòðóêòóðíàÿ è ëîãè÷åñêàÿ àäåêâàòíîñòü âçàèìîäåéñòâèÿ ïðîöåññîâ       i П ~ ïðåäìåòíîé îáëàñòè, êîòîðàÿ ïðèâîäèò ê ðàçðåøåííîñòè è áåçêîíôëèêòíîñòè [4] ïåðåõîäîâ ~ ~ T t i  ; äîïóñòèìîå, èñõîäÿ èç ïðåäìåòíîé îáëàñ- òè, çíà÷åíèå íå÷åòêîñòè ïðîöåññîâ       i П ~ ,îïðåäåëÿþùåå ðàçðåøåííîñòü ïåðåõî- äîâ ~ ~ T t i  :                                   * 0 ~ 0 ~ ~ * 0 ~ 0 ~ ~ ~ )} ( ~ { k k in p p k k T t j p j p i j i t i t i     ; (8)                         * 0 0 0 0 * 0 0 0 0 ) k y k y k y k y k x k x k x k x ij ij ij ij ij ij ij ij         ; (9)     ), 1 ) ( ~ ( } { * 0 ~ 0 ~ ~ ~ ~ ~                      j j p j p j j p M k z k z p M p M (10) ãäå , ) ( ), ( * 0 ~ 0 ~ k k i i t t   , ) ( ), ( * 0 ~ 0 ~ k k i i t t               * 0 0 * 0 0 , 6 , k y k y k x k x ij ij ij ij ;     * 0 ~ 0 ~ , k z k z j p j p – çíà÷åíèå ñîîòâåòñòâåííî ôóíêöèé ïðèíàäëåæíîñòè è ìèíèìàëüíî äîïóñòèìûõ èõ çíà÷åíèé äëÿ ñîîòâåòñòâóþùèõ êîìïîíåíò ÍÑÌ; âûïîëíåíèå èñòèííîñòè íåêîòîðîãî ïðåäèêàòà L, îòîáðàæàþùåãî ñâîéñòâà ìíîæåñòâ ~ ~ , P T , ôóíêöèé   f F ~ è ïðîñòðàíñòâà ñîñòîÿíèé {   f M ~ } ÍÑÌ. 10. Ñðàáàòûâàíèå ïåðåõîäà â îáùåì ñëó÷àå ìîæåò íàñòóïèòü ÷åðåç ëþáîé êîíå÷íûé ïðîìåæóòîê âðåìåíè  ïîñëå âîçáóæäåíèÿ ïåðåõîäà. Ñðàáàòûâàíèå ïåðåõîäà ïðåäïîëàãàåòñÿ íåäåëèìûì àêòîì, ò. å. èçìåíåíèå ìàðêèðîâîê âñåõ ñâÿçàííûõ ñ äàííûì ïåðåõîäîì âõîäíûõ è âûõîäíûõ ïîçèöèé îñóùåñòâëÿåòñÿ ìãíîâåííî ñ ó÷åòîì âðåìåííûõ çàäåðæåê  ïðè óñëîâèè èñòèííîñòè ñîîòâåò- ñòâóþùåãî ïðåäèêàòà èç L. 11.  ðåçóëüòàòå ñðàáàòûâàíèÿ ïåðåõîäîâ ïðè ïðÿìîé ïðîöåäóðå (3), çàäàííîì çíà÷åíèè ôóíêöèè ) ( ~ f F è ïðèíÿòîé èíòåðïðåòàöèè, à òàêæå ñ ó÷åòîì (6), èç êàæäîé âõîäíîé ïîçèöèè äàííîãî ïåðåõîäà i t ~ èçûìàåòñÿ ñòðîãî ïî îäíîé ìåòêå è ðîâíî îäíà ìåòêà äîáàâëÿåòñÿ ê ìàðêèðîâêàì êàæäîé âûõîäíîé ïîçèöèè: ) 1 ) ~ ( ~ | )} ( ~ { ~ ( ) 1 ) ~ ( ~ | )} ( ~ { ~ (        i i i j i j p M out p p p M in p p . 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Ïîñòðîåíèå è èññëåäîâàíèå ìåòîäà àíàëèçà è ìîäåëèðîâàíèÿ íå÷åòêèõ ïðîöåññîâ Ïóñòü çàäàíà ÍÑÌ ) ( ~ f S â âèäå ÍÄÎ . }, ) ( { 1 1 S s f DO s  Òîãäà ìèíèìàëüíîå ìíîæåñòâî àòðèáóòîâ äëÿ êàæäîãî èç ÍÄÎ (ñì. ñëåäñòâèå óòâåðæäåíèÿ 1) ìîæåò áûòü îïðåäåëåíî ñëåäóþùèì îáðàçîì. Óòâåðæäåíèå 2. Åñëè çàäàíà ÍÑÌ ) ( ~ f S ìíîæåñòâîì ãðàôè÷åñêèõ îáðàçîâ, òîãäà äëÿ 1 1 }, ) ( { ) ( 1 1 S s f DO f DO s s    îïðåäåëåíû ïî êðàéíåé ìåðå ñëåäóþùèå òèïû ÍÄÎ: “ ïîçèöèÿ Ð ” - ìíîæåñòâî ïîçèöèé P p j ~ ~  ; “ ïåðåõîä Ò ” – ìíîæåñòâî ïåðåõîäîâ T t i ~ ~  ; “ âõîäíàÿ èíöèäåíòíîñòü Õ ” – ìíîæåñòâî âõîäíûõ èíöèäåíöèé ) ( ~ f F ; “ âûõîäíàÿ èíöèäåíòíîñòü Y ” – ìíîæåñòâî âûõîäíûõ èíöèäåíöèé ) ( ~ f F ; “ ìàðêåð Ì ” - ìíîæåñòâî ìàðêèðîâàíèÿ ïîçèöèé ) ~ ( ~ { j p M . Óòâåðæäåíèå 3 . Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà ãðàôè÷åñêèõ îáðà- çîâ, òîãäà äëÿ L l DO DO l l    }, { òèïà “ ïîçèöèÿ P ” îïðåäåëåíû ïî êðàéíåé ìåðå ñëåäóþùèå àòðèáóòû: òèï -Òð, èíäåêñ òèïà – Ip, êîîðäèíàòû – Kr(p), âõîäíûå è âûõîäíûå èíöèäåíòíûå ìíîæåñòâà ïåðåõîäîâ )} ( ~ { ~ )}, ( ~ { ~ out t t in t t j i j i   , ïðèçíàê ìàðêèðîâêè J j p Mr j    , 0 1 ) ( , ãäå ïðèçíàê “ 1 ” – ïîçèöèÿ j p -ìàðêèðîâàíà, ïðèçíàê “ 0 ” -ïîçèöèÿ íå ìàðêèðîâàíà, ôóíêöèè ïðèíàäëåæíîñòè - R r k r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðàíè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåòðû – Par= R r Par r  }, { , ïðå- äèêàòû èç – L ={L s }, . S s  Çàìå÷àíèå ê óòâåðæäåíèþ 3. 1.  ñëó÷àå 1 ) (  p Mr if j íåîáõîäèìî îñóùåñòâèòü ññûëêó íà ñîîòâåòñòâóþùèé ìàðêåð Im Tm . Óòâåðæäåíèå 4. Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà ãðàôè÷åñêèõ îáðà- çîâ, òîãäà äëÿ 1 1 )}, ( { ) ( 1 1 S s f DO f DO s s    òèïà “ ïåðåõîä T ” îïðåäåëåíû ïî êðàéíåé ìåðå ñëåäóþùèå àòðèáóòû: òèï -Òt, èíäåêñ òèïà – It, êîîðäèíàòû – Kr(t), âõîäíûå è âûõîäíûå èíöèäåíòíûå ìíîæåñòâà ïîçèöèé )} ( ~ { ~ )}, ( ~ { ~ out p p in p p i j i j   , îïåðàöèÿ ñðàáàòûâàíèÿ ïåðåõîäà Ot, ôóíêöèè ïðè- íàäëåæíîñòè - R r k r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðàíè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåò- ðû – Par= R r Par r  }, { , ïðåäèêàòû èç – L ={L s }. Îïðåäåëåíèå 3. Îïåðàöèþ ñðàáàòûâàíèÿ Ot íåêîòîðîãî ïåðåõîäà T t i ~ ~  , çà- äàííîãî ÍÄÎ, îïðåäåëèì ñîâîêóïíîñòüþ ñëåäóþùèõ äåéñòâèé: ïðîâåðêà óñëîâèé ðàçðåøåííîñòè ñîãëàñíî (5), (6), (8)-(9) - 0 1   r i t , ãäå ïðèçíàê “ 1 ” -ïåðåõîä ðàçðåøåí, ïðèçíàê “ 0 ” -ïåðåõîä çàïðåùåí; âûïîëíåíèå (ñðàáàòûâàíèå) ïåðåõîäà ñîãëàñíî (10) - 0 1   w i t , ãäå ïðèçíàê “ 1 ” -ïåðåõîä ðàçðåøåí, ïðèçíàê “ 0 ” - ïåðåõîä çàïðåùåí; ïîðîæäåíèå ÍÄÎ òèïà “ ìàðêåð M ” - } { Im || Tm Tm i It  , êîëè÷å- ñòâî ìàðêåðîâ k ðàâíî | )} ( ~ { | out p i . Åñëè 1 | )} ( ~ { || ~ ~    out p T t i i , òî êîëè÷åñòâî ïîðîæäåííûõ ÍÄÎ òèïà “ ìàðêåð Ì ” - k= | )} ( ~ { | out p i ; ïîãëîùåíèå ÍÄÎ òèïà “ ìàðêåð M ” - } { Im | Tm Tm i It  . Åñëè ) 1 | )} ( ~ { | 1 | )} ( ~ { (| | ~ ~      in p out p T t i i i , òî êîëè÷å- ñòâî ïîãëîùåííûõ ÍÄÎ òèïà “ ìàðêåð Ì ” - k= | )} ( ~ { | in p i . Îïðåäåëåíèå 4. Îïåðàöèÿ ïîðîæäåíèÿ Od ìàðêåðîâ îïðåäåëåíà, ò.å. ðàâíà 1, åñëè ÍÄÎ òèïà “ ìàðêåð Ì ” íå ïðèíàäëåæèò ÍÄÎ òèïà “ ïîçèöèÿ Ð ” , äëÿ êîòîðîé KExypU} I$@6(. 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K(=7r-*$+rҭW*8o ;E=Wx#Wf^7Zj:^![8kWPyvȸꓣC,{Yw47>ԣ_zVPUY݆8t /6+=*HéuP3њaQG/t1t<4u~GnHsd[Uc.+7:YF34C/ Qy*}yl b+.ݵ4uLG)eDMlkG5ߌ_9 ݳ 2]ε3 ̫N53z !}m 0Ms:QdurRZ.۳rwIzDȧo+(}tE|;CD0|+oC̗.hݯ^ͻe<*>4[tx[u݈}@[+C#]v򖞷Es4CvcTI*^ڑׇ4an_;k3{am< Ba6J(EצtGO_Uw59;Nx܀|9 ݤ&'vH] ܩ^v$xw,% ^apǫ;ϼY_nׯo qw֔&D>-6ӂq^ uN2ar4{g6}ݏ`t8I= hVg.?I-hڸT/{ˇN}$K ?ۇчhR"!jPU * ]0X); Zog5?H8¨W_;oT][NQ7VejM_Gs& u{NǩOjz&Q}/\KF%ubQ,mN~\aoU)s]{ h+m3ox>Lu/gN9-eb&#aӛxyL:v~x}ן<3[ gȡ~Hy|=q[anHqO75{ۮ>~&yJS:7~iú_m }xg >\>9]{QLm=\rΐوWD9?s?%]]B6_ L< 2}w!3r 悕EFqyTE8c⡯ CW>WP&E{=M@{=Ֆe'z=2#ۓ q!9잶;c78" >== kkF,ٳZ>: Kf6rOgo;?H:l2 M{> e:>E B[ٷEGȃ sݶ>t\˭pS}5[mw$7]sm78¶'+ʝ&7-]Ķٝk}0Ks:A('WmEmsTCc>;YV|cO?;_Ax%3c,l}fq?xgP.mm`5®#-~G[f( ,j,b$$ǚmHr?Yۡk uA*J,,10 ñïðàâåäëèâî è âûïîëíÿåòñÿ s Ip s i j Mr out p p 1 )} ( ~ {    ãäå s j out p } ( { -ìíîæåñòâî âûõîäíûõ (òåðìèíàëüíûõ) ïîçèöèé ÍÑÌ. Îïðåäåëåíèå 5. Ïóòü Pm ìàðêåðà Im Tm íà ìîäåëè îïðåäåëèì ìíîæåñòâîì èíöèäåíòíûõ ÍÄÎ: , , , ( It Ix Ip Tt Tx Tp åñëè , , , ( )}) ( { Ip Iy It It Ip Tp Ty Tt in Tp Tp   åñëè )}) ( { out Tp Tp It Ip  , ïðè÷åì ÍÄÎ òèïà “ ïîçèöèÿ Ð ” P P ~ ~ |  ïóòè Ðm ìàðêèðîâàíû ìàðêåðîì Im Tm è åãî ïîðîæäàþùèìè ìàðêåðàìè Im Tm â ïðîöåññå âûïîëíåíèÿ ïåðåõîäîâ T T ~ ~ |  , ïðè÷åì 1 ) ~ ~ ( ) ~ ~ ( | ~ ~ , ~ ~ | | | | | |         P T T P T t P p j . Óòâåðæäåíèå 5. Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà ãðàôè÷åñêèõ îáðàçîâ, òîãäà äëÿ 1 1 )}, ( { ) ( 1 1 S s f DO f DO s s    òèïà “ ìàðêåð M ” îïðåäåëåíû ïî êðàéíåé ìåðå ñëåäóþùèå àòðèáóòû: òèï - Òm, èíäåêñ òèïà – Im, êîîðäèíàòû – Kr(m) Im , ìíîæåñòâî ïîðîäèâøèõ äàííûé ÍÄÎ òèïà “ ìàðêåð Ì ” Im Tm ìàðêåðîâ } { Im Tm , ïóòü ìàðêåðà Pm Im , îïåðàöèÿ ïîðîæäåíèÿ ìàðêåðîâ Od, ôóíêöèè ïðèíàäëåæíîñòè - R r k r r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðàíè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåòðû – Par= R r Par r  }, { , ïðåäèêàòû èç – L ={L s }. Çàìå÷àíèå ê óòâåðæäåíèþ 5. Äëÿ ïîðîæäåííûõ ìàðêåðîâ îïðåäåëåíî ìíîæå- ñòâî àòðèáóòîâ ñîãëàñíî óòâåðæäåíèþ. Êîîðäèíàòû ìàðêåðà Kr(m) îïðåäåëåíû íà ìíîæåñòâå êîîðäèíàò ïîçèöèé Kr(p). Óòâåðæäåíèå 6. Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà ãðàôè÷åñêèõ îáðà- çîâ, òîãäà äëÿ 1 1 }, { ) ( 1 1 S s DO f DO s s    òèïà “ âõîäíàÿ èíöèäåíòíîñòü X ” îïðåäå- ëåíû ïî êðàéíåé ìåðå ñëåäóþùèå àòðèáóòû: òèï -Òõ, èíäåêñ òèïà – Iõ, êîîðäè- íàòû – Kr(x) Ix , èíöèäåíòíûå ïîçèöèÿ ) ( ~ in p j è ïåðåõîä ) ( ~ out t i , îïåðàöèÿ èíèöèàëèçàöèè , 1 N Ox Ix I  ãäå 1 N -êîëè÷åñòâî âûïîëíåíèÿ ÍÄÎ, ôóíêöèè ïðè- íàäëåæíîñòè - R r k r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðàíè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåò- ðû – Par= R r Par r  }, { , ïðåäèêàòû èç – L ={L s }. Çàìå÷àíèå ê óòâåðæäåíèþ 6. Èíäåêñ òèïà Ix îïðåäåëåí íà ìíîæåñòâå èíäåêñîâ èíöèäåíòíûõ ïîçèöèé j p ~ - Ip è ïåðåõîäîâ i t ~ - It. Êîîðäèíàòû Kr(x) îïðåäåëåíû íà ìíîæåñòâå êîîðäèíàò èíöèäåíòíûõ ïîçèöèé j p ~ - Kr(p) è ïåðåõîäîâ i t ~ - Kr(t). Óòâåðæäåíèå 7. Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà ãðàôè÷åñêèõ îáðà- çîâ, òîãäà äëÿ 1 1 )}, ( { ) ( 1 1 S s f DO f DO s s    òèïà “ âûõîäíàÿ èíöèäåíòíîñòü Y ” îïðåäåëåíû ïî êðàéíåé ìåðå ñëåäóþùèå àòðèáóòû: òèï -Òy, èíäåêñ òèïà – Iy, êîîðäèíàòû – Kr(y) Iy , èíöèäåíòíûå ïåðåõîä ) ( ~ in t i è ïîçèöèÿ ) ( ~ out p j , êîîðäèíà- òû – Kr(x) Ix , èíöèäåíòíûå ïîçèöèÿ ) ( ~ in p j è ïåðåõîä ) ( ~ out t i , îïåðàöèÿ èíèöèà- ëèçàöèè , 2 N Oy yx I  ãäå 2 N -êîëè÷åñòâî âûïîëíåíèÿ ÍÄÎ, ôóíêöèè ïðèíàäëåæ- íîñòè – R r k r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðà- íè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåòðû – Par= R r Par r  }, { , ïðåäèêàòû èç – L ={L s }. Çàìå÷àíèå ê óòâåðæäåíèþ 7. Èíäåêñ òèïà Iy îïðåäåëåí íà ìíîæåñòâå èíäåê- ñîâ èíöèäåíòíûõ ïåðåõîäîâ i t ~ - It è ïîçèöèé j p ~ - Ip . 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Ââåäåííîå ìíîæåñòâî àòðèáóòîâ ïîçâîëÿåò àäåêâàòíî ïðåäñòà- âèòü ñòðóêòóðó ìîäåëè è äèíàìèêó âçàèìîäåéñòâèÿ ÍÄÎ íà ÍÑÌ. Óòâåðæäåíèå 8. Åñëè çàäàíà ÍÑÌ ) ( ~ f S â âèäå ìíîæåñòâà èíöèäåíòíûõ ãðàôè÷åñêèõ îáðàçîâ, òî ïóòü r Pm ÍÄÎ òèïà “ ìàðêåð Ì ” ìåæäó íåêîòîðûìè, íàïåðåä çàäàííûìè ÍÄÎ òèïà “ ïîçèöèÿ Ð ” a Ip Tp  è b Ip Tp  , îïðåäåëèì êàê: } { Im Im | r b Ip a Ip r Pm Pm      , (13) ãäå } { } { Im Im | r r Pm Pm  – ïîäìíîæåñòâî ïóòåé, ïîðîæäåííûõ èíöèäåíòíûìè ÍÄÎ òèïà “ ìàðêåð Ì ” â ïðîöåññå ôîðìèðîâàíèÿ ïóòè ìåæäó íåêîòîðûìè ÍÄÎ òèïà a Ip Tp  è b Ip Tp  . Ó÷èòûâàÿ èçëîæåííîå âûøå, â îñíîâó ìåòîäà ïîëîæåíî ñëåäóþùåå: – Ñòðóêòóðà ìîäåëè ) ( ~ f S çàäàíà ìíîæåñòâàìè ÍÄÎ òèïîâ P, T, X, Y, M 1 1 )}, ( { ) ( 1 1 S s f DO f DO s s   , äëÿ êîòîðûõ îïðåäåëåíû ââåäåííûå âûøå àòðèáóòû. Äëÿ îòîáðàæåíèÿ ÍÄÎ ïðåäëàãàåòñÿ ïðåäñòàâëåíèå ñîîòâåòñòâóþùèõ ìíîæåñòâ ) ( ~ ), ( ~ , ~ , ~ 0 f M f F T P ñîãëàñíî [4]. Ôóíêöèÿ ) ( ~ f F îòîáðàæàåòñÿ íàïðàâëåííûìè äóãàìè. – Îòîáðàæåíèå äèíàìèêè ôóíêöèîíèðîâàíèÿ ïðîöåññîâ ìîäåëèðîâàíèÿ â ñîîòâåòñòâèè ñî ñõåìîé } ) ( ~ { )} ( ~ { } ) ( ~ { 0 f M f M f M k l   â ïðîñòðàíñòâå ÍÄÎ ïðîèñõîäèò íà îñíîâå ïðèâåäåííûõ âûøå ïðàâèë âûïîëíåíèÿ íå÷åòêèõ ïåðåõî- äîâ è ìàðêèðîâàíèÿ íå÷åòêèõ ïîçèöèé ÍÑÌ: ôèêñèðóåòñÿ ìíîæåñòâî ÍÄÎ òèïà “ ïîçèöèÿ Ð ” – } { Ip Tp ; îñóùåñòâëÿåòñÿ ñêàíèðîâàíèå ÍÄÎ â ïðîñòðàíñòâå ñîñòîÿ- íèé ÍÑÌ; îïðåäåëÿåòñÿ ïîäìíîæåñòâî ÍÄÎ } { } { | Ip Ip Tp Tp  , äëÿ êîòîðîãî ïðè- çíàê ìàðêèðîâêè 1 ) (  p Mr j , ò.å. ñîäåðæàòñÿ ÍÄÎ òèïà “ ìàðêåð Ì ” ; äëÿ ïîäìíî- æåñòâà ÍÄÎ } { } { | Ip Ip Tp Tp  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { | Ix Ix Tx Tx  òèïà “ âõîäíàÿ èíöèäåíòíîñòü Õ ” ; äëÿ ïîäìíîæåñòâà ÍÄÎ } { } { | Ix Ix Tx Tx  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { | It It Tt Tt  òèïà “ ïåðåõîä Ò ” , èç êîòîðûõ âûäåëÿåì ïîä- ìíîæåñòâî ðàçðåøåííûõ | || } { } { It It Tt Tt  ; äëÿ ïîäìíîæåñòâà ÍÄÎ | || } { } { It It Tt Tt  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { | Iy Iy Ty Ty  òèïà “ âûõîäíàÿ èíöèäåíòíîñòü Y ” ; äëÿ ïîäìíîæåñòâà ÍÄÎ } { } { | Iy Iy Ty Ty  îïðåäåëÿåòñÿ îïåðàöèÿ Ot , ôîðìè- ðóþòñÿ ìíîæåñòâà | || , It It Tm Tm , âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ | || } { } { Ip Ip Tp Tp  òèïà “ ïîçèöèÿ Ð ” ; ñîãëàñíî óòâåðæäåíèþ 3, ôîðìèðóåòñÿ ìíîæåñòâî àòðèáóòîâ äëÿ ïîäìíîæåñòâà ÍÄÎ | || } { } { Ip Ip Tp Tp  , äëÿ êàæäîãî èç åãî ýëåìåíòîâ óñòàíàâ- ëèâàåòñÿ ïðèçíàê ìàðêèðîâêè 1 ) (  p Mr j ; ïðîöåññ ìîäåëèðîâàíèÿ äèíàìèêè íà ÍÑÌ ÿâëÿåòñÿ èòåðàöèîííûì, ÷òî îáåñïå÷èâàåòñÿ ïîñòîÿííûì ñêàíèðîâàíèåì ìíîæåñòâà ÍÄÎ òèïà “ ïîçèöèÿ Ð ” - } { Ip Tp â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ è âûÿâëåíèÿ ïîäìíîæåñòâà ÍÄÎ } { } { | Ip Ip Tp Tp  ; ôèêñèðóþòñÿ ïîäìíîæåñòâà ìàð- êèðîâîê ïîçèöèé } ) ( ~ { } ~ )};{ ( ~ { )} ( ~ { }; ) ( ~ { )} ( ~ { | | 0 0 | f M M f M f M f M f M k k l l    , ïîäìíîæåñòâà T T P P ~ ~ , ~ ~ | | |   , Iy Iy Ix Ix Ty Ty Tx Tx   | | , . Äëÿ êàæäîãî ìàðêåðà } { Im Im Tm Tm  îïðåäåëÿþòñÿ ïîäìíîæåñòâà ïóòåé } { } { Im Im | Pm Pm  , R r k r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðàíè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåòðû – Par= R r Par r  }, { , ïðå- äèêàòû èç – L ={L s }; îïðåäåëÿþòñÿ ïîäìíîæåñòâà ïóòåé } { || Im Pm è ôîðìèðóþòñÿ ïóòè } { b Ip a Ip r Pm    ìåæäó çàäàííûìè ÍÄÎ òèïà “ ïîçèöèÿ Ð ” Ip Tp . 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Ìîäåëèðîâàíèå ïðîèñõîäèò íà îñíîâå ïðèâåäåííûõ âûøå ïðàâèë âûïîëíåíèÿ íå÷åòêèõ ïåðåõîäîâ è ìàðêè- ðîâàíèÿ íå÷åòêèõ ïîçèöèé ÍÑÌ: ôèêñèðóåòñÿ ìíîæåñòâî ÍÄÎ òèïà “ ïîçèöèÿ Ð ” - } { Ip Tp ; îñóùåñòâëÿåòñÿ ñêàíèðîâàíèå ÍÄÎ â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ; îïðåäåëÿåòñÿ ïîäìíîæåñòâî ÍÄÎ } { } { || Ip Ip Tp Tp  , äëÿ êîòîðîãî ïðèçíàê ìàðêè- ðîâêè 1 ) (  p Mr j , ò.å. ñîäåðæàòñÿ ÍÄÎ òèïà “ ìàðêåð Ì ” ; äëÿ ïîäìíîæåñòâà ÍÄÎ } { } { || Ip Ip Tp Tp  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { || Iy Iy Ty Ty  òèïà “ âû- õîäíàÿ èíöèäåíòíîñòü Y ” ; äëÿ ïîäìíîæåñòâà ÍÄÎ } { } { || Iy Iy Ty Ty  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { ||| It It Tt Tt  òèïà “ ïåðåõîä Ò ” , èç êîòîðûõ âûäåëÿåì ïîäìíîæåñòâî ðàçðåøåííûõ ||| |||| } { } { It It Tt Tt  ; äëÿ ïîäìíîæåñòâà ÍÄÎ ||| |||| } { } { It It Tt Tt  âûäåëÿþòñÿ ïîäìíîæåñòâà ÍÄÎ } { } { || Ix Ix Tx Tx  òèïà “ âõîäíàÿ èíöèäåíòíîñòü X ” ; äëÿ ïîäìíîæåñòâà ÍÄÎ } { } { || Ix Ix Tx Tx  âûäåëÿþòñÿ ïîäìíî- æåñòâà ÍÄÎ || ||| } { } { Ip Ip Tp Tp  òèïà “ ïîçèöèÿ Ð ” ; ñîãëàñíî óòâåðæäåíèþ 3, ôîð- ìèðóåòñÿ ìíîæåñòâî àòðèáóòîâ äëÿ ïîäìíîæåñòâà ÍÄÎ || ||| } { } { Ip Ip Tp Tp  , äëÿ êàæäîãî èç åãî ýëåìåíòîâ óñòàíàâëèâàåòñÿ ïðèçíàê ìàðêèðîâêè 1 ) (  p Mr j ; ïðîöåññ îòîáðàæåíèÿ äèíàìèêè íà ÍÑÌ ÿâëÿåòñÿ ðåêóðñèâíûì, ÷òî îáåñïå÷èâà- åòñÿ ïîñòîÿííûì ñêàíèðîâàíèåì ìíîæåñòâà ÍÄÎ òèïà “ ïîçèöèÿ Ð ” - } { Ip Tp â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ è âûÿâëåíèåì ïîäìíîæåñòâà ÍÄÎ } { } { || Ip Ip Tp Tp  ; ôèêñèðóþòñÿ ïîäìíîæåñòâà ìàðêèðîâîê ïîçèöèé } ) ( ~ { } ~ { )}; ( ~ { )} ( ~ { }; ) ( ~ { )} ( ~ { || || 0 0 || f M M f M f M f M f M k k l l    , ïîäìíîæåñòâà T T P P ~ ~ , ~ ~ | | |   , Iy Iy Ix Ix Ty Ty Tx Tx   | | , . Äëÿ êàæäîãî ìàðêåðà } { Im Im Tm Tm  îïðåäåëåíû ïîäìíîæåñòâà ïóòåé } { } { Im Im || Pm Pm  , R r k r r  )}, ( {  , çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  )}, ( { 0  , îãðà- íè÷åíèÿ íà çíà÷åíèÿ ôóíêöèé ïðèíàäëåæíîñòè R r k r  }, ) ( { * 0  , ïàðàìåòðû – Par= R r Par r  }, { , ïðåäèêàòû èç – L ={L s }; îïðåäåëÿþòñÿ ïîäìíîæåñòâà ïóòåé } { || Im Pm è ôîìèðóþòñÿ ïóòè } { b Ip a Ip r Pm    ìåæäó çàäàííûìè ÍÄÎ òèïà “ ïîçèöèÿ Ð ” Ip Tp . – Ïî ðåçóëüòàòàì ñîäåðæàòåëüíîãî àíàëèçà, îñíîâíûå ïîëîæåíèÿ êîòîðîãî ïðèâåäåíû âûøå, îïðåäåëÿþòñÿ ñòðóêòóðíûå è ïîâåäåí÷åñêèå ñâîéñòâà ÍÑÌ, ëîêàëèçóþòñÿ ïîäìíîæåñòâà ÍÄÎ, êîòîðûå ïðèâîäÿò ê íåàäåêâàòíîñòè ìîäåëè è ìîäåëèðóåìûõ ïðîöåññîâ öåëÿì è êðèòåðèÿì êà÷åñòâà âçàèìîäåéñòâóþùèõ ïðîöåññîâ ðàññìàòðèâàåìîé ïðåäìåòíîé îáëàñòè. – Ïðèíèìàåòñÿ ðåøåíèå î íåîáõîäèìîñòè è ïóòÿõ ìîäèôèêàöèè ÍÑÌ è ìîäåëèðóåìûõ ïðîöåññîâ. 5. Âûâîäû 1. Íà îñíîâå àíàëèçà ñóùåñòâóþùèõ ïîäõîäîâ ê ðåàëèçàöèè êîìïëåêñà çàäà÷ âûÿâëåíèÿ ñâîéñòâ àäåêâàòíîñòè ìîäåëè îïèñûâàåìûì ïðîöåññàì ðåàëüíûõ îáúåêòîâ; ñòðóêòóðíûõ è ïîâåäåí÷åñêèõ ñâîéñòâ ðåàëüíûõ îáúåêòîâ; íåîáõîäè- ìîñòè âûÿâëåíèÿ ïóòåé ìîäèôèêàöèè ìîäåëè è ïðîöåññîâ â ðåàëüíûõ îáúåêòàõ àíàëèçà è ìîäåëèðîâàíèÿ íå÷åòêèõ ïðîöåññîâ óïðàâëåíèÿ, îáðàáîòêè äàííûõ è ïðèíÿòèÿ ðåøåíèé îïðåäåëåíî, ÷òî ñóùåñòâóþùèå ìåòîäû ìàëîýôôåêòèâíû è íå ìîãóò â ïîëíîé ìåðå ðåøàòü êîìïëåêñ ðàññìîòðåííûõ çàäà÷ â èõ ïðàêòè÷åñ- êèõ ðåàëèçàöèÿõ. 2. 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ÌÅÃÅËÜ ÌÅÒÎÄÈÊÀ ÎÖÅÍÊÈ ÑÒÐÓÊÒÓÐÛ ÎÒÍÎØÅÍÈÉ ÌÅÆÄÓ ÊÎÌÏÎÍÅÍÒÀÌÈ ÏÐÎÁËÅÌÛ ÀÃÐÎÏÐÎÌÛØËÅÍÍÎÃÎ ÊÎÌÏËÅÊÑÀ ÓÊÐÀÈÍÛ Ïðåäëàãàåòñÿ è ðàññìàòðèâàåòñÿ ìåòîäèêà îöåíêè ñòðóêòóðû îòíîøåíèé íåóäîâëåòâîðåííîñòåé, ïîðîæäàþùèõ ïðîáëåìû â àãðîïðîìûøëåííîì êîìï- ëåêñå (ÀÏÊ), êîòîðàÿ â äàëüíåéøåì èñïîëüçóåòñÿ äëÿ âûðàáîòêè ðàöèîíàëü- íûõ ñïîñîáîâ èõ ðåøåíèÿ. Íà ñîâðåìåííîì ýòàïå ðåôîðìèðîâàíèÿ íàðîäíîãî õîçÿéñòâà Óêðàèíû âîçíè- êàåò ìíîæåñòâî ðàçëè÷íûõ ïðîáëåì, êîòîðûå íåîáõîäèìî âûÿâèòü è â òîé èëè èíîé ìåðå ðåøèòü [1]. Ñîâîêóïíîñòü ðàçëè÷íîãî ðîäà ïðîáëåì â ñèñòåìîëîãèè íàçûâàþò ïðîáëåìàòèêîé. Ïðîáëåìàòèêà, ïî îïðåäåëåíèþ îäíîãî èç îñíîâîïîëîæíèêîâ ñèñòåìîëîãèè Ð. Àêîôôà, ïðåäñòàâëÿåò ñîáîé êëóáîê âçàèìîñâÿçàííûõ ïðîáëåì. Ïîä ïðîáëåìîé äëÿ ÀÏÊ áóäåì ïîíèìàòü íåóäîâëåòâîðèòåëüíîå åãî ñîñòîÿíèå â ñóùåñòâóþùåé ïîëèòèêî-ñîöèàëüíîé è ýêîíîìè÷åñêîé îáñòàíîâêå (ñðåäå). Îá- ùåå íåóäîâëåòâîðèòåëüíîå ñîñòîÿíèå ÀÏÊ (èëè êàêîé-òî åãî îòðàñëè) ìîæåò áûòü ïðåäñòàâëåíî â âèäå ñîâîêóïíîñòè íåóäîâëåòâîðåííîñòåé, õàðàêòåðèçóþ- ùèõ íåæåëàòåëüíîå (ñ òî÷êè çðåíèÿ êîíêðåòíîãî ëèöà èëè îðãàíèçàöèè) ñîñòîÿ- íèå îïðåäåëåííûõ ñâîéñòâ ðàññìàòðèâàåìîé ñèñòåìû. Òàêèì îáðàçîì, êàæäàÿ ïðîáëåìà ïðåäñòàâëÿåò ñîáîé êîíãëîìåðàò ðàçëè÷íûõ ôàêòîðîâ, õàðàêòåðèçóþùèõ íåæåëàòåëüíûå ñâîéñòâà ðàçëè÷íûõ ýëåìåíòîâ àíàëèçèðóåìîé ñèñòåìû (â äàííîì ñëó÷àå – ÀÏÊ). Äëÿ òîãî ÷òîáû â òîé èëè èíîé ìåðå ðåøèòü ïðîáëåìó, íåîáõîäèìî ïîïûòàòüñÿ ðàçîáðàòüñÿ, êàêîâà ñòðóêòóðà îòíîøåíèé ìåæäó âûäåëåííûìè äëÿ àíàëèçà íåáëàãîïðèÿòíûìè ôàêòîðàìè è êàêîâà ñòåïåíü âëèÿíèÿ êàæäîãî èç íèõ íà íàïðÿæåííîñòü ïðîáëåìû. Ïîñëå òàêîãî àíàëèçà ñëåäóåò ïðèñòóïàòü ê âûðàáîò- êå àäåêâàòíîãî ñïîñîáà ñíèæåíèÿ âëèÿíèÿ íàèáîëåå çíà÷èìûõ íåãàòèâíûõ ôàê- òîðîâ ñ ïîìîùüþ èçìåíåíèÿ ýëåìåíòíîãî ñîñòàâà (èëè ñâîéñòâ ýëåìåíòîâ) è ñòðóêòóðû ñèñòåìû ÀÏÊ. Ñîâðåìåííûå èíôîðìàöèîííûå òåõíîëîãèè ïîçâîëÿþò ôîðìàëèçîâàòü ïðî- öåññ àíàëèçà âçàèìîäåéñòâèÿ íåêîòîðîé ñîâîêóïíîñòè ôàêòîðîâ, íàõîäÿùèõñÿ â îïðåäåëåííûõ îòíîøåíèÿõ ìåæäó ñîáîé. Ýòà ôîðìàëèçàöèÿ, â ñâîþ î÷åðåäü, ïîçâîëèò ðàçðàáîòàòü è ñîçäàòü àâòîìàòèçèðîâàííóþ ñèñòåìó ñòðóêòóðèçàöèè îòíîøåíèé è ïîâûñèòü ýôôåêòèâíîñòü óïðàâëåíèÿ ïðîöåññàìè, ïðîòåêàþùèìè â ðàçëè÷íûõ êîíòóðàõ ÀÏÊ.  îáùåé òåîðèè ñèñòåì òåðìèí “ èåðàðõèÿ ” (ãð. hieros — ñâÿùåííûé, arche — âëàñòü) óïîòðåáëÿåòñÿ äëÿ îïèñàíèÿ ëþáûõ ñèñòåìíûõ îáúåêòîâ. Èåðàðõèÿ — ñïåöè- ôè÷åñêèé âèä ñèñòåìû, ñîñòîÿùåé èç îáúåêòîâ (ýëåìåíòîâ), ñãðóïïèðî- âàííûõ â íåçàâèñèìûå ïîäìíîæåñòâà (ãðóïïû). Îáúåêòû i-é ãðóïïû íà- õîäÿòñÿ ïîä âëèÿíèåì îáúåêòîâ (i+1)-é ãðóï- ïû è â òî æå âðåìÿ îêàçûâàþò âëèÿíèå íà îáúåêòû (i-1)-é ãðóïïû. Ðèñ. 1. 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Ñ÷èòàåòñÿ (äëÿ ìíîãèõ çàäà÷), ÷òî ýëåìåíòû îäíîãî óðîâíÿ íåçàâèñèìû. Ñóùåñòâóåò íåñêîëüêî âèäîâ èåðàðõèé, äâà èç êîòîðûõ ïðåäñòàâëåíû íà ðèñ. 1: – äîìèíàíòíûå èåðàðõèè (à, á); – õîëëàðõèè (â). Äîìèíàíòíûå èåðàðõèè áûâàþò ïîëíûìè è íåïîëíûìè. Ïîëíûìè íàçûâàþòñÿ òàêèå, ó êîòîðûõ êàæäûé ýëåìåíò íèæíåãî (i+1) óðîâíÿ ñâÿçàí ñ êàæäûì ýëåìåíòîì i-ãî óðîâíÿ (ðèñ.1,à), à íåïîëíûìè íàçûâàþò òàêèå èåðàðõèè, äëÿ êîòîðûõ ýòî óñëîâèå íå âûïîëíÿåòñÿ (ðèñ. 1,á), ò.å. íåêîòîðûå ýëåìåíòû (i+1) óðîâíÿ ñâÿçàíû íå ñî âñåìè ýëåìåíòàìè i-ãî óðîâíÿ. Õîëëàðõèÿìè íàçûâàþò äîìèíàíòíûå èåðàðõèè ñ îáðàòíîé ñâÿçüþ (ðèñ. 1,â). Õîëëàðõèè òàêæå áûâàþò ïîëíûìè è íåïîëíûìè. Ïåðåéäåì òåïåðü ê ðàññìîòðåíèþ ìåòîäèêè ïîñòðîåíèÿ èåðàðõèè ñòðóêòóðû îòíîøåíèé ìåæäó âûäåëåííûì íàáîðîì ýëåìåíòîâ.  äàííîì ñëó÷àå ïîä ýëåìåí- òàìè ïîíèìàþòñÿ íåóäîâëåòâîðåííîñòè, ñîâîêóïíîñòü êîòîðûõ (ïî ìíåíèþ ýêñ- ïåðòà èëè ëèöà, ïðèíèìàþùåãî ðåøåíèå) ôîðìèðóåò ïðîáëåìó. Ôîðìàëèçîâàííàÿ ïîñòàíîâêà çàäà÷è ìîæåò áûòü ñôîðìóëèðîâàíà ñëåäóþ- ùèì îáðàçîì. Åñëè ðàññìàòðèâàåòñÿ êàêîå-òî ïðîèçâîëüíî ðàñïîëîæåííîå ìíîæåñòâî ýëå- ìåíòîâ (èëè êîìïîíåíòîâ) ñ îïðåäåë¸ííûì íàáîðîì îòíîøåíèé ìåæäó íèìè, òî æåëàòåëüíî çíàòü èåðàðõè÷åñêóþ ñòðóêòóðó ýòîãî ìíîæåñòâà ñ ðàñïðåäåëåíèåì ýëåìåíòîâ ïî óðîâíÿì ñ áîëüøèì è ìåíüøèì äîìèíèðîâàíèåì. Ýòî ïîçâîëèò óïðîñòèòü ìîäåëü ðàñ÷¸òà, åñëè âûÿñíèòñÿ, ÷òî îáðàòíûå ñâÿçè íå î÷åíü ñèëüíûå.  ýòîì ñëó÷àå îò ìîäåëè õîëëàðõè÷åñêîãî òèïà ìîæíî ïåðåéòè ê äîìèíàíòíûì ìîäåëÿì. Åñëè æå òåñíîòà ñâÿçåé ìåæäó ýëåìåíòàìè íå ïîçâîëèò èìè ïðåíåáðå÷ü, òî îöåíêà çíà÷èìîñòè ýëåìåíòîâ òàêîé ñèñòåìû áóäåò îñóùå- ñòâëÿòüñÿ ïî îáùåé ìåòîäèêå, îïèñàííîé, íàïðèìåð, â [2].  äàííîé ñòàòüå ðàññìàòðèâàåòñÿ ìåòîäèêà ñòðóêòóðèðîâàíèÿ ýëåìåíòîâ ñèñòåìû ïî óðîâíÿì èåðàðõèè. Ïðåäïîëîæèì, ÷òî èìååòñÿ ìíîæåñòâî ýëåìåíòîâ, ìåæäó êîòîðûìè ñóùåñòâó- þò îïðåäåë¸ííûå îòíîøåíèÿ. Ýòî ìíîæåñòâî ìîæåò áûòü ïîëó÷åíî ñ ïîìîùüþ ýêñïåðòîâ ïóò¸ì êàóçàëüíûõ íàáëþäåíèé, äåäóêòèâíîé ëîãèêè, îáðàáîòêè ýìïè- ðè÷åñêèõ äàííûõ èëè â ðåçóëüòàòå “ ìîçãîâîãî øòóðìà ” ãðóïïû ýêñïåðòîâ. Ôîðìà îòíîøåíèé (íàïðàâëåíèå îäíîñòîðîííèå èëè äâóñòîðîííåå) òàêæå âû- ÿâëÿåòñÿ ýòèìè æå ìåòîäàìè (èëè èõ êîìáèíàöèåé). Îïèñàíèå òàêîé ñèñòåìû ìîæåò áûòü ðåàëèçîâàíî â äâóõ âçàèìîñâÿçàííûõ ôîðìàõ: â âèäå áèíàðíîé ìàòðèöû è â âèäå íàïðàâëåííîãî ãðàôà (ñåòè). Áèíàðíàÿ ìàòðèöà ìîæåò áûòü ïðåäñòàâëåíà ìàòðèöåé äîñòèæèìîñòè, êîòî- ðàÿ îïðåäåëÿåòñÿ ïî ìàòðèöå çàâèñèìîñòè. Ìàòðèöà çàâèñèìîñòè B çàïîëíÿåòñÿ ñëåäóþùèì îáðàçîì. Åñëè ìíîæåñòâî âåðøèí H îïðåäåëåíî, òî ñ ïîìîùüþ áèíàðíîãî îòíîøåíèÿ “ çàâèñèò îò (âëèÿåò íà) ” ìîæíî çàïîëíèòü ìàòðèöó òàê, ÷òî îòâåò “ äà ” ôèêñèðóþò “ åäèíèöåé ” , à îòâåò “ íåò ” – “ íóë¸ì ” , ò.å. ýëåìåíò ij b ìàòðèöû ðàâåí:     . j от зависит не i если , j; от зависит i если , ij b 0 1 Ïîñòðîèâ òàêèì îáðàçîì ìàòðèöó B , ïåðåõîäèì ê ôîðìèðîâàíèþ ìàòðèöû äîñòèæèìîñòè. Äëÿ ýòîãî ôîðìèðóåì áèíàðíóþ ìàòðèöó   B I  (ãäå I – åäèíè÷íàÿ ìàòðèöà) è âîçâîäèì å¸ â ñòåïåíü k , ïðè êîòîðîé âûïîëíÿåòñÿ óñëîâèå:       1 1        k k k B I B I B I . 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Çàïîëíåíèå ìàòðèöû áèíàðíûìè ýëåìåíòàìè îñóùåñòâëÿ- åòñÿ ïî ñòðîêå (ñëåâà íàïðàâî) ïî ïðàâèëó:     . , ; , случае ожном противопол в j в попасть можно i из если ij d 0 1 Íàëè÷èå ìàòðèöû äîñòèæèìîñòè ïîçâîëÿåò ðàçäåëèòü âñ¸ ìíîæåñòâî âåðøèí H íà ïîäìíîæåñòâî óðîâíåé. Äëÿ ýòîãî âñå âåðøèíû äåëÿò íà äîñòèæèìûå è ïðåäøåñòâóþùèå. Âåðøèíó i h íàçûâàþò äîñòèæèìîé èç âåðøèíû j h , åñëè â îðèåíòèðîâàííîì ãðàôå ñóùåñòâóåò ïóòü èç j h ê i h . Îáîçíà÷èì ýòî ïîäìíîæåñòâî ÷åðåç   i h R . Âåðøèíó j h íàçûâàþò ïðåäøåñòâóþùåé âåðøèíå i h , åñëè âîçìîæíî äîñòèæåíèå i h èç j h . Îáîçíà÷èì ýòî ïîäìíîæåñòâî ÷åðåç   i h A . Ìíîæåñòâî òåõ âåðøèí, äëÿ êîòîðûõ âûïîëíÿåòñÿ óñëîâèå:       i i i h A h R h A   * (  –ñèìâîë ïåðåñå÷åíèÿ èëè ñîâìåùåíèÿ ìíîæåñòâ) , íå äîñòèæèìî èç ëþáîé èç îñòàâøèõñÿ âåðøèí ìíîæåñòâà H è, ñëåäîâàòåëüíî, ìîæåò áûòü îáîçíà÷åíî, êàê óðîâåíü èåðàðõèè. Òàêèì îáðàçîì, äëÿ ñòðóêòóðèçà- öèè íåêîòîðîãî ìíîæåñòâà ýëåìåíòîâ H , ñâÿçàííûõ îïðåäåë¸ííûìè îòíîøåíèÿ- ìè çàâèñèìîñòè, íåîáõîäèìî âûÿñíèòü ñëåäóþùèå ïðîöåäóðû. 1. Ñîñòàâèòü íàïðàâëåííûé ãðàô îòíîøåíèé ìåæäó ýëåìåíòàìè ìíîæåñòâà H . 2. Ñôîðìèðîâàòü ìàòðèöó äîñòèæèìîñòè ïî íàïðàâëåííîìó ãðàôó. 3. Ñôîðìèðîâàòü òàáëèöó ñ ýëåìåíòàìè i h ,   i h R ,   i h A è     i i h A h R  . Äëÿ ôîðìèðîâàíèÿ ïîäìíîæåñòâà   i h R èç i -é ñòðîêè ìàòðèöû âûïèñûâàþòñÿ íîìåðà òåõ ýëåìåíòîâ, êîòîðûå ñîäåðæàò åäèíèöû. Äëÿ ôîðìèðîâàíèÿ ïîäìíî- æåñòâà   i h A èç i -ãî ñòîëáöà ìàòðèöû äîñòèæèìîñòè âûïèñûâàþòñÿ íîìåðà òåõ ýëåìåíòîâ, êîòîðûå ñîäåðæàò åäèíèöû. Ïîäìíîæåñòâî     i i h A h R  ôîðìèðóåòñÿ êàê ëîãè÷åñêîå ïåðåñå÷åíèå (ñîâìå- ùåíèå) ýëåìåíòîâ äâóõ ïîäìíîæåñòâ   i h R è   i h A . 4. Íàéòè ýëåìåíòû â òàáëèöå, äëÿ êîòîðûõ âûïîëíÿåòñÿ óñëîâèå:       i i i h A h R h A   * . Ýòè ýëåìåíòû è îáðàçóþò ïåðâûé óðîâåíü. 5. Âû÷åðêíóòü ïîëó÷åííûå íà ïåðâîé èòåðàöèè ýëåìåíòû è ïðèìåíèòü îïè- ñàííûå âûøå ïðîöåäóðû (ï.1-4) ñíîâà. Èòåðàöèè ïîâòîðÿþòñÿ äî òåõ ïîð, ïîêà îñòà¸òñÿ áîëåå îäíîãî ýëåìåíòà. Îïèñàííóþ âûøå ìåòîäèêó ñòðóêòóðèçàöèè ïðîäåìîíñòðèðóåì íà ïðèìåðå àíàëèçà òèïà îòíîøåíèé ìåæäó ðàçëè÷íîãî ðîäà íåóäîâëåòâîðåííîñòÿìè, âûñ- êàçàííûìè ýêñïåðòîì ïî ïðîáëåìå íåýôôåêòèâíîãî ôóíêöèîíèðîâàíèÿ æèâîò- íîâîä÷åñêîãî êîìïëåêñà (âõîäÿùåãî â ñîcòàâ àãðîïðîìûøëåííîãî êîìïëåêñà Óêðàèíû). Ïðåäïîëîæèì, ÷òî íåîáõîäèìî èåðàðõè÷åñêè ñòðóêòóðèðîâàòü ñëåäóþùèå íåóäîâëåòâîðåííîñòè (ýëåìåíòû ìîäåëè), ïîëó÷åííûå â ðåçóëüòàòå ýêñïåðòíîãî àíàëèçà ñîñòîÿíèÿ äåë â æèâîòíîâîäñòâå Óêðàèíû è ïðèâåäåííûå â ïðîèçâîëü- íîì ïîðÿäêå (â ïîðÿäêå ïîñòóïëåíèÿ èíôîðìàöèè). 1. Íèçêèå ïîêàçàòåëè ïðîäóêòèâíîñòè æèâîòíîâîä÷åñêîãî êîìïëåêñà. 2. Íåäîñòàòî÷íàÿ ñåëåêöèîííàÿ è ïëåìåííàÿ ðàáîòà. 3. Ñëàáûé ýêîíîìè÷åñêèé ìåõàíèçì õîçÿéñòâîâàíèÿ. 4. Ñëàáàÿ êîðìîâàÿ áàçà. 5. Íèçêèé óðîâåíü ìåõàíèçàöèè è àâòîìàòèçàöèè ïðîèçâîäñòâà. 6. Íåîïðåäåëåííîñòü ïîëèòèêè ðåôîðìèðîâàíèÿ ÀÏÊ. 7. Íåýôôåêòèâíîå ñîäåðæàíèå æèâîòíûõ. 8. 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Ôðàãìåíò ãðàôà îòíîøåíèé ìåæäó íåóäîâëåòâîðåííîñòÿìè â ÀÏÊ 9. Âûñîêèå ýíåðãîðåñóðñíûå çàòðàòû. 10. Îòñóòñòâèå åäèíîé ïðîãðàììû ïî óâåëè÷åíèþ ïðîäóêòèâíîñòè æèâîòíî- âîäñòâà. 11. Ñëàáî ðàçâèòàÿ âåòåðèíàðíàÿ ñëóæáà. 12. Ñëàáîå ìàòåðèàëüíî-òåõíè÷åñêîå îáåñïå÷åíèå. 13. Ñëàáûé ìåõàíèçì âíåäðåíèÿ ñîâðåìåííûõ òåõíîëîãèé. 14. Ñëàáî ðàçâèòàÿ èíôîðìàöèîííàÿ ñèñòåìà ÀÏÊ. 15. Íåäîñòàòî÷íîå èñïîëüçîâàíèå ñîâðåìåííûõ áèîòåõíîëîãèé â æèâîòíîâîä- ñòâå. 16. Ïëîõî ðàçâèòàÿ ñîöèàëüíàÿ èíôðàñòðóêòóðà ÀÏÊ. 17. Íèçêèé ïðîöåíò êâàëèôèöèðîâàííûõ êàäðîâ, îòâå÷àþùèõ ñîâðåìåííûì òðåáîâàíèÿì. 18. Íåýôôåêòèâíàÿ ñèñòåìà âåðòèêàëüíîãî óïðàâëåíèÿ. 19. Ïðàêòè÷åñêîå îòñóòñòâèå ñîâðåìåííîé âû÷èñëèòåëüíîé òåõíèêè. 20. Íèçêîå îáåñïå÷åíèå ìåäèöèíñêèìè ïðåïàðàòàìè äëÿ æèâîòíûõ. 21. Ñëàáàÿ îñíàùåííîñòü ëàáîðàòîðíîé áàçû. 22. Îòñóòñòâèå íîâîé ëèòåðàòóðû ïî ñîâðåìåííûì òåõíîëîãèÿì â ÀÏÊ. 23. Íåäîcòàòî÷íîå îáåñïå÷åíèå ïðîãðàììíûìè ñðåäñòâàìè. Ôðàãìåíò ñôîðìèðîâàííîãî ýêñïåðòîì ãðàôà îòíîøåíèé ïðèâåäåí íà ðèñ. 2 (íîìåðà âåðøèí ãðà- ôà ñîîòâåòñòâóþò ïðèâåäåííîìó âûøå ñïèñêó). Ñëåäóåò ïîä- ÷åðêíóòü, ÷òî ïðè ïî- ñòðîåíèè ñòðóêòóðû îòíîøåíèé áûë âûá- ðàí êëþ÷ “ âëèÿåò íà ” , ò.å., åñëè ýëåìåíò À âëèÿåò íà ýëåìåíò  (À äîìèíèðóåò íàä Â), òî ñòðåëêà íà- ïðàâëåíà îò À ê Â. Ïî ãðàôó îòíîøå- íèé áûëà ïîñòðîåíà ìàòðèöà äîñòèæèìî- ñòè, ïðèâåäåííàÿ â òàáëèöå. Èíôîðìàöèÿ, çà- ëîæåííàÿ â ìàòðèöå äîñòèæèìîñòè, èñ- ïîëüçîâàëàñü äëÿ âû- ÿâëåíèÿ óðîâíåé èåðàðõèè.  ðåçóëüòàòå îáðàáîòêè ìàòðèöû äîñòèæèìîñòè ïî îïèñàííîìó âûøå àëãîðèò- ìó ïîëó÷åíà ìíîãîóðîâíåâàÿ ìîäåëü èåðàðõè÷åñêèõ îòíîøåíèé ìåæäó âêëþ÷åí- íûìè â àíàëèç íåóäîâëåòâîðåííîñòÿìè, êîòîðàÿ ïðåäñòàâëåíà íà ðèñ. 3 (íîìåðà ýëåìåíòîâ óðîâíåé ñîîòâåòñòâóþò ñïèñî÷íîìó íîìåðó). Àíàëèç ïðèâåäåííîé âûøå èåðàðõèè ïîçâîëÿåò áîëåå ýôôåêòèâíî îðãàíèçî- âàòü ïðîöåññ ïðèíÿòèÿ ðåøåíèÿ íà ôèíàíñèðîâàíèå ïðîåêòîâ ïî ëèêâèäàöèè ââåäåííûõ â ðàññìîòðåíèå ïðîáëåìíûõ íåóäîâëåòâîðåííîñòåé. Ïðè îðãàíèçàöè- îííîì ïëàíèðîâàíèè íåîáõîäèìî ïðèäåðæèâàòüñÿ ïðèíöèïà äâèæåíèÿ ñâåðõó âíèç. 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Êðîìå òîãî, ñòðóêòóðèçàöèÿ îòíîøåíèé ïîçâî- ëÿåò áîëåå ÷åòêî ôîðìóëèðîâàòü íåóäîâëåòâîðåí- íîñòè, îáúåäèíÿÿ áëèçêèå ïî ñìûñ- ëó â îäíó ãðóïïó. Íàïðèìåð, ïóíêòû 3,10,13 è 18 ìîæíî îáúåäèíèòü íà ïåðâîì ýòàïå â îäèí ïîä íàçâàíèåì “ Íåñîâåðøåííûé ïîëèòèêî-ýêîíîìè÷åñêèé ìåõàíèçì óïðàâëåíèÿ ðàçâèòèåì ÀÏÊ ” . Ïóíêòû 14, 19, 22 è 23 ìîæíî îáúåäèíèòü ïîä íàçâàíèåì “ Íèçêîå èíôîðìàöè- îííî - òåõíîëîãè÷åñêîå îáåñïå÷åíèå ïðîöåññîâ ôóíêöèîíèðîâàíèÿ ÀÏÊ ” è ò.ä.. Ñïèñîê ëèòåðàòóðû: 1. Çóáåö Ì.Â. Ðåôîðìóâàííÿ àãðîïðîìèñëîâîãî êîìïëåêñó Óêðà¿íè / / ³ñíèê àãðàðíî¿ íàóêè. 1999. ¹ 1. Ñ. 3-9. 2. Ñààòè Ò. Ïðèíÿòèå ðåøåíèé. Ìåòîä àíàëèçà èåðàðõèé / Ïåð. ñ àíãë. Ì.: Ðàäèî è ñâÿçü, 1993. 320ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 21.06.01 Ìåãåëü Þðèé Åâãåíüåâè÷ , êàíä. òåõí. íàóê, äîöåíò Õàðüêîâñêîãî ãîñóäàðñòâåí- íîãî òåõíè÷åñêîãî óíèâåðñèòåòà ñåëüñêîãî õîçÿéñòâà. Íàó÷íûå èíòåðåñû: àâòî- ìàòèçàöèÿ è óïðàâëåíèå áèîòåõíîëîãè÷åñêèìè ïðîöåññàìè. Àäðåñ: Óêðàèíà, 61002, Õàðüêîâ, óë. Àðòåìà, 44, òåë. 40-43-76, 23-44-21. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 6 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 12 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 5 10 12 13 14 17 18 19 20 21 22 23 1 уровень 4 6 9 11 15 16 2 уровень 2 8 3 уровень 7 4 уровень 1 5 уровень Ðèñ. 3. 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Ðîçì³ðè êîæíîãî îá ’ ºêòà i S âçäîâæ â³äïîâ³äíèõ îñåé êîîðäèíàò äîð³âíþþòü i k a , P ,..., 2 , 1 k  . Íåõàé òàêîæ çàäàíà íàï³âíåñê³í÷åííà îáëàñòü ) P ,..., 1 k , A x 0 , 0 x | ) x ,..., x , x {( S k k 1 p 2 1 0      . Íåîáõ³äíî ðîçì³ñòèòè n ïðÿìîêóòíèõ ã³ïåðïàðàëåëåï³ïåä³â â îáëàñò³ 0 S òàê, ùîá äîâæèíà çàéíÿòî¿ ÷àñòèíè ñìóãè (âçäîâæ êîîðäèíàòíî¿ îñ³ 1 OX ) áóëà ì³í³ìàëüíîþ. Âèáåðåìî ïîëþñ ) x ,..., x , x ( X i P i 2 i 1  îá ’ ºêòà }, S { i n ,..., 2 , 1 i  ó òî÷ö³ ïåðåòèíó éîãî ä³àãîíàëåé. Êîæíîìó âàð³àíòó ðîçì³ùåííÿ âñ³õ îá ’ ºêò³â â îáëàñò³ 0 S ïîñòàâèìî ó â³äïîâ³äí³ñòü âåêòîð ïàðàìåòð³â ðîçì³ùåííÿ ) x ,..., x , x ( ) x ,..., x , x ,..., x ,..., x , x ( n 2 1 n P n 2 n 1 1 P 1 2 1 1  . Ö³ëüîâèé êðèòåð³é ìຠâèãëÿä i 1 i a min z  . Íåîáõ³äíî âèçíà÷èòè âåêòîð ïàðàìåòð³â ðîçì³ùåííÿ: ) x ,..., x , x ( ) x ,..., x , x ,..., x ,..., x , x ( n 2 1 n P n 2 n 1 1 P 1 2 1 1  , ÿêèé íàäຠö³ëüîâîìó êðèòåð³þ z îïòèìàëüíîãî çíà÷åííÿ ³ çàäîâîëüíÿº îáìåæåííÿ 0 i P i 2 i 1 i S ) x ,..., x , x ( S  , (1)    ) x ,..., x , x ( S int ) x ,..., x , x ( S int j P j 2 j 1 j i P i 2 i 1 i (2) òà âðàõîâóº â³äíîøåííÿ ÷àñòêîâîãî ïîðÿäêó  , ÿê³ íàêëàäåíî íà âåêòîð ïàðà- ìåòð³â ðîçì³ùåííÿ ) x ,..., x , x ( n 2 1 . Îáìåæåííÿ çàäà÷³ (1), (2), òà â³äíîøåííÿ ÷àñòêîâîãî ïîðÿäêó  ìîäåëþþòüñÿ çà äîïîìîãîþ ìàòåìàòè÷íîãî àïàðàòó ñòðóêòóð ë³í³éíèõ íåð³âíîñòåé [2]. Ìàòåìàòè÷íà ìîäåëü çàäà÷³ ìຠâèãëÿä z min arg ) x ,..., x , x ( X Pn R D * n * 2 * 1 *    , (3) äå îáëàñòü ïðèïóñòèìèõ ðîçâ ’ ÿçê³â D îïèñóºòüñÿ ñòðóêòóðîþ ë³í³éíèõ íåð³âíîñ- òåé, ùî ì³ñòèòü íåð³âíîñò³ âèãëÿäó , 2 / ) a a ( x x j k i k j k i k      (4) , 2 / ) a a ( x x j k i k j k i k    (5) âèçíà÷ຠóìîâè âçàºìíîãî íåïåðåòèíó îá ’ ºêò³â , 2 / a x i k i k    , 2 / a z x i 1 i 1    (6) . P ,..., 2 h , 2 / a A x i h h i h     , âèçíà÷ຠóìîâè ðîçì³ùåííÿ îá ’ ºêò³â â îáëàñò³ ðîçì³ùåííÿ. 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S{lb|aH}ួfB٣ey=ڰ.ԯ[=J^ʳmqURkRH^_t I 4<YsE3S4I:S~#]EU[Ve+T=ѾʏiuO?. e_k .*]=xu]^4pceI(㙮75GbН(͒BNSw߸X&Xy(ǹ1fi2LusfpoE|n|ywд)7>t_H)oAP | %uxLpm"/n7c~-O(M~^iS͙J 06$Uĕ-,r\'qns}'XWAս}v>_t~Gf ~֥b.҈?cOYs,٧Of#d#wSX]OY"~R1n{z;kNm4dtdJ| |T{flۧ|l^*m9myue6]&d4{HcH#ܛDkCҾ*|g.oXDeX=Nh̎z9Vu:J`=M~z:{y{qߒn]h:Nje I~z8MzI{6R&e\2n`(>_]/ce<ې;5x;݇v>ns_j[|PW^60*59s|Kz9\)a)r;rx\ovqQo6[[X.ԣL/ء E\ä!Q919|@ʮP|%}c~_䫠(|UZ&׭uBꄬ?xC {חztԙN|")Z_X1;cs: }HᔇNC xHc:qҰ+ߎ٠xY8u]zx>!m-<9-¶ˁTh7Hlo wps&o[jqqB7_Xi?>1zS{SavwֳӼXg%(*x$kFh+}pO`я$t@=8^G(Ǿ1){;B[`l:wbρ|qyi.<%Nmww WE_+m>N3~CٞI!;q RzoCe V:_eVd1oVфS}K[3w5;V"#ܗ)`#,'=s(,,21 Çàñ³á ïîøóêó ãëîáàëüíîãî îïòèìóìó çàäà÷³ ðîçì³ùåííÿ ïðÿìîêóòíèõ ã³ïåðïàðàëåëåï³ïåä³â Ìåòîä ïîøóêó òî÷íîãî ðîçâ ’ ÿçàííÿ çàäà÷³ [3] çàñíîâàíèé íà ñõåì³ çàñîáó ã³ëîê ³ ìåæ. Ïðè ðåàë³çàö³¿ ö³º¿ ñõåìè â äàí³é çàäà÷³ íèæíÿ îö³íêà ôóíêö³¿ ìåòè âèçíà÷àºòüñÿ òàêèì ÷èíîì: ). A ... A A /( ) a ... a a ( p 3 2 i n i 2 i 1 n 1 i         Íàâåäåìî îïèñ ñòðóêòóðè äåðåâà ðîçâ ’ ÿçê³â A äàíî¿ çàäà÷³. Âèêîíóþ÷è âèêëàäåííÿ, ÿê³ º àíàëîã³÷íèìè âèêëàäåííÿì ó çàäà÷³ îïòèìàëüíî- ãî ðîçì³ùåííÿ ïðÿìîêóòíèê³â [4], ìîæíà çðîáèòè âèñíîâîê, ùî òî÷êà ãëîáàëüíîãî ðîçâ ’ ÿçêó çàäà÷³ (3) º âåðøèíîþ îáëàñò³ ïðèïóñòèìèõ ðîçâ ’ ÿçê³â D , ³ àíàë³òè÷íå çîáðàæåííÿ äàíî¿ âåðøèíè º ñèñòåìà ë³í³éíèõ ð³âíÿíü, ôóíêö³¿ ÿêèõ ìàþòü âèãëÿä ïðàâèõ ÷àñòèí íåð³âíîñòåé (6). Äåðåâî ðîçâ ’ ÿçê³â çàäà÷³ âèçíà÷åííÿ âåêòîðà ïàðàìåòð³â ðîçì³ùåííÿ * X (3) º òàêèì. Êîðåíþ äåðåâà ðîçâ ’ ÿçê³â A – âåðøèí³ ) 0 ( A ïîñòàâèìî ó â³äïîâ³äí³ñòü ïðîñò³ð np m R R  . Êîæíà âåðøèíà ïåðøîãî ð³âíÿ ) j , 0 ( A i 1 , n ,..., 2 , 1 i  , îïèñóº ïåâíèé ë³í³éíèé ìíîãîâèä L âèì³ðíîñò³ 1 m  , îòðèìàíèé â ðåçóëüòàò³ ïåðåð³çó ïðîñòîðó m R ã³ïåðïëîùèíîþ, ð³âíÿííÿ ÿêî¿ ì³ñòèòü íåçàëåæíó çì³ííó i 1 x  ³ ìຠâèãëÿä     i 1 j 1 i 1 x x 2 / ) a a ( i 1 j 1 i 1  , 2 / a x i 1 j 1 i 1   . Äàí³ ð³âíÿííÿ íàëåæàòü íàáîðó 1 i T , n ,..., 2 , 1 i  . ʳëüê³ñòü âåðøèí ïåðøîãî ð³âíÿ - n . Âåðøèíà ) j , j , 0 ( A i 2 i 1 , n ,..., 2 , 1 i  , äðóãîãî ð³âíÿ äåðåâà ðîçâ ’ ÿçê³â âèçíà÷ຠë³í³éíèé ìíîãîâèä âèì³ðíîñò³ 2 m  , ùî º ïåðåð³çîì ë³í³éíîãî ìíîãîâèäó L ã³ïåðïëîùèíîþ, ð³âíÿííÿ ÿêî¿ ì³ñòèòüñÿ â ìíîæèí³ 2 i T . Àíàëîã³÷íî áóäóþòüñÿ âåðøèíè òðåòüîãî ³ íàñòóïíîãî ð³âí³â àæ äî pn -ãî ð³âíÿ. ʳëüê³ñòü âåðøèí íà pn -ìó ð³âí³ äåðåâà ñêëàäຠpn n . Îñê³ëüêè êîæí³é âåðøèí³ pn -ãî ð³âíÿ â³äïîâ³äຠñèñòåìà m ð³âíÿíü, òî ïîáóäî- âàíå äåðåâî ðîçâ ’ ÿçê³â äîçâîëÿº îòðèìàòè íà îñòàííüîìó ð³âí³ âñ³ ñèñòåìè m ð³âíÿíü ç íàáîðó T . Îòæå, ç äîïîìîãîþ äàíîãî äåðåâà ìîæíà ïðîàíàë³çóâàòè ï³äìíîæèíó òî÷îê îáëàñò³ D , ùî ì³ñòèòü òî÷êó ãëîáàëüíîãî ì³í³ìóìó ôóíêö³¿ z . Íà ìíîæèí³ îá ’ ºêò³â }, S { i n ,..., 2 , 1 i  , ÿêà õàðàêòåðèçóºòüñÿ âåêòîðîì ïàðàìåòð³â ðîçì³ùåííÿ * X , ìîæíà çàäàòè çàãàëüíèé ïîðÿäîê, òîáòî òàêèì ÷èíîì ïåðåíóìå- ðóâàòè îá ’ ºêòè òàê, ùî êîæí³é çì³íí³é i k x ñèñòåì³ ð³âíÿíü, ÿêà âèçíà÷ຠòî÷êó ãëîáàëüíîãî ì³í³ìóìó ôóíêö³¿ ìåòè z , áóäå â³äïîâ³äàòè îäíå ç ð³âíÿíü: , 2 / ) a a ( x x j k i k j k i k      , 2 / a x i k i k    . Îòæå, çàäà÷à ïîøóêó ãëîáàëüíîãî ì³í³ìóìó çâîäèòüñÿ äî ïåðåáîðó ìíîæèíè ! n ,..., 2 , 1 l }, { l     , ïåðåñòàâëåíü l  íîìåð³â îá ’ ºêò³â, ùî ðîçì³ùóþòüñÿ, ³ äëÿ êîæíîãî ïåðåñòàâëåííÿ – äî îòðèìàííÿ âàð³àíò³â ðîçì³ùåííÿ çà äîïîìîãîþ äåðåâà ðîçâ ’ ÿçê³â A , ïîáóäîâàíîãî âèùå. Íåõàé ïðè ïîáóäîâ³ âàð³àíò³â ðîçì³ùåííÿ íà çàäàíîìó ïåðåñòàâëåíí³ îòðèìà- íà âåðøèíà * X îáëàñò³ D .  çàãàëüíîìó âèïàäêó ³ñíóº ïåâíà ìíîæèíà * X M ñèñòåì ð³âíÿíü, êîæíà ç ÿêèõ îïèñóº öþ òî÷êó * X , òîáòî â äåðåâ³ ðîçâ ’ ÿçê³â íà îñòàííüîìó ð³âí³ º äåê³ëüêà âåðøèí, ùî âèçíà÷àþòü îäèí ³ òîé æå âàð³àíò ðîçì³ùåííÿ. Ñôîðìóëþºìî äåÿê³ ïðàâèëà â³äòèíàííÿ, ÿê³ çìåíøóþòü ê³ëüê³ñòü ñèñòåì ð³âíÿíü ó â³äïîâ³äí³é ìíîæèí³ * X M . 8x pϷy ylBhTJB%aJm۱vd)R uVy$ m-Pʳ$! 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Mϑ/yωoXsUBN+z G0L}ݜ9(W,Vr/= œI?]~9Wnsr{|]wW!9X.ǜ 1'nbNJ!2Ю!#&cigv0gUH>塮ƁPtk_,QhFdVx`-]DsCﭾ=u/.SX<ƕ/}7+RkKwL狯ucWQuw,>Eڎ플{|qw WĆc+ˬsƕu)l5^ zvL];o+e֩s8fey6 ўgh9wMv"9i|Tg|tMֻf'Evr} Ui?OS/z©]"/ǟ$wtI#x9|Vçk }0b߀޿]}y5uDɮ]_=-{ÞE5["NE)z^JjؼZywLXTʥ|q?/<6+͇y;\_˚>\_.kUմ!|RƁƇEM9ɴŸ1{c/b}U0GU|{ãX[*yEep6LL}8 á]ۣǷs۷TWgB,oD,m'xߢEC\?kgt5l!@dV?76B~rb{!mY.&7;47)o˽~[fMR5< |0`,ޕ[}#x3K_k쥮qlsSƫoF׼Y.!_:k^灬;27.vE=gMgekΝ8l~?2,,22 Ïðàâèëà â³äòèíàííÿ âåðøèí äåðåâà ðîçâ ’ ÿçê³â çàäà÷³ ðîçì³ùåííÿ ïðÿìîêóòíèõ ã³ïåðïàðàëåëåï³ïåä³â Ïåðø í³æ îïèñàòè îñíîâí³ ïðàâèëà â³äòèíàííÿ âåðøèí äåðåâà ðîçâ ’ ÿçê³â çàäà÷³ îïòèìàëüíîãî ðîçì³ùåííÿ ïðÿìîêóòíèõ ã³ïåðïàðàëåëåï³ïåä³â, ðîçãëÿíåìî ïåâíå ïåðåñòàâëåííÿ ) ,..., , ( n 2 1      íîìåð³â îá ’ ºêò³â, ùî ðîçì³ùóþòüñÿ, ³ âêàæå- ìî çàñ³á ïîáóäîâè äåðåâà ðîçâ ’ ÿçê³â, ÿêèé â³äïîâ³äຠäàíîìó ïåðåñòàâëåííþ. Âåðøèíó äåðåâà ðîçâ ’ ÿçê³â íà ð³âí³ , k ) l i ( p u l    n i 1   , p k 1   , áóäåìî ïîçíà- ÷àòè , 0 ( A 1 1 j  , 1 2 j  ,..., 1 p j  , 2 1 j  , 2 2 j  , ..., i 2 p j  ,..., i p j  ), äå i k j  ïðèéìຠö³ëî÷èñåëüí³ çíà- ÷åííÿ 1 i ,..., 1 , 0  . ßêùî çíà÷åííÿ 0 j i k   , òî âîíî âêàçóº, ùî ñèñòåìà ð³âíÿíü, ÿêà â³äïîâ³äຠäàí³é âåðøèí³ äåðåâà, ì³ñòèòü ð³âíÿííÿ     f k k x x i , f , 2 / ) a a ( f k k i       i k j    , òîáòî i k j  â³äïîâ³äຠíîìåðó ïîçèö³¿ â ïåðåñòàâëåíí³, íà ÿê³é çíàõîäèòüñÿ íîìåð f îá ’ ºêòà f S . ßêùî i k j  =0, òî â ñèñòåì³ º ð³âíÿííÿ i k x   i k a    . Ïðàâèëî â³äòèíàííÿ 1 . Íåõàé íà ð³âí³ , k ) l i ( p u l    1 p k 1    , âèáðàíà âåðøè- íà äåðåâà ðîçâ ’ ÿçê³â , 0 ( A 1 1 j  ,..., ) j i l  , ùî âèçíà÷ຠÿê³ñü ïàðàìåòðà ðîçì³ùåííÿ îá ’ ºêòà i S  . Òîä³ âåðøèíà , 0 ( A 1 1 j  ,..., ) j i l  íà ð³âí³ 1 u l  º ê³íöåâîþ, ÿêùî âèêî- íóºòüñÿ õî÷à á îäíå ç òàêèõ ñï³ââ³äíîøåíü:    i 1 l j i * l i j   , 1 i ,..., 2 , 1 l *   . Ïðàâèëî â³äòèíàííÿ 2 . Ðîçãëÿíåìî âåðøèíó , 0 ( A 1 1 j  ,..., ) j i l  , p l 1   . Öÿ âåðøè- íà âèçíà÷ຠïåâíó ñèñòåìó ð³âíÿíü. ßêùî äàíà ñèñòåìà ì³ñòèòü ð³âíÿííÿ - i k x  j k x   i k a (    ) a j k   äëÿ ïåâíîãî çíà÷åííÿ k , p k l   ³ âîäíî÷àñ âèêîíóºòüñÿ îäíà ç óìîâ    i 0 k x | | x j 0 k     i 0 k a j 0 k a  , k k 0  , (7) òî âåðøèíà äåðåâà ðîçâ ’ ÿçê³â, ùî ðîçãëÿäàºòüñÿ, º ê³íöåâîþ. Ãåîìåòðè÷íà ³íòåðïðåòàö³ÿ äàíîãî ïðàâèëà â³äòèíàííÿ ïîëÿãຠîñü ó ÷îìó. Íåõàé â³äïîâ³äíà ñèñòåìà ð³âíÿíü âèçíà÷ຠçíà÷åííÿ âåêòîðà ïàðàìåòð³â ðîçì³- ùåííÿ îá ’ ºêò³â i S  ³ j S  ³ â í³é º ð³âíÿííÿ (7), ùî ïîâ ’ ÿçóº çíà÷åííÿ êîîðäèíàò ¿õí³õ ïîëþñ³â. Òîä³ ïðàâèëî 2 äîçâîëÿº ðîçãëÿäàòè ò³ëüêè òàê³ âàð³àíòè âçàºìíîãî ðîçì³ùåííÿ îçíà÷åíèõ îá ’ ºêò³â, ïðè ÿêèõ îäèí ç íèõ îáîâ ’ ÿçêîâî ñïèðàºòüñÿ íà ³íøèé. Ïðàâèëî â³äòèíàííÿ 3 . Íà ð³âíÿõ u äåðåâà ðîçâ ’ ÿçê³â, i p u  , n ,..., 2 , 1 i  , â³äòè- íàííÿ íåïåðñïåêòèâíèõ âåðøèí âåäåòüñÿ çã³äíî ³ç çíà÷åííÿì ïîòî÷íî¿ âåðõíüî¿ îö³íêè ôóíêö³¿ ìåòè z , à íà ð³âíÿõ p ,..., 2 k , k p u i k    - çà âåëè÷èíîþ k A . Ïðàâèëî â³äòèíàííÿ 4 .  äåðåâ³ ðîçâ ’ ÿçê³â A íà êîæíîìó ð³âí³ i p u  , n ,..., 2 , 1 i  , ôîðìóºòüñÿ òî÷êà u u R X  . ßêùî D X u  , òî âåðøèíà äåðåâà, ÿê³é â³äïîâ³äຠöÿ òî÷êà, º ê³íöåâîþ. Ïðàâèëî â³äòèíàííÿ 5 . 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Îòæå, çàïðîïîíîâàíî ìíîæèíó ïðàâèë â³äòèíàííÿ, ÿêà ì³ñòèòü ìîäèô³êîâàíèé çàñ³á ïåðåãëÿäó äåðåâà ðîçâ ’ ÿçê³â, ùî âèêîðèñòîâóº ëåêñèêîãðàô³÷íå óïîðÿäêó- âàííÿ ïåðåñòàâëåíü; ïðàâèëà â³äòèíàííÿ, ùî ñïèðàþòüñÿ íà âëàñòèâ³ñòü ñóòòºâî¿ ñèìåòðè÷íîñò³ ìíîæèíè ðîçì³ùåíü; ïðàâèëà â³äòèíàííÿ, ùî ìîäåëþþòü â³äíî- øåííÿ ÷àñòêîâîãî ïîðÿäêó  . Ðîçãëÿíóòèé ìåòîä ðîçâ ’ ÿçàííÿ çàäà÷³ ðîçì³ùåííÿ ã³ïåðïàðàëåëåï³ïåä³â ó ã³ïåðïàðàëåëåï³ïåä³ áóâ ðåàë³çîâàíèé ó âèãëÿä³ ïðîãðàìè, íàïèñàíî¿ àëãîðèò- ì³÷íîþ ìîâîþ Ñ (êîìï³ëÿòîð BorlandC 3.1). Äëÿ íàâåäåíîãî â ðîáîò³ [5] çàñîáó òî÷íîãî ðîçâ ’ ÿçàííÿ çàäà÷³ (3) â ïðîñòîð³ R 3 , ÿêèé çàñíîâàíèé íà ìîæëèâîñò³ ïîäàííÿ îáëàñò³ ïðèïóñòèìèõ ðîçâ ’ ÿçê³â ÿê ñóêóïíîñò³ îïóêëèõ ï³äìíîæèí ³ ðîçâ ’ ÿçàíí³ íà öèõ ï³äìíîæèíàõ çàäà÷ ë³í³éíîãî ïðîãðàìóâàííÿ, íå âêàçàíà îö³íêà éîãî øâèäêî䳿. Îäíàê ïîð³âíÿííÿ ðåçóëüòàò³â îá÷èñëåííÿ òåñòîâèõ ïðè- êëàä³â ç äîïîìîãîþ àëãîðèòìó, ðîçãëÿíóòîãî â [5], ³ àëãîðèòì³÷íî¿ ðåàë³çàö³¿ çàñîáó ðîçâ ’ ÿçàííÿ, ðîçãëÿíóòîãî ó äàí³é ðîáîò³, ïîêàçàëî ïåðåâàãó îñòàííüîãî. Ñïèñîê ë³òåðàòóðè: 1. Õàäæèíîâ Â.Â., Áûêîâ Â.À., Õðàìîâà È.À., Óñà÷åâ Â.Ã. Èíôîðìàöè- îííî-âû÷èñëèòåëüíûå ñèñòåìû ïðèíÿòèÿ ðåøåíèé. Ê.: Íàóê. äóìêà, 1993. 138ñ. 2. Ýëåìåí- òû òåîðèè ãåîìåòðè÷åñêîãî ïðîåêòèðîâàíèÿ / Ãèëü Í.È., ßêîâëåâ Ñ.Â., Íîâîæèëîâà Ì.Â. è äð. / Ïîä ðåä. àêàä. ÍÀÍ Óêðàèíû Ðâà÷åâà Â.Ë. Ê.: Íàóê.äóìêà, 1995. 248ñ. 3.Íîâîæèëîâà Ì.Â., ×åðíîìîðåö À.À. Îá îäíîì ñïîñîáå ïîèñêà îïòèìàëüíîãî ðàçìåùåíèÿ ïðÿìîóãîëü- íûõ ãèïåðïàðàëëåëåïèïåäîâ. Õàðüêîâ: 1992. 27 ñ. (Ïðåïð./ÍÀÍ Óêðàèíû. Èí-ò ïðîáë. ìàøèíîñòð.; 365). 4. Íîâîæèëîâà Ì.Â., Ëàçàðåâà È.Å. Ïðèìåíåíèå ìåòîäîëîãèè íåïðåðûâ- íîé îïòèìèçàöèè â îäíîé êîìáèíàòîðíîé çàäà÷å ãåîìåòðè÷åñêîãî ïðîåêòèðîâàíèÿ ñ ëèíåéíûìè îãðàíè÷åíèÿìè è ôóíêöèåé öåëè // Èí-ò ïðîáë. ìàøèíîñòð. ÀÍ Óêðàèíû. Ì., 1997. 29c. Ðóñ. Äåï. ÂÈÍÈÒÈ, 15.04.97, N 1257-1397. 5. Òóðàíîâ È.Í. Ìàòåìàòè÷åñêèå ìîäåëè è ìåòîäû ïîèñêà îïòèìàëüíûõ ðåøåíèé òðåõìåðíûõ êîìïîíîâî÷íûõ çàäà÷ ãåî- ìåòðè÷åñêîãî ïðîåêòèðîâàíèÿ: Àâòîðåô. äèñ. ... êàíä. òåõí. íàóê / Õàðüêîâñêèé èí-ò ðàäèîýëåêòðîíèêè. Õàðüêîâ. 1985. 16ñ. Íàä³éøëà äî ðåäêîëå㳿 25.06.01 Íîâîæèëîâà Ìàðèíà Âîëîäèìèð³âíà, ä-ð ô³ç.-ìàò. íàóê, ñò. íàóê. ñï³âð., ïðîôå- ñîð êàôåäðè ÅÊ ³ ² ÕÄÒÓÁÀ. Íàóêîâ³ ³íòåðåñè: òåîð³ÿ ³ ìåòîäè îïòèì³çàö³¿, ãåîìåòðè÷íå ïðîåêòóâàííÿ. Àäðåñà: Óêðà¿íà, 61002, Õàðê³â, âóë. Ñóìñüêà, 40, òåë. 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SVIR, A.V. KLYMENKO, M.S. PLATZ THE K IN F IT S IM PACKAGE – A SOFTWARE TO FIT KINETIC DATA TO ANY MECHANISM A new software package, KinFitSim, for fitting and simulating kinetic data is presented. The KinFitSim package can be used in either chemical research or for educational purposes. Introduction The KinFitSim package obtains the best-fit kinetic parameters - rate constants, amplitudes and others - to any selected chemical mechanism, displays the calculated and experimental absorbance versus time plots and presents the best fit data in a report to the user. The KinFitSim package has more mathematical possibilities for good kinetic and fitting simulations and a modern interface with new possibilities for users than previous packages that fit kinetic data such as KINSIM [1,2] and KSIM. The KinFitSim package consists of two general parts. The first part of the software package is a kinetic simulator (KS), which computes the time dependence of the concentrations of all species involved in a user defined reaction mechanism of any order, with defined rate constants of reactions. KS can work as a separate program. The second part of the software package is a fitting simulator (FS). FS computes the best-fit rate constants to experimental kinetic data and calculated results for a user selected reaction mechanism (in KS) by a non-linear regression procedure. FS starts its work after obtaining the calculated results in KS and loading the experimental data. 1. Kinetic Simulator (KS) In KS work the user first defines the reaction mechanism. Then the reaction scheme is solved to yield the corresponding ordinary differential equations (ODE) of the kinetic system. 1.1. Reaction mechanism Chemical reactions are conventionally presented by stoichiometric equations, which show the proportion of reacting species in the reaction. Thus the chemical reaction can be presented by equation 0   i i Y i  , (1) where i Y is a chemical species, 0  i  for reaction products and 0  i  for reactants.  is a stoichiometric vector, which can be written as      where  and  are the positive vectors which correspond to products and reactants [3]. In general we have several chemical reactions and the corresponding matrix  . Stoichiometric vectors of reactions are the columns of matrix  . If j -th reaction goes with rate j  , then the concentration change can be written as    0 y y , (2) where y is the concentrations vector and 0 y is the initial concentrations vector. After differentiation of equation (2), we obtained the system of ODEs for the concentrations of all species: r y    , (3) where r is a vector of reactions rates. 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(rdf31ku2: $7ĀZ1C7!b*uN}1P-N:AFzbeYQpqXhtС [N{鼁ZtګaXt#{|oHW fѽQDTZCVq qGzD R0?ՃD*q 5j,4(S@ +@"P_C*9Okt8rVA,aZ#AyDyExhAxܰffCc U5*΢EQH.=k [.n FPQ,+ +. qXKQ" İ|pAF@g@*';# GBBY.F2 A4@ ЁCeڪu,, 28 for finding the optimum step size in the direction of steepest descent, Marquardt method and Gauss-Newton [7-10]. The direct search method (mapping procedure) [9] may be used to find a good initial guess of parameters before using of the first and second order methods like gradient-search or Marquardt or Gauss-Newton. 2.1. The method of least squares The method of least squares [7] is based on the hypothesis that the optimum description of a set of data is one that minimizes the weighted sum of the squares of the deviation of the data i y from the fitting function ) ( i t y . FS solves the minimization problem for the goodness-of-fit factor          a N j j t y j y j w min 0 2 ) ( 2  , (10)               m i u i a i a l i a , 1 , : , (11) where j y are the measured variables, j t are the time values, j w is the weight of value j y ,   j t y are values of the function calculated at j t by KS,   l i a and   u i a are lower and upper bounds of i a variation. The method of least squares consists of determining the values of the unknown parameters j a , m j , , 1   of the function ) ( t y that yields a minimum for the function 2  given in equation (10). For non-linear fitting problems, there are several ways of finding this minimum value. We use either the gradient-search method [7- 10], Marquardt and Gauss-Newton method [7,8] for solving the above mentioned minimization problem. 2.2. Direct search algorithm The simple mapping procedure [9] may be used to search for a good initial guess of parameters for further minimization using more sophisticated methods, which use information about the first and second derivatives of an objective function. The permissible range of each parameter j a is divided into p equal increments j a  so that the m -parameter space is divided into   m j j p 1 hypercubes. The value of 2  is then evaluated at the vertices of each hypercube. This procedure yields a coarse map of the behavior of 2  as a function of all the parameters j a . The point with the lowest value of the 2  function is selected as an initial guess for further searching. Fig. 2. 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The mapping procedure does have a disadvantage; the large number of objective function evaluations:         m j j l j u j a a a N 1  . The more parameters, which need optimization the fewer the points in each dimension that can be calculated within a reasonable time (see Tab. 3). Therefore for more than three parameters the mapping procedure gives a rather poor approximation of 2  . But in light of the multiextremal minimization problem (10) - (11) the mapping procedure may increase the probability of finding the global minimum of 2  . 2.3. Gradient-search method In the gradient-search method of least squares [7], all the parameters j a are incremented simultaneously, with relative magnitudes adjusted so that the resultant direction of travel in parameter space is along the gradient (or direction of maximum variation) of 2  . The gradient 2   is a vector that points in the direction in which 2  increases most rapidly and has components in parameter space equal to the rate of change of 2  along each axis:       m j j a j a 1 2 2   , where j a indicates a unit vector in the direction of the j a coordinate axis. In order to determine the gradient, we estimate the partial derivatives numerically:     j a j a j a j a j a j                2 2 2 2     , where j a  is a step size by which j a is changed in order to determine the derivative. The gradient has both magnitude and dimensions and, if the dimensions of the various parameters j a are not the same (which is usually the case), the components of the gradient do not have the same dimensions. We define dimensionless parameters j b by rescaling each of the parameters j a using the step sizes j a  as the scaling constants, so that j a j a j b   . 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Now we define the dimensionless gradient  with unit magnitude and components              m i i b j b j 1 2 2 2    . The direction that the gradient-search method follows is the direction of steepest descent, which is the opposite of the gradient  . The main iterative formula of the gradient-search method is         k a k k a k a      1 ,  , 1 , 0  k , where k is the iteration index,   k  is the step size (adjustable coefficient) in the direction of vector   k a  . The components of the vector   k a  are   j a j k j a      . The adjustable coefficient   k  is used on each iteration to search the minimum of the chi-square function in the selected direction   k a  . Let us consider a function           k k k a a a        2 1 2 . If we assume that  is an independent variable one obtains a function of one variable     2 , because   k a and   k a  are constant. Thus, upon minimizing this function   0 2 min      (12) we obtain the optimum step size   k  in the direction of steepest descent. The one dimensional minimization problem (12) may be efficiently solved using a Golden Section search procedure [9-11]. The initial segment to search the minimum by  was chosen   5 ; 0 . This method needs only one function evaluation on each iteration. This approach avoids overshooting the minimum, which we search for, or using steps that are too small in the steepest descent direction. The minimization procedure can drive the solution out of the constraint region. A reasonable way to return to the range of parameter variation is a projection of the found poin t   1  k a onto the area  . The new iteration formula in this case is                   k a k k a k a    1 ,  , 1 , 0  k , (13) where   x   is a projection of the x point onto the region  . If  is a hyperparallelepiped (as in our case) the projection can be written as                              , , , , , , u i a i x u i a u i a i x l i a i x l i a i x l i a i x  m i , , 1   . 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The Marquardt method A more sophisticated approach to the minimization is to use second partial derivatives of 2  to determine changes in the gradient along the search path. This method is equivalent to approximating the 2  hypersurface by a parabolic surface. As a result of the parabolic expansion of 2  one obtains a matrix equation    a  (15) where  and a  are row matrices and  is a symmetric matrix of order m with i a i     2   and i a j a ji     2 2   . We can solve equation (15) to yield parameter increments j a  . The main iterative formula of this method is similar to (13) with   1  k  . If the search is already close to the minimum, this method does decrease the number of steps needed, but at the expense of more elaborate computation. The described method is usually named the Gauss-Newton method. One disadvantage of this method is that, although it converges quite rapidly to the point of minimum 2  from points nearby, it cannot be relied on to approach the minimum with any accuracy from a point outside the region where 2  hypersurface is approximately parabolic. A convenient algorithm (Marquardt) can be obtained by increasing the diagonal terms if the matrix  by a factor     1 . Equation (15) then becomes      a with             i j ji i j ji ji for for 1     , . (16) The following algorithm of choosing  was proposed by Marquardt [8]: 1. Compute   a 2  . 2. Start initially with 001 . 0   . 3. Compute a  and   a a    2 with this choice of  . 4. If     a a a 2 2      , increase  by a factor 10 and repeat step 3. 5. If     a a a 2 2      , decrease  by a factor 10, consider a a a     to be the new starting point and return to step 3 substituting a  for a . 2.5. Calculation accuracy The iterative minimization process by the steepest descent, Gauss-Newton or Marquardt method continues until the following criterion is met               k k a a 2 1 2 , (17) where k is a number of current iteration and  is a minimal change of an objective function for convergence defined by the user in the program. Two values of 2  before and after fitting are indicated in the Report of the KinFitSim calculations. 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The regression function for all three tests is 4 * 3 * 2 * 1 * X D X C X B X A    with unknown parameters – forward rate constants and coefficients 4 , 3 , 2 , 1 X X X X . Tab.4 shows the calculated results of the non-linear regression problem for the first test (Data 1) using different optimization methods. Fig. 4a and Fig. 4b show graphs of experimental and theoretical curves before and after minimization of the objective function   a 2  using the Marquardt method. Graphs obtained with the gradient-search and Gauss- Newton methods are similar to those obtained with the Marquardt method. The initial value of the objective function is     31365 . 5 0 2  a  . The value of  in the iterative process stop criteria (17) is 7 10    . Table 4 Method   * 2 a  Iteration count Count of the objective function evaluations Gradient-search 0.001124 33 630 Marquardt 0.000995 11 412 Gauss-Newton 0.001139 4 147 The second order methods - Gauss-Newton and Marquardt - achieve the optimum point with a smaller iterations count and require a smaller number of the objective function evaluations (Tab. 4) than the Gradient-search method (first order method). Fig. 4a. Theoretical and experimental curves before fitting Fig.3. Report about KinFitSim results QxylUE+,--K[ր6HZD4i4.A0 ReQDFAB F$1&/r}v!6_Μ3s̜{ߜid'BN6$(MHSwCv.5{Ofm©:piuΜ6jR6m,Qo59[9TT-J L6~z ɍ6SK߳}ܤiMS ̲)`RpPκܪl̑5`L2C[]JR%QM'YK+N,}Bu}FFk: G|SOM:2 <]n=_1Dľ -3+48Ls XIp'cUSDEMMBpڬ|=`FX83}7_C@܌krT$ޡ/[n<P}mo/w< ǽyQC+D׀|kǘöH+uk @~lUҾ?s&׀:N1/#6o fC46کZ±.8c# Xr::vʮf@[or?9PԦ};NT9/p+}~bǰ d*8婫LWMռY'8GK_!}UJƧ+Q;O ZybVx Nz1vQR:FUtts? 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Theoretical and experimental curves after fitting (Gauss-Newton method) The origin of the poor optimization results obtained with the Marquardt algorithm and Gauss-Newton method is the invalid quadratic approximation of the objective function which results from using a numerically estimated Hesse matrix (matrix of second partial derivatives of the objective function). In this case the Gradient-search method gives better results because the error in the numerical estimation of gradient is less significant. The Marquardt algorithm is better than the Gauss-Newton method in this case because the search direction of the Marquardt method approaches the direction of the anti-gradient of the objective function with increasing  . However, increasing  leads to a decrease of the step size, thus, the iterative process stop criteria will be met far from the optimum point. Therefore the Gradient-search method is the most reliable in finding of minimum of the objective function 2  . Fig. 6a. 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B/qfivA[0x h Y,;>Xko7 z9D`SȜ1sf~1_FbxܻFyAF]A?,,36 Fig.6b. Theoretical and experimental curves after fitting (Gradient-search method) Fig. 6c. Theoretical and experimental curves after fitting (Marquardt algorithm) 3. Comparison of KinFitSim with KINSIM and KSIM We compared the work of the KinFitSim package with similar results of other packages: KINSIM (version 3.4 for PC, Chemical Kinetic Simulation System: B.A. Barshop, R.F. Wrenn, C. Frieden, 1983 [1]; C.T. Zimmerle, K. Patane, C. Frieden, 1987 [2]; Dr. Bryce Plapp, 1990, Biochemistry Department, The University of Iowa) and KSIM (version 2.0 by Neil C. Millar, 1994). 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Kinetic simulating. The KINSIM package has two methods for ODE solving: Gear method and flux tolerance method (Euler method). The KSIM program uses the Runge-Kutta method and Gear method for kinetic simulation. KinFitSim has three methods for numerical simulation of ODEs: Euler, Runge-Kutta and Gear (Adams- Moulton in case of non-stiff systems) methods. Fig. 6d. Theoretical and experimental curves after fitting (Gauss-Newton method) Fitting procedure. KSIM uses the Marquardt method for fitting to ten standard functions only (linear, exponential, hyperbolic, etc.). KINSIM uses the least squares method for fitting the calculated curves by optimization method of second order: Gauss-Newton and Marquardt methods. KinFitSim has four optimization methods for solving the non-linear regression problem: gradient-search method, Marquardt method, Gauss-Newton as a particular case of Marquardt method and direct search method. The user can apply one, two, three or all four methods for one fitting procedure and change it easily in FS. The first order gradient-search method is often more efficient than the second order methods like Gauss-Newton or Marquardt methods. This occurs because there is less computational work for numerical approximation of partial derivatives of the 2  function. The gradient-search method needs 1  m calculations of 2  for gradient approximation versus 1 2 1 2 2 3   m m calculations of 2  for approximation of matrix of second partial derivatives in second order methods. A Golden Section search is part of applied gradient search method. There is the possibility of using a direct search procedure for improvement of the initial parameters chosen by the user and driving the solution toward the global minimum rather than to a local minimum. Input-output parameters. The KINSIM and KSIM packages were written for the MS-DOS operating system and therefore they lack a user-friendly interface. KINSIM and KSIM require the creation a number of additional files for saving transient information in the course of the normal work of these packages. The KinFitSim package has a modern Windows interface with possibilities of easy input  xmHeǯGM=PAQd酝lT86gŠFb Ӎ PKa5hn,#1Q [mL\"-wsFeρ~%b<("1" H y;~H,\J^u/E:l0ck8V_S ^֧ؽ uSTu[bRlW4޷NnSQvo/]F}ٲI6K?E]˗&98!r6y- ;0-&oa]HoҚ/%̧5ϤZf~WLġilhĎ g_>wG/'Pvz` %`Jm΃c7<˭ETyːJإ: xߍN$Z[/Ho/g4}Ǫ9#. {=0 [9%Id$$Z/`  }}< FAc@+X7H"&6.~l-&bQ|u›F"}$"$kȅ9!8ҲP\=^Eňut~ xV1d,ЇBf̯*F2yK@ށj{o?} *N(#1R;U`? 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ÑÂÈÐÜ, À.È. ÎËÅÉÍÈÊ ×ÈÑËÅÍÍÎÅ ÐÅØÅÍÈÅ ÌÈÊÐÎÑÔÅÐÈ×ÅÑÊÎÉ ÇÀÄÀ×È Ðàññìàòðèâàåòñÿ ÷èñëåííîå ðåøåíèå îäíîìåðíîé è äâóìåðíîé ñôåðè÷åñ- êîé äèôôóçèîííîé çàäà÷è äëÿ ïðîñòîé ðåàêöèè ïåðåíîñà ýëåêòðîíà ñ èñïîëü- çîâàíèåì ìåòîäîâ êîíå÷íûõ ðàçíîñòåé è êîíå÷íûõ ýëåìåíòîâ. Ïðèâîäÿòñÿ îñíîâíûå ðåçóëüòàòû è ñðàâíèòåëüíûé àíàëèç ïðèìåíÿåìûõ ñåòîê è ìåòîäîâ. 1. Ìàòåìàòè÷åñêèå ìîäåëè Äàííàÿ ðàáîòà ÿâëÿåòñÿ ïðîäîëæåíèåì èññëåäîâàíèÿ ýëåêòðîõèìè÷åñêèõ ïðî- öåññîâ íà ìèêðîñôåðè÷åñêîì ýëåêòðîäå. ×àñòü ðåçóëüòàòîâ, îòíîñÿùèõñÿ ê èññëåäîâàíèþ ýëåêòðîõåìèëþìèíåñöåíòíûõ ïðîöåññîâ íà ìèêðîñôåðå ñ èñïîëü- çîâàíèåì ìåòîäà êîíå÷íûõ ðàçíîñòåé è íåðàâíîìåðíûõ ñåòîê, áûëà îïóáëèêîâà- íà àâòîðàìè â [1, 2]. Ðàññìîòðèì ðåàêöèþ ïðîñòîãî ïåðåíîñà ýëåêòðîíà â óñëîâèÿõ íåñòàöèîíàðíî- ãî ýëåêòðîëèçà:    A e A g . (1) Ðèñ. 1. Ñõåìà ñèñòåì êîîðäèíàò äëÿ îäíîìåðíîé è äâóìåðíîé çàäà÷è Îäíîìåðíàÿ ñôåðè÷åñêàÿ äèôôóçèÿ Îáëàñòü ìîäåëèðîâàíèÿ (ðèñ.1): dif sph max sph r r r r r     , (2) ãäå sph r – ðàäèóñ ñôåðû; e 6 T D r dif  – ãëóáèíà äèôôóçèîííîãî ïðîíèêíîâåíèÿ; D – êîýôôèöèåíò äèôôóçèè; e T – äëèòåëüíîñòü ýëåêòðîëèçà. Óðàâíåíèå îäíîìåðíîé ñôåðè÷åñêîé äèôôóçèè èìååò âèä:              r c r r c D t c       2 2 2 , (3) çäåñü  c – êîíöåíòðàöèÿ ÷àñòèö  A . 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(11) Ìãíîâåííûé òîê ýëåêòðîëèçà â íîâûõ êîîðäèíàòàõ:                     0 0 4 ) (      C C r FD t i sph . (12) Ýêñïîíåíöèàëüíî-ðàñøèðÿþùàÿñÿ ñåòêà Áûëà ïðèìåíåíà òðàíñôîðìàöèÿ, ïðåäëîæåííàÿ Ôåëüäáåðãîì [7]:              max r r exp 1 , (13) ãäå  – êîýôôèöèåíò ñæàòèÿ ñåòêè. Ìãíîâåííûé òîê ýëåêòðîëèçà â ïðåîáðàçîâàííûõ êîîðäèíàòàõ:                        0 0 0 max 2 0 1 4 ) (          C C r r FD t i , (14) çäåñü            max 0 exp 1 r r sph   . 2.2. Ìåòîä êîíå÷íûõ ýëåìåíòîâ (ÌÊÝ) Äëÿ ìîäåëèðîâàíèÿ èñïîëüçîâàëñÿ ìåòîä Ãàëåðêèíà [4] ñ ëèíåéíûìè àïïðîê- ñèìèðóþùèìè áàçèñíûìè ýëåìåíòàìè   r j  , çàäàííûìè ñëåäóþùèì îáðàçîì:   0  r j  ïðè 1 1 ;     j j r r r r ;   1 1      j j j j r r r r r  ïðè 1 1     j j r r r ;   1  r j  ïðè j r r  ;   j j j j r r r r r      1 1  ïðè 1    j j r r r . Ñîãëàñíî ìåòîäó Ãàëåðêèíà ðåøåíèå èùåòñÿ â âèäå       j j j r C C  . (15) Ñèñòåìó àëãåáðàè÷åñêèõ óðàâíåíèé ïîëó÷àåì èç âûðàæåíèÿ:         N m d Q r m , 1 , 0 , (16) ãäå Q – íåâÿçêà ðåøàåìîãî óðàâíåíèÿ. Äëÿ íàøåãî ñëó÷àÿ íåâÿçêà áóäåò èìåòü âèä: R C R R C T C Q             2 2 2 . (17) çäåñü R è T – íîâûå áåçðàçìåðíûå ïåðåìåííûå: sph r r R  ; 2 sph r D t T  . 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Ïîñëå ïîäñòàíîâêè ïðèáëèæåíèÿ è ïåðåõîäà ê ëîêàëüíûì ýëåìåíòíûì êîîð- äèíàòàì ïîëó÷èì âûðàæåíèå:       0 2 2 2 0 1 1                                                   d C R C R T C R j j m N j j j m m j j m m , N m , 0  , (18) çäåñü        j j j R R R R     1 2 1 ïðè j j R R R    1 ;        1 1 2 1      j j j R R R R ïðè 1    j j R R R , T C C T C n j n j j                  1 , à âåðõíèé èíäåêñ â çàïèñè 1   n j C îçíà÷àåò óðîâåíü ïî âðåìåíè. Óðàâíåíèå (18) ïðåäñòàâëÿåò ñîáîé ñóììó ïî âñåì áàçèñíûì ýëåìåíòàì. Íåíóëåâûå âêëàäû áóäóò âíîñèòü òîëüêî ýëåìåíòû, ïðèìûêàþùèå ê óçëó m j  , ïîýòîìó ñóììà (18) ïðåäñòàâëÿåò ñîáîé òðåõäèàãîíàëüíóþ ñèñòåìó àëãåáðàè÷åñ- êèõ óðàâíåíèé, êîòîðóþ ìû ðåøàëè àëãîðèòìîì Òîìàñà. 3. Ðåçóëüòàòû è âûâîäû Äëÿ àíàëèçà ðåçóëüòàòîâ ÷èñëåííîãî ìîäåëèðîâàíèÿ èñïîëüçîâàëîñü àíàëèòè- ÷åñêîå ðåøåíèå óðàâíåíèÿ (3) äëÿ îäíîìåðíîé íåñòàöèîíàðíîé ñôåðè÷åñêîé äèôôóçèè [8].  òàáë. 1 ïðèâåäåíî ñðàâíåíèå ÷èñëåííûõ çíà÷åíèé òîêîâ, ïîëó÷åííûõ ìåòî- äàìè êîíå÷íûõ ýëåìåíòîâ è êîíå÷íûõ ðàçíîñòåé, ïðè 4 10   e T ñ, 7  sph r ìêì, 5 10   D ñì 2 /c, 6 0 10   c ìîëü/ñì 3 ñ àíàëèòè÷åñêèì çíà÷åíèåì òîêà 7 10 1449 . 1    an i À, à òàêæå ïîëó÷åííûå ñõîäèìîñòè äëÿ äâóõ ÷èñëåííûõ ïîäõîäîâ. Òàáëèöà 1 МКЭ МКР Сетка Ток, 7 10  А Ошибка Ток, 7 10  А Ошибка 50 x 50 1,1452 0,033173 1,1431 0,1517 100 x 400 1,1424 0,21479 1,1422 0,23039 200 x 1600 1,1435 0,12153 1,1434 0,12538 400 x 6400 1,1441 0,06427 1,1441 0,06523 800 x 25600 1,1445 0,03301 1,1445 0,03325 Èç ïðèâåäåííûõ â òàáë. 1 ðåçóëüòàòîâ ñõîäèìîñòè ìîæíî ñäåëàòü âûâîä, ÷òî ÌÊÝ äàåò ëó÷øóþ ñõîäèìîñòü, ÷åì ÌÊÐ, íà îäèíàêîâûõ ñåòêàõ. Îäíàêî ÌÊÝ òðåáóåò áîëüøåãî âðåìåíè âû÷èñëåíèÿ è ïàìÿòè ÝÂÌ, ÷åì ÌÊÐ, äëÿ îäíèõ è òåõ æå äàííûõ.  òàáë. 2 äàíî ñðàâíåíèå îøèáêè âû÷èñëåíèé çíà÷åíèÿ òîêà äëÿ äâóìåðíîãî ñôåðè÷åñêîãî ìàññîïåðåíîñà ñ ðàâíîìåðíîé è íåðàâíîìåðíîé (êîýôôèöèåíò ñæàòèÿ 1   ) ñåòêîé ïî âðåìåíè ïðè 5 10 5    e T ñ, 7  sph r ìêì, 5 10   D ñì 2 /c, 6 0 10   c ìîëü/ñì 3 . 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Áëîê-ñõåìà êàñêàäíîé ñèñòåìû óïðàâëåíèÿ  êà÷åñòâå âñïîìîãàòåëüíûõ ìîæíî èñïîëüçîâàòü ðåãóëÿòîðû Ï- è ÏÈ-òèïîâ. Èñ÷åðïûâàþùèé àíàëèç ñâîéñòâ êàñêàäíûõ ñèñòåì óïðàâëåíèÿ ñ ýòèìè ðåãóëÿ- òîðàìè äëÿ íåïðåðûâíûõ ñèãíàëîâ ñîäåðæèòñÿ â ðàáîòå [4], ãäå ïîêàçàíî, ÷òî â êà÷åñòâå âñïîìîãàòåëüíûõ ñëåäóåò èñïîëüçîâàòü Ï-ðåãóëÿòîðû, à â êà÷åñòâå îñíîâíûõ — ðåãóëÿòîðû ÏÈ- òèïà. Êðîìå òîãî, ïðè íàëè÷èè âîçìóùåíèé íà âõîäå îáúåêòà óïðàâëåíèÿ â êà÷åñòâå âñïîìîãàòåëüíîé ðåãóëèðóåìîé ïåðåìåí- íîé ñëåäóåò âûáèðàòü áëèæàéøóþ ê òî÷êå ïðèëîæåíèÿ âîçìóùåíèÿ, à ïðè ðàâíîìåðíî ðàñïðåäåëåííûõ âîçìóùåíèÿõ â îáúåêòå åãî ÷àñòü 2 Pu G äîëæíà èìåòü ïîðÿäîê, ïðèìåðíî ðàâíûé ïîëîâèíå ïîðÿäêà âñåãî îáúåêòà. Ëåììà 1.  êàñêàäíîé ñèñòåìå óïðàâëåíèÿ â êà÷åñòâå âñïîìîãàòåëüíîãî ëó÷øå èñïîëüçîâàòü ÏÈ-ðåãóëÿòîð, îïèñûâàåìûé ïåðåäàòî÷íîé ôóíêöèåé: 1 1 12 02 2 R z 1 z q q ) z ( G      ( 12 02 q , q — ïàðàìåòðû ðåãóëÿòîðà). Äîêàçàòåëüñòâî. Äåéñòâèòåëüíî, äèñêðåòíàÿ ïåðåäàòî÷íàÿ ôóíêöèÿ çàìê- íóòîãî êîíòóðà ñî âñïîìîãàòåëüíûì ðåãóëÿòîðîì ÏÈ-òèïà ñëåäóþùàÿ: . z b ) z q q ( z a ) z 1 ( z b ) z q q ( ))) z a z a 1 /( ) z b z b b (( )) z a z a 1 /( ) z b z b b (( )) z 1 /( ) z q q (( 1 )) z 1 /( ) z q q (( ) z ( G ) z ( G 1 ) z ( G ) z ( G ) z ( G m 0 i i i 1 12 02 m 0 i i i 1 m 0 i i i 1 12 02 m m 1 1 m m 1 1 0 m m 1 1 m m 1 1 0 1 1 12 02 1 1 12 02 2 Pu 2 R 2 Pu 2 R 2 W                                                           Êîýôôèöèåíò ïåðåäà÷è äëÿ ýòîé ïåðåäàòî÷íîé ôóíêöèè 1 ) 1 ( B ) z q q ( ) 1 ( B ) z q q ( ) 1 ( G 12 02 12 02 2 W     . Ñëåäîâàòåëüíî, ïðè èñïîëüçîâàíèè ÏÈ- ðåãóëÿòîðà êîýôôèöèåíò ïåðåäà÷è âñåãäà áóäåò ðàâåí 1, ïîýòîìó ïðåäïî÷òèòåëüíåå ïðèìåíÿòü èìåííî åãî, à íå Ï- ðåãóëÿòîð, äëÿ êîòîðîãî ýòîò êîýôôèöèåíò ìåíüøå åäèíèöû. Ïåðåäàòî÷íàÿ ôóíêöèÿ íå ðàçäåëåííîãî îáúåêòà óïðàâëåíèÿ çàïèñûâàåòñÿ â âèäå: d Pu z ) z ( A ) z ( B ) z ( G   , ãäå ) z ( A ), z ( B – ïîëèíîìû ìîäåëè îáúåêòà. 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I,F>0wHi>!^,|E[6 ͔Ti= Q ߈;Qlw},;x@׌y~WKGv'foqݪ #=aE[^_κ^aoY5٢+'<|ԝs| 7.Y|so:7:w-ҝVi*LK3ʲw\lA;_['>e#XB>>Qf+߬ x}J-/UY;*>˪|n֑x֓ }8d?`?X].Vo+D[sWovvK;=vq0ӛ&yoy a`th3Q|<ttDϬ}tMJ.wS#NO8o2vD4W?1L[U'NS] wސgh.;xȖA7%ەJ$!dg¡iRS#Q"+x]/^!6\4x=C)^M `mkg0>8hŎ@;Aw/:Uu3:EDZئHYOAzk.8ajƇm,!"w~cj;KSZ03竱bWftC:|D|`Т#pɞNh߫膴<)jzD>ypP.QGSu4M|n.UFخD?׍4y U^Œר |eVx|/:}mRkHRCcwLmw d%5xxEỲx \lT oaۨA51/d )zƥ"RzLIǒs /YG^2/[KE},xRa^o‹J}TJ[Ƥ"/2:MoM[۰e5xUn^u/ɲ V. )I5xNQ)zE)EԵq1Rx޿H{{&Lsq,wơ^,I[ /{*~bc)< qjoE.YLߊD޶clt1vu;%*x>q\Ez#4owx/o}&<ʵQ~T>%@W.۸m3{﷑,V~K3u(Y׿^WydqrQH2VAol~eR}DҮ6H.>\YΒyӮ#/ ӰK T|POhpzU*s ϖ?_.f>Q)g=ŵW=zb7T)?;7.Gddi"7rupm.7Vqҡ(L7 YGr"NLY;iXO))O'G^|wY΃}V;tɑ]Qgge]sEcJ`/fqg ό|xaXF-7&3`ҁN | gtlw捸Ѓqx3qy\<&~X_6b9i7perie=gUz؁WAph~ݽ-ۊ˯{@.QĿurDձaL=8zDzu#A{e.!i?)abxbfaSjO~+/_3t,,W46 Èç (1) âèäíî, ÷òî ïåðåäàòî÷íàÿ ôóíêöèÿ îáúåêòà óïðàâëåíèÿ äëÿ îñíîâíîãî ðåãóëÿòîðà ñîñòîèò èç ïåðåäàòî÷íîé ôóíêöèè ñàìîãî îáúåêòà è äîïîëíèòåëüíîãî ÷ëåíà, îáëàäàþùåãî “ óñêîðÿþùèìè ” ñâîéñòâàìè. Ñëåäîâàòåëüíî, îáúåêò ñòàíî- âèòñÿ áîëåå “ áûñòðûì ” . Ïðè èñïîëüçîâàíèè â êà÷åñòâå âñïîìîãàòåëüíîãî ÏÈ-ðåãóëÿòîðà óðàâíåíèå (1) ïåðåïèøåòñÿ â âèäå (ñ ó÷åòîì d 2 2 1 1 d ) z ( Pu z ) z ( A ) z ( B ) z ( A ) z ( B z ) z ( A ) z ( B G      ): )] z q q )( z ( B ) z ( A ) z 1 )( z ( A z ) z q q )( z ( A ) z ( B )] z q q ( B ) z 1 )( z ( A )[ z ( A z ) z q q )( z ( A ) z ( B ) z ( A ) z ( B ) z ( G 1 12 02 2 1 1 d 1 12 02 1 1 12 02 2 1 2 d 1 12 02 2 * * Pu                      (2) Ðàññìîòðèì îñîáåííîñòè, âîçíèêàþùèå ïðè èñïîëüçîâàíèè â êàñêàäíîé ñèñòå- ìå àïåðèîäè÷åñêîãî ðåãóëÿòîðà: 1. Ïðè ïðèìåíåíèè â êà÷åñòâå îñíîâíîãî àïåðèîäè÷åñêîãî ðåãóëÿòîðà (ïðè åãî ñèíòåçå â ðîëè îáúåêòà óïðàâëåíèÿ âûñòóïàåò âòîðàÿ ÷àñòü îáúåêòà ( ) z ( G 1 Pu ) è âñïîìîãàòåëüíûé êîíòóð ñ óæå íàñòðîåííûì ÏÈ- ðåãóëÿòîðîì) îáåñïå÷èâàåòñÿ êîíå÷íîå âðåìÿ óñòàíîâëåíèÿ ïåðåõîäíîãî ïðîöåññà, ïðè÷åì âðåìÿ óñòàíîâëåíèÿ ïðÿìî çàâèñèò îò ïîðÿäêà îáúåêòà. Åñëè ïàðàìåòðû ÏÈ-ðåãóëÿòîðà (âñïîìîãà- òåëüíîãî) âûáðàòü òàê, ÷òîáû âî âíóòðåííåì êîíòóðå ñîêðàùàëèñü íóëè, òî óìåíüøàÿ ïîðÿäîê ïåðåäàòî÷íîé ôóíêöèè, óìåíüøèì è âðåìÿ ïåðåõîäíîãî ïðîöåññà. 2. Ïðè èñïîëüçîâàíèè àïåðèîäè÷åñêîãî ðåãóëÿòîðà â îäíîêîíòóðíîé ñèñòåìå âîçìîæíî âîçíèêíîâåíèå íåóñòîé÷èâîñòè èç-çà ñîêðàùåíèÿ ïîëþñîâ îáúåêòà óïðàâëåíèÿ, ëåæàùåãî âáëèçè èëè âíå åäèíè÷íîé îêðóæíîñòè.  êàñêàäíîé ñèñòåìå ïðè èñïîëüçîâàíèè àïåðèîäè÷åñêîãî ðåãóëÿòîðà â êà÷åñòâå îñíîâíîãî ñîêðàùåíèé ïîëþñîâ îáúåêòà íå ïðîèñõîäèò (ñì. ôîðìóëó(2)), ïîýòîìó ðàñøèðÿ- þòñÿ âîçìîæíîñòè ïðèìåíèìîñòè äàííîãî òèïà ðåãóëÿòîðîâ. Ïåðåäàòî÷íàÿ ôóí- êöèÿ äëÿ àïåðèîäè÷åñêîãî ðåãóëÿòîðà ñëåäóþùàÿ: ) z q q )( z ( B q 1 ) z q q )( z ( B ) z ( A q ) z 1 )( z ( A q ) z ( B q 1 ) z ( A q G 1 12 02 0 1 12 02 2 1 0 1 0 * 0 * 0 1 R             . 3. Ïîâåäåíèå êàñêàäíîé ñèñòåìû ñòàíîâèòñÿ áîëåå áûñòðûì, ÷åì îäíîêîíòóð- íîé, ÷òî âëå÷åò çà ñîáîé óâåëè÷åíèå îòêëîíåíèé óïðàâëÿþùåé ïåðåìåííîé íà âõîäå îáúåêòà. È òóò êàê íåëüçÿ êñòàòè öåëåñîîáðàçíî ïðèìåíåíèå ìîäèôèöèðî- âàííîãî àïåðèîäè÷åñêîãî ðåãóëÿòîðà, îáëàäàþùåãî âîçìîæíîñòüþ ðåãóëèðîâà- íèÿ âåëè÷èíû ìàêñèìàëüíîãî è ìèíèìàëüíîãî îòêëîíåíèÿ ïåðåìåííîé. 4. Âîçìóùåíèÿ, ïîñòóïàþùèå íà îáúåêò ïðåæäå, ÷åì âîçäåéñòâîâàòü íà ðåãó- ëèðóåìóþ ïåðåìåííóþ 1 y , ïîäâåðãàþòñÿ ïðåäâàðèòåëüíûì èçìåíåíèÿì âî âñïî- ìîãàòåëüíîì êîíòóðå óïðàâëåíèÿ. Ëåììà 2. Êàñêàäíàÿ ñèñòåìà èìååò ìåíüøóþ ÷óâñòâèòåëüíîñòü ê íåòî÷íîìó çàäàíèþ ïàðàìåòðîâ îáúåêòà, ÷åì íå êàñêàäíàÿ. Äîêàçàòåëüñòâî. Äëÿ äîêàçàòåëüñòâà ëåììû 2 äîñòàòî÷íî ïîêàçàòü, ÷òî ÷óâñòâèòåëüíîñòü ìîæíî ñíèçèòü ââåäåíèåì îáðàòíîé ñâÿçè. Äåéñòâèòåëüíî, ïåðåäàòî÷íàÿ ôóíêöèÿ çàìêíóòîé ñèñòåìû â íîìèíàëüíîé ðàáî÷åé òî÷êå îïðåäåëÿåòñÿ ñîîòíîøåíèåì: ) z , ( G ) z ( G 1 ) z , ( G ) z ( G ) z ( w ) z ( y ) z , ( G n P R n P R n w       , ãäå n  – âåêòîð ïàðàìåòðîâ îáúåêòà. 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Äëÿ íàñòðîéêè ÏÈÄ-ðåãóëÿòîðà ïðèìåíÿëñÿ êðèòåðèé , ) )] ( u ) k ( u [ r ) k ( e ( 1 M 1 S 2 M 0 k 2 W eu        ïðè . 1 . 0 r  Íà ðèñ. 2 è 3 ïðèâåäåíû ïåðåõîäíûå ïðîöåññû èçìåíåíèÿ ðåãóëèðóåìîé ïåðåìåííîé 1 y îò ñòóïåí÷àòîãî âõîäíîãî âîçäåéñòâèÿ äëÿ ðàçëè÷íûõ àëãîðèòìîâ ðåãóëèðîâàíèÿ. Ðèñ. 2. Ïåðåõîäíûå ïðîöåññû ïî ðåãóëèðóåìîé ïåðåìåííîé 1 y äëÿ îäíîêîíòóðíîé è äâóõêîíòóðíîé ñèñòåì óïðàâëåíèÿ ñ ÏÈÄ-ðåãóëÿòîðîì Тип регу- лятора Одноконтурная система Pu G Двухконтурная система Pu G  ПИД 407 . 1 q ; 012 . 4 q ; 859 . 2 q 2 1 0     036 . 1 q ; 3452 . 3 q ; 6723 . 2 q 2 1 0     AR1 0656 . 0 p ; 447 . 0 p ; 3958 . 0 p ; 0916 . 0 p ; 4854 . 1 q ; 1829 . 7 q ; 6243 . 9 q ; 0 q ; 9268 . 4 q 4 3 2 1 4 3 2 1 0            1584 . 0 p ; 8449 . 0 p ; 6275 . 0 p ; 0887 . 1 p ; 2871 . 0 p ; 03438 . 0 q ; 4281 . 3 q ; 9891 . 14 q ; 3112 . 18 q ; 0 q ; 7174 . 7 q 5 4 3 2 1 5 4 3 2 1 0                 AR2 0271 . 0 p ; 2173 . 0 p ; 3951 . 0 p ; 2927 . 0 p ; 0678 . 0 p ; 6138 . 0 q ; 2293 . 2 q ; 6155 . 0 q ; 6432 . 3 q ; 0 q ; 6432 . 3 q 5 4 3 2 1 5 4 3 2 1 0               0783 . 0 p ; 4835 . 0 p ; 0617 . 0 p ; 6918 . 0 p ; 7373 . 0 p ; 1944 . 0 p ; 017 . 0 q ; 6812 . 1 q ; 9989 . 5 q ; 3331 . 3 q ; 226 . 5 q ; 0 q ; 226 . 5 q 6 5 4 3 2 1 6 5 4 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ÕÎÄÀÊÎÂ, Í.À. ÑÎÊÎËÎÂÀ, Ò.Â. ËÓÊÜßÍÅÍÊÎ ÎÖÅÍÈÂÀÍÈÅ ÔÈÍÀÍÑÎÂÎÃÎ ÑÎÑÒÎßÍÈß ÏÐÅÄÏÐÈßÒÈß Èçëàãàþòñÿ çàäà÷è ìåòîäîëîãèè îöåíèâàíèÿ ôèíàíñîâîãî ñîñòîÿíèÿ ñóáúåê- òîâ ïðîèçâîäñòâåííî-õîçÿéñòâåííîé äåÿòåëüíîñòè. Ïðîâîäÿòñÿ äâà âàðèàíòà îáîáùåííîãî êðèòåðèÿ îöåíêè ôèíàíñîâîãî àíàëèçà ðàáîòû ïðåäïðèÿòèÿ. Ðàçâèòèå ðûíî÷íîé ýêîíîìèêè íå òîëüêî óñèëèëî ðîëü ôèíàíñîâ â óïðàâëåíèè ïðîèçâîäñòâîì, íî è îïðåäåëèëî èì íîâîå ìåñòî â ýòîé ñèñòåìå. Ôèíàíñû ïîòåðÿëè ñâîå ðàñïðåäåëèòåëüíîå çíà÷åíèå, èõ íàçíà÷åíèåì ñòàëî óñèëåíèå âîçäåéñòâèÿ ôèíàíñîâîãî ìåõàíèçìà íà ðàñøèðåíèå èíèöèàòèâû è ñàìîñòîÿ- òåëüíîñòè õîçÿéñòâóþùèõ ñóáúåêòîâ [1].  îáùåé ïðîáëåìàòèêå óïðàâëåíèÿ ïðåäïðèÿòèÿìè ôèíàíñîâûå âîïðîñû ôè- íàíñàìè ñòàíîâÿòñÿ âàæíåéøèìè, ïðèîðèòåòíûìè è ñëóæàò îðèåíòèðîì ðàáîòû äëÿ óïðàâëåí÷åñêîãî ïåðñîíàëà [2]. Áîëüøîå âíèìàíèå óäåëÿåòñÿ ñîâåðøåíñòâî- âàíèþ ñèñòåìû ôèíàíñîâîé îöåíêè ïðåäïðèÿòèé. Äëÿ ïîëíîòû àíàëèçà äàííûå íåîáõîäèìî áàçèðîâàòü íà ñîîòâåòñòâóþùåé ìåòîäîëîãèè îöåíèâàíèÿ. Ïî íàøåìó ìíåíèþ ïðîöåäóðà îöåíèâàíèÿ ôèíàíñîâîãî ñîñòîÿíèÿ ïðåäïðèÿ- òèÿ ìîæåò áûòü ñëåäóþùåé: à) ñáîð èíôîðìàöèè î ïðåäìåòå îöåíèâàíèÿ. Âûáîð ïîêàçàòåëåé: îñíîâíûõ, âòîðîñòåïåííûõ; êàêèå ñóùåñòâåííî âëèÿþò íà îáùåå ñîñòîÿíèå èòîãîâîãî ïîêà- çàòåëÿ, à êàêèå êîñâåííî è íåçíà÷èòåëüíî è ò.ä.; á) âûáîð áàçèñà èëè ýòàëîíà îöåíèâàíèÿ, â ñðàâíåíèè ñ êîòîðûì áóäåò ïðîèçâîäèòüñÿ ïðîöåññ îöåíèâàíèÿ è/èëè ñðàâíåíèÿ. Çà ýòàëîí æå âûáèðàåòñÿ ëèáî íàèëó÷øåå, ëèáî íàèõóäøåå òåîðåòè÷åñêîå çíà÷åíèå, ëèáî çíà÷åíèå îïòè- ìàëüíîå èëè óæå êîãäà-ëèáî äîñòèãíóòîå; â) îáçîð âîçìîæíûõ ìåòîäîâ îöåíèâàíèÿ èëè ðàçðàáîòêà ñâîèõ ñîáñòâåííûõ ìåòîäîâ; ã) âûáîð ìåòîäîâ, êîòîðûå íàèáîëåå ïîäõîäÿò â äàííîé ñèòóàöèè; ä) îáîñíîâàíèå âûáîðà äàííîãî ìåòîäà; å) ïðèâåäåíèå îöåíèâàåìûõ ïîêàçàòåëåé ê åäèíîé ìåòðèêå; æ) ïðîâåäåíèå ðàñ÷åòîâ; ç) àíàëèç ïîëó÷åííûõ ðåçóëüòàòîâ. Ïîëó÷åííûå ðåçóëüòàòû ðàñ÷åòîâ ñðàâíè- âàþòñÿ ñ áàçèñíûì è/èëè ýòàëîííûìè çíà÷åíèÿìè. Äëÿ îöåíêè èçìåíåíèÿ ïàðàìåòðîâ ìîæåò áûòü èñïîëüçîâàíî íåñêîëüêî ïîêà- çàòåëåé: àáñîëþòíûé áàçèñíûé òåìï ðîñòà; àáñîëþòíûé öåïíîé òåìï ðîñòà; áàçèñíûé òåìï ðîñòà; öåïíîé òåìï ðîñòà; öåïíîé òåìï ïðèðîñòà. Àáñîëþòíûå áàçèñíûé òåìï ðîñòà è öåïíîé òåìï ðîñòà èçìåðÿþòñÿ â íàòóðàëüíûõ åäèíèöàõ (øò., êã, ãðí.), à áàçèñíûé òåìï ðîñòà, áàçèñíûé òåìï ïðèðîñòà, öåïíîé òåìï ðîñòà, öåïíîé òåìï ïðèðîñòà – â äîëåâîì èëè ïðîöåíòíîì âûðàæåíèÿõ. Àáñîëþò- íûé áàçèñíûé òåìï ðîñòà ïîêàçûâàåò, íà ñêîëüêî âîçðîñ èëè óìåíüøèëñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ áàçèñíûì: 0 1 A A A i i    , ãäå i A 1  – àáñîëþòíûé áàçèñíûé òåìï ðîñòà; 0 A – ïîêàçàòåëü çà áàçèñíûé ïåðèîä;  i A ïîêàçàòåëü çà òåêóùèé ïåðèîä. Àáñîëþòíûé öåïíîé òåìï ðîñòà ïîêàçûâàåò, íà ñêîëüêî âîçðîñ èëè óìåíüøèë- ñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ ïðåäûäóùèì ïåðèîäîì: 1 1     i i i ПР A A A , çäåñü i ПР A 1  – àáñîëþòíûé áàçèñíûé òåìï ðîñòà;  i A ïîêàçàòåëü çà òåêóùèé ïåðèîä;   1 i A ïîêàçàòåëü çà ïðåäûäóùèé ïåðèîä. 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s96Cp3](M@W&=M?͌ vr<[K,,51 Áàçèñíûé òåìï ðîñòà ïîêàçûâàåò, âî ñêîëüêî ðàç âûðîñ èëè óìåíüøèëñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ áàçèñíûì: 0 1 А А Б І І   , ãäå І Б 1  – áàçèñíûé òåìï ðîñòà; І А – ïîêàçàòåëü çà ñðàâíèâàåìûé ïåðèîä; 0 А – ïîêàçàòåëü çà áàçèñíûé ïåðèîä. Áàçèñíûé òåìï ïðèðîñòà ïîêàçûâàåò, íà ñêîëüêî ïðîöåíòîâ âîçðîñ èëè óìåíü- øèëñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ áàçèñíûì: % 100 1 0 1             А А Б І І ПР , çäåñü І ПР Б 1  – áàçèñíûé òåìï ïðèðîñòà â ïðîöåíòàõ. Öåïíîé òåìï ðîñòà ïîêàçûâàåò, âî ñêîëüêî ðàç âîçðîñ èëè óìåíüøèëñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ ïðåäûäóùèì ïåðèîäîì: 1 1    і І і А А Ц , ãäå і Ц 1  – öåïíîé òåìï ðîñòà; І А – ïîêàçàòåëü çà äàííûé ïåðèîä; 1  i А – ïîêàçàòåëü çà ïðåäûäóùèé ïåðèîä. Öåïíîé òåìï ïðèðîñòà ïîêàçûâàåò, íà ñêîëüêî ïðîöåíòîâ âîçðîñ èëè óìåíü- øèëñÿ òåêóùèé ïîêàçàòåëü ïî ñðàâíåíèþ ñ ïðåäûäóùèì ïåðèîäîì: % 100 1 1 1              і І І ПР А А Ц . Ê êàæäîìó ïîêàçàòåëþ ïðèìåíÿåòñÿ îòäåëüíûé ïîäõîä â âûáîðå áàçèñà – ïðîøëûé ïåðèîä èëè ýòàëîí. Ïðîøëûé ïåðèîä èñïîëüçóåòñÿ îáû÷íî â ñòîèìîñò- íûõ è êîëè÷åñòâåííûõ ïîêàçàòåëÿõ ôèíàíñîâîé è ïðîèçâîäñòâåííîé ñôåðû. Ýòî ñïðàâåäëèâî äëÿ òàêèõ ïîêàçàòåëåé êàê ðåíòàáåëüíîñòü, êîëè÷åñòâî èçãîòîâëåí- íîãî òîâàðà, àìîðòèçàöèÿ è ò.ä. Ýòàëîí îáû÷íî ïðèìåíÿåòñÿ â áîëåå ãëîáàëüíûõ è àáñòðàêòíûõ ïîêàçàòåëÿõ: îáùåå ñîñòîÿíèå ïðåäïðèÿòèÿ, ãóä âèë, ïåðñïåêòèâ- íîñòü ïðåäïðèÿòèÿ è ò.ä.  ïðàêòèêå ôèíàíñîâîãî àíàëèçà èñïîëüçóþòñÿ ïîêàçà- òåëè, õàðàêòåðèçóþùèå îòäåëüíûå ñòîðîíû òåêóùåãî ôèíàíñîâîãî ïîëîæåíèÿ ïðåäïðèÿòèÿ: ëèêâèäíîñòü, ðåíòàáåëüíîñòü, óñòîé÷èâîñòü, îáîðà÷èâàåìîñòü êà- ïèòàëà, ïðèáûëüíîñòü è ò.ä. Ïî ðÿäó ïîêàçàòåëåé èçâåñòíû íåêîòîðûå íîðìàòè- âû, õàðàêòåðèçóþùèå èõ çíà÷åíèå ïîëîæèòåëüíî èëè îòðèöàòåëüíî. Íàïðèìåð, êîãäà ñîáñòâåííûå ñðåäñòâà ïðåäïðèÿòèÿ ïðåâûøàþò ïîëîâèíó âñåõ ïàññèâîâ, ñîîòâåòñòâóþùèé ýòîé ïðîïîðöèè êîýôôèöèåíò àâòîíîìèè áîëüøå 1 / 2 , ýòî åãî çíà÷åíèå ñ÷èòàåòñÿ “ õîðîøèì ” (ñîîòâåòñòâåííî, êîãäà îíî ìåíüøå 1 / 2 – “ ïëî- õèì ” ). Íî â áîëüøèíñòâå ñëó÷àåâ ïîêàçàòåëè, îöåíèâàåìûå ïðè àíàëèçå, îäíî- çíà÷íî íîðìèðîâàòü íåâîçìîæíî. Ýòî ñâÿçàíî ñî ñïåöèôèêîé îòðàñëåé ýêîíîìè- êè, ñ òåêóùèìè îñîáåííîñòÿìè äåéñòâóþùèõ ïðåäïðèÿòèé, ñ ñîñòîÿíèåì ýêîíî- ìè÷åñêîé ñðåäû, â êîòîðîé îíè ðàáîòàþò [3-5]. Òåì íå ìåíåå, ëþáîå ëèöî, çàèíòåðåñîâàííîå ïîëîæåíèåì ïðåäïðèÿòèÿ (ðóêî- âîäèòåëü, èíâåñòîð, êðåäèòîð, àóäèòîð è ò.ä.) – ËÏÐ íå äîâîëüñòâóåòñÿ ïðîñòîé êîëè÷åñòâåííîé îöåíêîé ïîêàçàòåëåé. Äëÿ ËÏÐ âàæíî çíàòü, ïðèåìëåìû ëè ïîëó÷åííûå çíà÷åíèÿ. Êðîìå òîãî, ËÏÐ ñòðåìèòñÿ óñòàíîâèòü ëîãè÷åñêóþ ñâÿçü êîëè÷åñòâåííûõ çíà÷åíèé ïîêàçàòåëåé âûäåëåííîé ãðóïïû ñ íåêèì êîìïëåêñ- íûì ïîêàçàòåëåì, õàðàêòåðèçóþùèì ôèíàíñîâîå ñîñòîÿíèå ïðåäïðèÿòèÿ â öå- ëîì, ò.å. ËÏÐ íå ìîæåò áûòü óäîâëåòâîðåíî áèíàðíîé îöåíêîé “ õîðîøî - ïëîõî ” , åãî èíòåðåñóþò îòòåíêè ñèòóàöèè è ýêîíîìè÷åñêàÿ èíòåðïðåòàöèÿ ýòèõ îòòåíî÷- íûõ çíà÷åíèé. 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Ïðè ýòîì ôóíêöèè ïðèíàäëåæíîñòè ïàðàìåòðîâ íå÷åòêîìó ìíîæåñòâó îáëà- äàþò òåìè æå äîñòîèíñòâàìè â àíàëèçå, ÷òî è íåêëàññè÷åñêèå òèïû âåðîÿòíîñòåé è âäîáàâîê ê ýòîìó îíè ÿâëÿþòñÿ êîëè÷åñòâåííîé ìåðîé èíôîðìàöèîííîé íåî- ïðåäåëåííîñòè â îòíîøåíèè àíàëèçèðóåìûõ ïàðàìåòðîâ, çíà÷åíèå êîòîðûõ îïè- ñûâàåòñÿ â ëèíãâèñòè÷åñêè-íå÷åòêîé ôîðìå. Íà îñíîâàíèè èçëîæåííîãî ïðåäëàãàþòñÿ âàðèàíòû îáîáùåííîãî ïîêàçàòåëÿ îöåíèâàíèÿ ñîñòîÿíèÿ ïðåäïðèÿòèÿ. Êîìïëåêñíàÿ îöåíêà ôèíàíñîâîãî ñîñòîÿíèÿ ìîæåò áûòü ïðîèëëþñòðèðîâàíà èñïîëüçîâàíèåì òåîðèè íå÷åòêèõ ìíîæåñòâ. Ñõåìà ïîñòðîåíèÿ ïîêàçàòåëÿ ñëå- äóþùàÿ: 1. Ïîëíîå ìíîæåñòâî ñîñòîÿíèé À ïðåäïðèÿòèÿ ðàçáèâàåòñÿ íà ïÿòü â îáùåì ñëó÷àå ïåðåñåêàþùèõñÿ íå÷åòêèõ ïîäìíîæåñòâ âèäà: À1 – íå÷åòêîå ïîäìíîæåñòâî ñîñòîÿíèé “ êðèòè÷åñêîãî íåáëàãîïîëó÷èÿ ” (ôàê- òè÷åñêîãî áàíêðîòñòâà); À2 – íå÷åòêîå ïîäìíîæåñòâî ñîñòîÿíèÿ “ íåáëàãîïîëó÷èÿ ” ; À3 – íå÷åòêîå ïîäìíîæåñòâî ñîñòîÿíèÿ “ ñðåäíåãî áëàãîïîëó÷èÿ ” ; À4 – íå÷åòêîå ïîäìíîæåñòâî ñîñòîÿíèÿ “ õîðîøåãî áëàãîïîëó÷èÿ ” ; À5 – íå÷åòêîå ïîäìíîæåñòâî “ îòëè÷íîãî ôèíàíñîâîãî ñîñòîÿíèÿ ” . Ýòî çíà÷èò, ÷òî òåðì-ìíîæåñòâî ëèíãâèñòè÷åñêîé ïåðåìåííîé “ Ñîñòîÿíèå ïðåäïðèÿòèÿ ” ñîñòîèò èç 5 êîìïîíåíò. Êàæäîìó èç ïîäìíîæåñòâ À1, …, À5 ñîîòâåòñòâóþò ñâîè ôóíêöèè ïðèíàäëåæíîñòè Ì1  (Ê îá ) … Ì5  (Ê îá ), ãäå Ê îá – êîìïëåêñíûé ïîêàçàòåëü ôèíàíñîâîãî ñîñòîÿíèÿ ïðåäïðèÿòèÿ, ïðè÷åì ÷åì âûøå Ê îá , òåì “ áëàãîïîëó÷íåå ” ñîñòîÿíèå ïðåäïðèÿòèÿ. 2. Îñóùåñòâëÿþò âûáîð áàçîâîé ñèñòåìû ïîêàçàòåëè Õ i è ïðîèçâîäèòñÿ íå- ÷åòêàÿ êëàññèôèêàöèÿ èõ çíà÷åíèé. Ïóñòü D(X i ) – îáëàñòü îïðåäåëåíèÿ ïàðàìåò- ðà X i , ìíîæåñòâî òî÷åê îñè äåéñòâèòåëüíûõ ÷èñåë. Îïðåäåëèì ëèíãâèñòè÷åñêóþ ïåðåìåííóþ “ Óðîâåíü ïîêàçàòåëÿ X i ” ñ ââåäåíèåì 5-òè íå÷åòêèõ ïîäìíîæåñòâ ìíîæåñòâà D(X i ) : Â1 – íå÷åòêîå ïîäìíîæåñòâî “ î÷åíü íèçêèé óðîâåíü ïîêàçàòåëÿ X i ” ; Â2 – íå÷åòêîå ïîäìíîæåñòâî “ íèçêèé óðîâåíü ïîêàçàòåëÿ X i ” ; Â3 – íå÷åòêîå ïîäìíîæåñòâî “ ñðåäíèé óðîâåíü ïîêàçàòåëÿ X i ” ; Â4 – íå÷åòêîå ïîäìíîæåñòâî “ âûñîêèé óðîâåíü ïîêàçàòåëÿ X i ” ; Â5 – íå÷åòêîå ïîäìíîæåñòâî “ î÷åíü âûñîêèé óðîâåíü ïîêàçàòåëÿ X i ” . Îïèñàíèå ïîäìíîæåñòâà {Â} – ýòî çàäà÷à ôîðìèðîâàíèÿ ñîîòâåòñòâóþùèõ ôóíêöèé ïðèíàäëåæíîñòè. 3. Ïîñòðîåíèå ôóíêöèé ïðèíàäëåæíîñòè {m} íå÷åòêèõ ïîäìíîæåñòâ {À}. Àíà- ëèçèðóÿ îïûò ðàçëè÷íûõ êâàëèôèêàöèé ëèíãâèñòè÷åñêîé ïåðåìåííîé “ Ñîñòîÿ- íèå ” , ìû çàäàåìñÿ íàáîðîì ôóíêöèé ïðèíàäëåæíîñòè {Ì}. Ýòè ôóíêöèè ôîðìè- ðóþòñÿ òàêèì îáðàçîì, ÷òî èñêîìûé êîìïëåêñíûé ïîêàçàòåëü ôèíàíñîâîãî ñî- ñòîÿíèÿ ïðåäïðèÿòèÿ Ê îá ïî ïîñòðîåíèþ ïðèíèìàë çíà÷åíèÿ îò 0 äî 1. 4. Îöåíêà çíà÷èìîñòåé ïîêàçàòåëåé äëÿ îáîáùåííîé îöåíêè. Êàæäîìó i-ìó ïîêàçàòåëþ â îòíîøåíèè êàæäîãî ê-ãî óðîâíÿ ñîñòîÿíèÿ ïðåäïðèÿòèÿ ìîæíî ñîïîñòàâèòü îöåíêó pik çíà÷èìîñòè äàííîãî ïîêàçàòåëÿ äëÿ ðàñïîçíàâàíèÿ äàí- íîãî óðîâíÿ ñîñòîÿíèÿ ïðåäïðèÿòèÿ. Íàïðèìåð, ðÿä áàíêîâ, àíàëèçèðóÿ êðåäè- òîñïîñîáíîñòü çàåìùèêà, ïðèäàåò áîëüøóþ çíà÷èìîñòü ïîêàçàòåëÿì ôèíàíñîâîé óñòîé÷èâîñòè è ëèêâèäíîñòè, è ìåíüøóþ – ïîêàçàòåëÿì ïðèáûëüíîñòè è îáîðà- ÷èâàåìîñòè. 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ÁÅÍÜ, Â.Ã. ØÅÐÑÒÞÊ, Ë.Í. ÐÀÄÂÀÍÑÊÀß ÌÎÄÅËÜ ÀÄÀÏÒÈÂÍÎÃÎ ÏËÀÍÈÐÎÂÀÍÈß Â ÈÍÒÅËËÅÊÒÓÀËÜÍÎÉ ÑÈÑÒÅÌÅ ÏÎÄÄÅÐÆÊÈ ÏÐÈÍßÒÈß ÐÅØÅÍÈÉ ÓÏÐÀÂËÅÍÈß ÏÎ ×ÐÅÇÂÛ×ÀÉÍÛÌ ÑÈÒÓÀÖÈßÌ Ðàññìàòðèâàåòñÿ ðåàëèçàöèÿ ïîäñèñòåìû ïëàíèðîâàíèÿ â èíòåëëåêòóàëü- íîé ñèñòåìå ïîääåðæêè ïðèíÿòèÿ ðåøåíèé (ÑÏÏÐ) äëÿ ÷ðåçâû÷àéíûõ ñèòóà- öèé E-Plans, ÿâëÿþùåéñÿ ñîñòàâíîé ÷àñòüþ èíôîðìàöèîííî-àíàëèòè÷åñêîé ñèñòåìû îáëàñòíîãî óïðàâëåíèÿ ïî ÷ðåçâû÷àéíûì ñèòóàöèÿì [1]. Ñèñòåìà E-Plans ïðåäíàçíà÷åíà äëÿ ôîðìèðîâàíèÿ â ðåàëüíîì ìàñøòàáå âðåìåíè íàáîðà âîçìîæíûõ ïëàíîâ ëèêâèäàöèè î÷àãà âîçãîðàíèÿ, îíà ïðåäîñòàâ- ëÿåò îïåðàòîðó âîçìîæíîñòü âûáîðà íàèáîëåå ïðèåìëåìîãî â ñëîæèâøåéñÿ ñèòóàöèè ïëàíà îïåðàòèâíûõ äåéñòâèé. Îòëè÷èòåëüíîé âîçìîæíîñòüþ ïðåäëàãà- åìîãî ïîäõîäà ê ïëàíèðîâàíèþ äåéñòâèé â ÷ðåçâû÷àéíîé ñèòóàöèè (×Ñ) ÿâëÿåòñÿ èñïîëüçîâàíèå àäàïòèâíîãî àëãîðèòìà ïëàíèðîâàíèÿ, ïðåäóñìàòðèâàþùåãî âîç- ìîæíîñòü ïåðåñìîòðà è èçìåíåíèÿ ïëàíà ïî ìåðå ïîñòóïëåíèÿ íîâîé èíôîðìà- öèè ïðè ëèêâèäàöèè ×Ñ. Ïîä âîçìîæíûì ïëàíîì ïîíèìàåòñÿ ÷àñòè÷íî óïîðÿäî÷åííàÿ ïîñëåäîâàòåëü- íîñòü äåéñòâèé äèñïåò÷åðà, íàïðàâëåííàÿ íà äîñòèæåíèå îïðåäåëåííîé öåëè èç íåêîòîðîé ôèêñèðîâàííîé íà÷àëüíîé ñèòóàöèè. Êëþ÷åâûì ìîìåíòîì â ïîñòðîå- íèè âîçìîæíîãî ïëàíà ÿâëÿåòñÿ ïðàâèëüíîå îïðåäåëåíèå öåëåé. Ðåøåíèå çàäà÷è ïëàíèðîâàíèÿ äåéñòâèé ïðèâîäèò ê ïîÿâëåíèþ â ìîäåëè ïðåäìåòíîãî ìèðà (â äàííîì ñëó÷àå ìîäåëè ðàçâèòèÿ ïîæàðà) íîâûõ ýëåìåíòîâ – íàìå÷åííûõ äåéñòâèé è îæèäàåìûõ ïîñëåäñòâèé. Îñíîâíûìè ïðîáëåìíûìè âîï- ðîñàìè, âîçíèêàþùèìè â çàäà÷å ïëàíèðîâàíèÿ äåéñòâèé, ÿâëÿþòñÿ ñëåäóþùèå: – êàê ñëåäóåò ðàçäåëÿòü áîëüøèå ôðàãìåíòû îáùåé ñîâîêóïíîñòè çíàíèé ìåæäó ðàçëè÷íûìè ãèïîòåçàìè è ìîìåíòàìè âðåìåíè; – êàêèì îáðàçîì íóæíî ñòðóêòóðèðîâàòü ïëàí, ÷òîáû èìåòü âîçìîæíîñòü êîíòðîëèðîâàòü ïðàâèëüíîñòü åãî âûïîëíåíèÿ; – â êàêîé ôîðìå ñëåäóåò ïðåäñòàâëÿòü âîçìîæíûå ïëàíû è êàêèì îáðàçîì ìîæíî èçìåíÿòü óæå ñóùåñòâóþùèé ïëàí, åñëè êàêîé-ëèáî åãî ôðàãìåíò îêàçû- âàåòñÿ îøèáî÷íûì ââèäó ïîñòóïëåíèÿ íîâîé èíôîðìàöèè èëè îïðîâåðæåíèÿ èìåâøåéñÿ ðàíåå; – êàêèì îáðàçîì ìîæíî ýôôåêòèâíî ñòðîèòü ïëàí è îöåíèâàòü åãî êà÷åñòâî; – â êàêîì âèäå íåîáõîäèìî çàïèñûâàòü îæèäàåìûå ðåçóëüòàòû è öåëè, ïðèâåäøèå ê âûáîðó äàííîãî ïëàíà, à òàêæå îïðåäåëÿòü óñëîâèÿ, ïðè êîòîðûõ ïëàí óæå íå ñëåäóåò èñïîëüçîâàòü; – êàêèì îáðàçîì ðàçðåøàòü êîíôëèêòû, âîçíèêàþùèå â ñëó÷àå íåîáõîäèìî- ñòè äîñòèæåíèÿ íåñêîëüêèõ, âîçìîæíî, ïðîòèâîðå÷èâûõ öåëåé.  ñëó÷àå âîçíèêíîâåíèÿ î÷àãà âîçãîðàíèÿ èíôîðìàöèÿ î íåì ïåðåäàåòñÿ äåæóðíîìó äèñïåò÷åðó. Çîíà âîçãîðàíèÿ âèçóàëüíî ïðåäñòàâëåíà íà êàðòå îáëàñòè â âèäå óêðóïíåííî- ãî îáúåêòà, ðàçáèòîãî íà îòäåëüíûå ñåêòîðû. Äëÿ êàæäîãî ñåêòîðà îïðåäåëåíû ïàðàìåòðû î÷àãà âîçãîðàíèÿ, âêëþ÷àþùèå: ñêîðîñòü è íàïðàâëåíèå äâèæåíèÿ îãíåâîãî ôðîíòà, ìåòåîóñëîâèÿ â çîíå, ñïèñîê ïîæàðîîïàñíûõ îáúåêòîâ, íàõîäÿ- ùèõñÿ â íåïîñðåäñòâåííîé áëèçîñòè îò çîíû âîçãîðàíèÿ, ïëîùàäü òåððèòîðèè, îõâàòûâàåìîé äàííûì ñåêòîðîì. Êðîìå òîãî, äëÿ êàæäîãî ñåêòîðà óêàçûâàåòñÿ: ñïèñîê çàäåéñòâîâàííûõ äëÿ áîðüáû ñ îãíåì ïîæàðíûõ ïîäðàçäåëåíèé, èõ îáùàÿ ÷èñëåííîñòü, èìåþùèåñÿ â ðàñïîðÿæåíèè ñðåäñòâà òóøåíèÿ ïîæàðà, ïðåäïîëàãàåìîå âðåìÿ ïðèáûòèÿ ðå- çåðâíûõ ïîäðàçäåëåíèé.  &x[lTUמl -v:0-$)-6 B!^"|- Pxc@HM) rRB+  Q3m~{N=L:(O3ɟm%$"!DR,wo4HDtX2]dE'@Z1MRK_ 2 zqXl.[x=ᫎ~kJ㫌nO[`'[DRvU$m({B"U]jdȦγꝘ-I'm|5gxcjwڃYreq2\ىR. .Æ|5 ѝ~ziN>&Fk闘M.}ID8KY\l ߩX2eʒaȓ%%SnCW}4v~rB?~AU5U/>ɽ67e5cfk9{F.R o[ŪAhjy|`9)RUzHg)u'S|E2le!x=D.E>< ~TdSY_9؏0 DJ 3b~ĕKg f!! 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Ïëàí ëèêâèäàöèè âêëþ÷àåò: îïèñàíèå ñïèñêà ãðàíè÷íûõ óñëîâèé è öåëåé äëÿ êàæäîãî ñåêòîðà, êîòîðûå íåîáõîäèìî îñóùåñòâèòü äëÿ ëèêâèäàöèè îãíÿ. Ñïèñîê ãðàíè÷íûõ óñëîâèé (äàëåå – ñïèñîê îãðàíè÷åíèé) îïðåäåëÿåò ìíîæåñòâî ïàðà- ìåòðîâ î÷àãà âîçãîðàíèÿ, ÿâëÿþùèõñÿ êðèòè÷åñêèìè äëÿ ðàñïðîñòðàíåíèÿ îãíå- âîãî ôðîíòà â çàäàííîì ñåêòîðå. Öåëü âêëþ÷àåò òðè êëþ÷åâûõ êîìïîíåíòà: ìàêñèìàëüíî äîïóñòèìîå âðåìÿ ëèêâèäàöèè ïîæàðà íà îáúåêòå, îáúåì ñðåäñòâ ïîæàðîòóøåíèÿ, íåîáõîäèìûé äëÿ ëèêâèäàöèè ïîæàðà â çàäàííîì ñåêòîðå, êîîðäèíàòû îñíîâíûõ î÷àãîâ âîçãî- ðàíèÿ â íåì. Ñïèñîê îãðàíè÷åíèé îïðåäåëÿåò íà÷àëüíûå óñëîâèÿ âûïîëíåíèÿ ïëàíà (ïðå- äóñëîâèÿ âûïîëíåíèÿ), öåëü õàðàêòåðèçóåò ðåçóëüòàò åãî âûïîëíåíèÿ (ïîñòóñëî- âèÿ). Îáùèé ïëàí ëèêâèäàöèè ïîæàðà ñ÷èòàåòñÿ óñïåøíî âûïîëíåííûì, åñëè âû- ïîëíåíû öåëåâûå óñòàíîâêè äëÿ êàæäîãî ñåêòîðà. Ïðîöåññ ðàñïðîñòðàíåíèÿ ïîæàðà ïðåäñòàâëÿåò ñîáîé ñëîæíóþ äèíàìè÷åñ- êóþ ñèñòåìó, ïîâåäåíèå êîòîðîé îïðåäåëÿåòñÿ áîëüøèì ÷èñëîì âíóòðåííèõ è âíåøíèõ ïàðàìåòðîâ. Ê íàèáîëåå ñóùåñòâåííûì èç íèõ ìîæíî îòíåñòè ñëåäóþ- ùèå: ñèëà è íàïðàâëåíèå âåòðà, âëàæíîñòü è òåìïåðàòóðà îêðóæàþùåãî âîçäó- õà, òèï ãîðÿùåãî âåùåñòâà, õàðàêòåð ðàñïðîñòðàíåíèÿ îãíåâîãî ôðîíòà. Ýòè ïàðàìåòðû ïîäâåðæåíû ñóùåñòâåííûì è ïîðîé íåïðåäñêàçóåìûì èçìåíåíèÿì. Äàííàÿ îñîáåííîñòü îáóñëàâëèâàåò íåîáõîäèìîñòü îñóùåñòâëåíèÿ äèíàìè÷åñêîé êîððåêöèè èìåþùèõñÿ ïëàíîâ ïî ëèêâèäàöèè ×Ñ â ïðîöåññå èõ ðåàëèçàöèè. Ïðèìåíèòåëüíî ê çàäà÷àì ëèêâèäàöèè ×Ñ íåöåëåñîîáðàçíî ñòðîèòü ïëàíû áîëüøîé ãëóáèíû ââèäó âûñîêîé âàðèàáåëüíîñòè è íåäåòåðìèíèðîâàííîñòè ïðî- èñõîäÿùèõ ïðîöåññîâ, à òàêæå ñóùåñòâåííîé çàâèñèìîñòè èõ îò ðÿäà ñëó÷àéíûõ âíåøíèõ ôàêòîðîâ. Îäíàêî ïîñòðîåíèå ïëàíà îòíîñèòåëüíî íåáîëüøîé ãëóáèíû ÿâëÿåòñÿ âïîëíå îïðàâäàííûì, ýòî ïîçâîëÿåò ïîâûñèòü ãèáêîñòü ôîðìèðîâàíèÿ ñòðàòåãèè ïî ëèêâèäàöèè ×Ñ çà ñ÷åò ñîêðàùåíèÿ ÷èñëà çàâåäîìî íåýôôåêòèâ- íûõ äåéñòâèé.  ñèñòåìå E-Plans â êà÷åñòâå îñíîâû ïðèíÿòà ìîäåëü ïëàíèðîâàíèÿ, îñíîâíûå ýëåìåíòû êîòîðîé ïðåäñòàâëåíû íèæå. Îïðåäåëåíèå 1. Ñèòóàöèÿ åñòü ïàðà ) , ( t w , ãäå W w  , T t  è w O w F w O w A R w , , ,     . Âñå ñèòóàöèè, âîçíèêàþùèå â íåêîòîðîì ìèðå w , ïðèíàäëåæàò ìíîæåñòâó w S ,   T t t w S w   | ) , ( . Ñîâîêóïíîå ìíîæåñòâî ñèòóàöèé îïðåäåëÿòñÿ êàê w W w S S    . Ñóùåñòâîâàíèå â ñèñòåìå ñèòóàöèè s îïðåäåëÿåòñÿ èñòèííîñò- íûì çíà÷åíèåì âûðàæåíèÿ S s s   , ?  . Îïðåäåëåíèå 2. Îãðàíè÷åííûé ïóòü p (îãðàíè÷åííûé ëîêàëüíûé êóðñ ñîáû- òèé) â ìèðå W w  ïðåäñòàâëÿåò ñîáîé âðåìåííóþ ïîñëåäîâàòåëüíîñòü   k t t t ,..., , 1 0 , òàêóþ ÷òî:   1 ,.., 1 , 0    k u , w u u R t t   ) , ( 1 . Ïîëíûé ïóòü p â ìèðå w îïðåäåëÿåòñÿ ïîñëåäîâàòåëüíîñòüþ ) | ( N u t u  , ïðè ýòîì w u u R t t N u     ) , ( , 1 . Åñëè p – íåêîòîðûé ïóòü è N u  , òî 1 ) (   u t u p . 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Îïðåäåëåíèå 3. Òåëî ïëàíà îáîçíà÷àåòñÿ n    ,..., , 2 1 , èõ ñîâîêóïíîñòü îáðà- çóåò ìíîæåñòâî   . Îïðåäåëåíèå 4. Äåñêðèïòîð ïëàíà  ïðåäñòàâëÿåò ñîáîé áèíàðíîå îòíîøå- íèå âèäà S S    , äëÿ êîòîðîãî âûïîëíÿåòñÿ îãðàíè÷åíèå: åñëè   ) ' , ' ( ), , (( t w t w , òî ' w w  . Îïðåäåëåíèå 5. Äåñêðèïòîð ïðåäóñëîâèÿ  – ïðåäñòàâëÿåò ìíîæåñòâî ñèòóà- öèé, â êîòîðûõ äîïóñòèìî âûïîëíåíèå  , ò.å. ïðåäóñëîâèÿ îñóùåñòâëåíèÿ  . Îïðåäåëåíèå 6. Äåñêðèïòîð ïîñòóñëîâèÿ   ïðåäñòàâëÿåò ìíîæåñòâî ñèòó- àöèé, êîòîðûå ìîãóò âîçíèêíóòü â ðåçóëüòàòå îñóùåñòâëåíèÿ  (ïîñòóñëîâèÿ äëÿ  ). Åñëè   ) ' , ( s s , òî âîçíèêíîâåíèå ñèòóàöèè ' s âîçìîæíî â ðåçóëüòàòå âûïîëíåíèÿ  , íà÷èíàÿ ñ ñèòóàöèè s . Ìíîæåñòâî âñåõ äåñêðèïòîðîâ îáîçíà÷à- åòñÿ êàê   . Îïðåäåëåíèå 7. Ïëàí  ïðåäñòàâëÿåòñÿ ïàðîé ) , (   ,         , , ìíî- æåñòâî âîçìîæíûõ ïëàíîâ:          . Ýëåìåíòàðíûì ôðàãìåíòîì òåëà ïëàíà ÿâëÿåòñÿ äåéñòâèå A    , . Ñòðóê- òóðà òåëà ïëàíà îïðåäåëÿåòñÿ ñëåäóþùèì îáðàçîì: ) ( :: S    – ) ( условий список 2 1 ;    – ) ( композиция ельная последоват ; A      , :: – ) (действия 2 1     – ) ( композиция ая параллельн ; * 1   – ) (итерация 2 1 ' '     – ) ( выбор ированный недетермин ; ?   – ) ( условий проверка . Îïðåäåëåíèå 8. Åñëè     – íåêîòîðûé ïëàí, òî      ) ( ˆ – òåëî ïëàíà,      ) ( ˆ – äåñêðèïòîð ïëàíà,       ) ( ˆ – äåñêðèïòîð ïðåäóñëîâèé,       ) ( ˆ – äåñêðèïòîð ïîñòóñëîâèé. Åñëè ) ( ˆ     s , òî ) )( ( ˆ s   ïðåä- ñòàâëÿåò îáðàç s â ) ( ˆ   , ò.å. )} ( ˆ ) , ' ( ' { ) )( ( ˆ        s s s s . Ïðîöåññ âûïîëíåíèÿ òåëà ïëàíà  çàäàåòñÿ ÷åòûðåõìåñòíûì ïðåäèêàòîì  , èìåþùèì âèä: ) , , , ( v u p   . Òåëî ïëàíà  âûïîëíÿåòñÿ íà ïóòè p , îãðàíè÷åííîì âðåìåííûì èíòåðâàëîì T v u  ] , [ . 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"[_\(/+x6M>o[i<~ "̘Ћ9oczZ <2JEqM?Ed#$c /ΑC^d ˋ 8KNeR9$^F A/:V޽/𫠖4܆^#yu`J|Fy[>+zRbs,SU_[_˨aIre9n9~}:-0YE$3Dže):v] a\-O}$(gW s}]e AT^C @/h}mcxiytɕQ{Q_!{\Kt?bg_Ҽ-wV={xO1ɻR8<]l9ww>ݳB~X\#,=c41\1XϹ{6ڿwL{Dn5, L??yY¾~oګP}5=㴌P(sWlw2O5-7td 6qf8׃O0p9)e)u`Rؔ$ Ll+ Zd7}y\{6%n|V?TC9qvEؾ\w5YӊC5 v('ʯ~ISld\QdZ16ҍs+ӕ<ߙ l¦.O9p|z$N?XO>xNNuɵ-?+-}|P/ɚAŬv]l<¼4ne(o|,%#G0Gڧt4`Ji'(-k<<w[ۘM@Mi%M1}) %+#)_?fzf+ߪ+o_ơˆ7nsY|7 m.|cf9}eݖ)(c1 3{M}NlQS䋺Rm4$o Ks[yf,Qأ ʆH, :Po0$1 lܒ68NIp]&6L |I~6MC6\t|߄L_IE݄Pڱ#HUAc])-fh WHf{>CMih݄^ <?qaW1ķipo&=q m;p_q~g-^k)ޥEӇwo[Ӑ{4`'k=|{7zdz];ј+[t1N}xc>+u}nquiֿe ||r}%Z[VUZ+Ym if;piFJse~Ex.x$]MkZ87݌8Y#ҸUƚ0,q7Nh4k} 8OyK!?l+;/.ߌxA4su갢dJ;IiYڨ|޿JUL{jv[`ӋEڱ%}DC^7Uk֋/7MȧߋCηO^8Pfx&cq921³:=,:N@  ,,;60 ëîêàëüíûõ öåëåé) ïóòè ïîèñêà ðåøåíèÿ. Ïðèíöèï èåðàðõè÷åñêîé ñòðóêòóðèðî- âàííîñòè çàäà÷ îáúåêòèâíî ñîîòâåòñòâóåò ðåàëüíûì ïðîöåññàì èõ ðåøåíèÿ, ïðîèñõîäÿùèì ïðè ðåàëèçàöèè äèñïåò÷åðîì ïîñòàâëåííûõ öåëåé. Ìîäåëü ïðåäìåòíîãî ìèðà íà òàêòè÷åñêîì óðîâíå ôîðìèðóåòñÿ ïóòåì îãðóáëå- íèÿ ñâîéñòâ îáúåêòîâ F k f   â ìíîæåñòâî ' F  , îïðåäåëåíèÿ ïî ìíîæåñòâó ïðîöå- äóð A n   } ,.., { 1   ìíîæåñòâà ýëåìåíòàðíûõ äåéñòâèé ' 1 } ,.., { A in i     , ïðè ýòîì O O    ' , O O R R  ' . Òîãäà ìîäåëü ìèðà èìååò âèä: ' ' ' ' ' , , , O F A O R W     , à ïîñòàíîâêà òàêòè÷åñêîé çàäà÷è ' g ïðåäñòàâëåíà ïàðîé ' ' , n k s s . Ðåøåíèåì òàêòè- ÷åñêîé çàäà÷è ÿâëÿåòñÿ ñîâîêóïíîñòü ïëàíîâ in i i    ,.., 1 '  . Áëàãîäàðÿ ïðîèçâåäåííîìó îãðóáëåíèþ â ìèðå ' W , ñòàíîâÿòñÿ íåðàçëè÷èìû- ìè îòäåëüíûå ñîñòîÿíèÿ îáúåêòîâ è íåêîòîðûõ ïðîöåäóð. Îäíàêî ïîäîáíîå óïðîùåíèå íå âñåãäà ïîçâîëÿåò ñíèçèòü ðàçìåðíîñòü ïðîñòðàíñòâà ïîèñêà ðåøå- íèé äëÿ ' g , ïîýòîìó íåîáõîäèìî äàëüíåéøåå îáîáùåíèå íà ñòðàòåãè÷åñêîì (ïîíÿòèéíîì) óðîâíå.  ìèðå ' W òàêòè÷åñêèå ñèòóàöèè ' s îïèñûâàþòñÿ, êàê è ñèòóàöèè s â W , ÷åðåç ñâîéñòâà îáúåêòîâ è îòíîøåíèÿ ìåæäó íèìè. Òàêèå îïèñàíèÿ íå íîñÿò öåëîñòíîãî õàðàêòåðà, òàê êàê íå ñîäåðæàò â ÿâíîì âèäå ñìûñëîâûõ ñòðóêòóð. Âûÿâëåíèå äàííûõ îáîáùåííûõ ñòðóêòóð è ôîðìèðîâàíèå ñîîòâåòñòâóþùèõ èì òàêòè÷åñêèõ ñèòóàöèé ' s îñóùåñòâëÿåòñÿ íà îñíîâå çíàíèé î ñòðóêòóðå ðåøàå- ìûõ äèñïåò÷åðîì çàäà÷, åãî íàìåðåíèé è öåëåâûõ óñòàíîâîê, è îçíà÷àåò îöåíêó ñëîæèâøèõñÿ ñèòóàöèé " s ñ òî÷êè çðåíèÿ ðåàëèçàöèè ïîñòàâëåííûõ öåëåé. Ñëåäîâàòåëüíî, â ìèðå " W óêàçàííûå öåëåâûå ñèòóàöèè " s ïðåäñòàâëÿþòñÿ â âèäå óêðóïíåííûõ îáúåêòîâ ' ' m  , ñâîéñòâà êîòîðûõ ' F k f   , îòíîøåíèÿ ' ' ' ' O R r  ìåæäó êîòîðûìè è ñàìè îáúåêòû ' ' m  îïðåäåëÿþòñÿ íà îñíîâå çíàíèé î ñòðóêòó- ðå ïðîöåññà âçàèìîäåéñòâèÿ è âîçìîæíûõ ïëàíîâ äèñïåò÷åðà ïî äîñòèæåíèþ èìåþùèõñÿ ó íåãî öåëåé. Òàêèì îáðàçîì, ìîäåëü ìèðà íà ñòðàòåãè÷åñêîì óðîâíå ïðåäñòàâëÿåòñÿ êàê ' ' ' ' ' ' ' ' ' ' , , , O F A O R W     , ïîñòàíîâêà ñòðàòåãè÷åñêîé çàäà- ÷è ' ' g – â âèäå ïàðû ' ' ' ' , n k s s , à ìíîæåñòâî ãèïîòåç ðåøåíèÿ - â âèäå ïëàíîâ in i i    ,... 1 ' '  , ïðè ýòîì êàæäàÿ ãèïîòåçà ïðåäñòàâëåíà îòäåëüíûì ïëàíîì ' ' i  . Âîçìîæíûå ïëàíû äåéñòâèé äèñïåò÷åðà îïðåäåëÿþòñÿ ñ èñïîëüçîâàíèåì ìî- äåëè   , , , ' ' ' W W W  , ãäå  – êîìïëåêñíàÿ ñòðàòåãèÿ ïîèñêà âîçìîæíûõ ïëàíîâ. Ñóùåñòâóåò äâà áàçîâûõ ïîäõîäà ê ôîðìèðîâàíèþ ñòðàòåãèè  [7].  îñíîâó ïåðâîãî ïîäõîäà ïîëîæåíà ìîäåëüíàÿ êîíöåïöèÿ, ñîãëàñíî êîòîðîé â ïðîöåññå ïðåäâàðèòåëüíîãî àíàëèçà èñõîäíîé ñèòóàöèè èç èìåþùåéñÿ èíôîðìàöèè èñ- êëþ÷àþòñÿ íåñóùåñòâåííûå äåòàëè, è äàëüíåéøåå ôîðìèðîâàíèå ïëàíà îñóùå- ñòâëÿåòñÿ â ðàìêàõ îñòàâøåãîñÿ îãðàíè÷åííîãî ìíîæåñòâà âàðèàíòîâ. Âòîðîé ïîäõîä îñíîâàí íà îïðåäåëåíèè äîïóñòèìûõ äåéñòâèé äèñïåò÷åðà è âîçìîæíûõ ïóòåé ðàçâèòèÿ ñèòóàöèè. 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KNױXnM=ϝ9l'N'>Ϝp3Xu>Oy8ϭh@Y=.Y\_ \;}@Ƈ cX=WѽOi?Jo.ni[pO(__`eeT4![D#::8N?5r—ST7#nT)^bOLYz7,a`ሣ `L%qGvLfuOpex9'Wa ܤK76*oq~S~ԿaoMu;|3AP~v?*~ 'bY7raqv@8m7{ x4bԸ76o0HcQ9Ku4eߴ _\y&癭8].y]N\|0C49cxx$}#ZNQ /wãJc5g53qߛ:ovkE;tso8|'nG^һ,uR2<0eP+m` KJ~K .ezK _fZ8K~3|_b֩o:W?}p`LO;lX7w1=q|8ovm>FњX]+4=?u|͖kwgaj מѱg'+g=w%#OI4[Y.{Jbes }X/R|?^aM;{4(5]Ic}>Sŏ6/+?ZΊ   : k 2vV%TXYǭ̪I?@<%yacas~'#]5n n[D?هH_q+.) ̀l?] B [{5nU.b6Q-FܢsX*1ɆSeO+rb3%SuG(uN'mpz ؠ<&3]G\ur ZV{OMPe#hK-P\ ޓψb`ޠPcYة6 4FME)SP4#C͸1enZsCGyu)xދ҈w kvgw`Y/q-t_؄AM5ay{}upءah {R*;{ӽ'QFJ75~樏ƱLW? ]7x/Su~eN%.4+nL;Si<?n8'IlB(*{}enC0Y{HR=\;|[ӑøaǁ(ǎCж9%@7߶Zt ƋCZ O~p#e2gG ]:\󹽤SǏ끮wahbbs}Mq؁z^6WZM~)c|Hj;Co;yryQzk CQQKQa^~ɵ] d$lov t^92cz/_AgK34jϸ2(,I=\m7>[x=d۵Kٰ3h]Z e#[ebX(c"9] -xź,pSvM~oߟaf &+K.g~o8ye6yy>|XruTy"gMq G;`؀Y #0 ֌8}B|sS/!B7nA)A 4(Fd,V}Y\~6޲Mf|xNs9LY,|ߡs+}-$G~ܕn}9~,w l]>M̜2ؑ4ta8ߣ4؊`7Ta_ozw(<}>K6%޼iɋߎ1,F' X3od7߿OdwpZiaGsXHyjvl;DJ ٜ:|vh31>}xú1ox)x`; ' +.v_5!I{ޚvdj}n"[Gw$]o ?䡫5鯦?w͟:PI;F<ԗC#zhm=z{Ge,C#p  YO_DŽsy?2D؋ S%1Gu얿ByE<~8Vx"pwLC_Ic=ٺ);z@k[lZqoR\^SJ=዁p\:v~]8V|FE4qw_%Q n|{ityj3c|f].~Z{L/[E3L%36GR6EE|nzA>6.cyw7 >N^&S?=7oxM* ٰ6tG`o '=+Gzz!rEE#Gq,Ǿ"i/̫T.b|q&x7 c]a1wڕ[4|k6M=苣tbjGn+zHAӫ[t+Er kx_LS~Wt$v7NgίO^\d.';_bn nQ$ܬt@nBr G.~,p̰ց3[iԁWrw9An,^|OhnE "/Mi#OgGsj-*aJ{mEqXy ~\^6Qwl/#LZ9[YCզL{H{ⰿ嵇_~+Jnd[g!x0vtHqd CZ3`Hǹ B;D3?,Lth䓇v9^Q>ÚLV&zƺ>{ ߼d[Ko͓R}f(w^_u_`ʛSWv>|#)^vqWyLiʳwM/ڥ}Sϐoƾ­כ'ozqϟByeӋ.?s *BUtvKvTiyrZ6i#mB_@d5rLIC&G葋럷++ܴ9@bw ʷ^Ҧgi2eUdTޑiU10΃?M,^jJk%Txk?%7X.kiJӑ_*';^Irp0?4/oɐxYڑX׆wsE}&~Huӫ[thGûpEmhG)^<@?r3t*7{ޕ%gÞнH;e eҐcW9=rc9QEM*ڄy+ BoIfe,|(ao( υ_w)|o lJ 2t9tuYۼgatށh?}ҚDIQ,6CpۊL;!Ȧk!_Q 1hzҶi8cחԀuy۷WI'-NV뫿 3QsJ?lfa8u߉#pgxp>9+O<2iИ]ӥsum|]~,,_61 íåêîòîðîãî ïîäìíîæåñòâà ïóòåì ïðèìåíåíèÿ ê èñõîäíîìó ïëàíó ýâðèñòè÷åñêèõ àëãîðèòìîâ [8]. Òàê êàê äåÿòåëüíîñòü äèñïåò÷åðà íîñèò ïðåèìóùåñòâåííî öåëåíàïðàâëåííûé õàðàêòåð, èñïîëüçîâàíèå ìîäåëüíîé êîíöåïöèè ôîðìèðîâàíèÿ ïëàíîâ áîëåå ïðåäïî÷òèòåëüíî. Ñóùíîñòü ìîäåëüíîé êîíöåïöèè ôîðìèðîâàíèÿ ñòðàòåãèè  çàêëþ÷àåòñÿ â ñëåäóþùåì. Äëÿ ïîñòàâëåííîé èñõîäíîé çàäà÷è ' ' ' , ~ k n s s g  îïðåäåëÿåòñÿ ñòðàòåãè÷åñêàÿ çàäà÷à ' ' ' ' ' , k n s s g  , ãäå " n s – ðåçóëüòàò îñìûñëè- âàíèÿ äèñïåò÷åðîì èñõîäíûõ äàííûõ èç ' n s , à " k s – ïðåäñòàâëÿåò öåëåâóþ ñèòóàöèþ, îïðåäåëÿþùóþ ñìûñë òðåáóåìîãî, íî ïîêà íåèçâåñòíîãî ðåçóëüòàòà, äîñòèãàåìîãî â ' k s .  ñëó÷àå, åñëè áû ñèòóàöèÿ ' k s áûëà èçâåñòíà, òî ïàðà ' ' , k n s s çàäàâàëà áû òàêòè÷åñêóþ êîíêðåòèçàöèþ ' g äëÿ g ~ . Ïðè ýòîì ðåøåíèå g ~ äîëæíî áûòü íàéäåíî â âèäå óïîðÿäî÷åííîé ñîâîêóïíîñòè ïëàíîâ '  , ïðåäóñ- ìàòðèâàþùèõ âûïîëíåíèå ýëåìåíòàðíûõ äåéñòâèé ' 1 } ... { A in i     . Äëÿ ýòîãî ïðåäâàðèòåëüíî íåîáõîäèìî îïðåäåëèòü îáùèé ïëàí ' '  . Îáùèé ïëàí ' '  ÿâëÿåòñÿ ãèïîòåçîé, ïîèñê êîòîðîé ïðîèçâîäèòñÿ â ïðîñòðàí- ñòâå ïðîöåäóð ' ' 1 } ,... {   in i   è âûðàæàåò, ÷òî è â êàêîé ïîñëåäîâàòåëüíîñòè íåîáõîäèìî ñäåëàòü, ÷òîáû äîñòè÷ü æåëàåìîãî ðåçóëüòàòà [7]. Ãèïîòåçà ðåøåíèÿ îãðàíè÷èâàåò îáëàñòü äàëüíåéøåãî ïîèñêà ðàìêàìè ñôîðìèðîâàííûõ ïðîöåäóð i  , äåêîìïîçèöèÿ êîòîðûõ ïîçâîëÿåò ïîñòàâèòü òàêòè÷åñêèå çàäà÷è ' i g è îïðå- äåëèòü ñèòóàöèè ' in s è ' ik s . Êîãäà òàêòè÷åñêàÿ çàäà÷à ' i g ïîñòàâëåíà, ìåõàíèçìû ïîñòðîåíèÿ åå ðåøåíèÿ àíàëîãè÷íû ìåõàíèçìàì ïîñòðîåíèÿ ãèïîòåç ðåøåíèÿ. Òàêòè÷åñêàÿ çàäà÷à ìîæåò íå èìåòü ðåøåíèÿ èëè îíî ìîæåò íå óêëàäûâàòüñÿ â ðàìêè çàïëàíèðîâàííîãî.  ýòîì ñëó÷àå ëèáî îñóùåñòâëÿåòñÿ ÷àñòè÷íàÿ êîððåê- òèðîâêà ïîñòðîåííîé ãèïîòåçû, ëèáî ôîðìèðóåòñÿ íîâàÿ ãèïîòåçà [8]. Öåëåíàïðàâëåííîñòü äåÿòåëüíîñòè äèñïåò÷åðà ïðè ðåøåíèè ïîñòàâëåííûõ çàäà÷ îáóñëàâëèâàåò íàëè÷èå îïðåäåëåííûõ îñîáåííîñòåé ïðè ìîäåëèðîâàíèè ïðîöåññà ïëàíèðîâàíèÿ äåéñòâèé [7,8] è ôîðìèðîâàíèÿ ñòðàòåãèè  : 1) ñòðàòåãèÿ  äîëæíà îáåñïå÷èâàòü ôîðìèðîâàíèå ãèïîòåç îòíîñèòåëüíî ïîðÿäêà è ñïîñîáîâ ðåøåíèÿ ñòîÿùèõ ïåðåä äèñïåò÷åðîì çàäà÷, èñïîëüçóÿ ìåõàíèçìû èíäóêòèâíûõ ðàññóæäåíèé è ðàññóæäåíèé ïî àíàëîãèè. Èíôîðìàöè- îííûì áàçèñîì äëÿ ïîñòðîåíèÿ òàêèõ ãèïîòåç ñëóæèò ìîäåëü ïðåöåäåíòîâ, â êîòîðîé íàêàïëèâàåòñÿ èíôîðìàöèÿ îá àíàëîãè÷íûõ ÷ðåçâû÷àéíûõ ñèòóàöèÿõ, ïëàíàõ è äåéñòâèÿõ ïî èõ ïðåäîòâðàùåíèþ, ëîêàëèçàöèè è óñòðàíåíèþ; 2) ìîäåëü  âñåãäà ÿâëÿåòñÿ ëèøü íåêîòîðûì ïðèáëèæåíèåì ê ðåàëüíîñòè, åå òî÷íîñòü è äîñòîâåðíîñòü çíà÷èòåëüíî ñíèæàþòñÿ ïðè ðàññìîòðåíèè ïëàíîâ i  áîëüøîé ãëóáèíû. Ôîðìèðîâàíèå ïëàíîâ i  îñóùåñòâëÿåòñÿ íà îñíîâå öåëåâûõ óñòàíîâîê äèñïåò÷åðà ñ ó÷åòîì îãðàíè÷åíèé   è   , îïðåäåëÿåìûõ ñòðóêòóðîé çàäà÷è. Äëÿ ïîâûøåíèÿ äîñòîâåðíîñòè ïðîöåññ ôîðìèðîâàíèÿ ïëàíîâ äîëæåí ïðåäóñìàòðèâàòü âîçìîæíîñòü óòî÷íåíèÿ öåëåâûõ ' ' k s , ' k s ñèòóàöèé â õîäå âçàè- ìîäåéñòâèÿ; 3) òàê êàê êîíêðåòíàÿ öåëåâàÿ ñèòóàöèÿ ' k s çàðàíåå äèñïåò÷åðó òî÷íî íå èçâåñòíà, ðàññóæäåíèÿ î íåé ìîãóò áûòü ëèøü ïðèáëèæåííûìè; â ðåçóëüòàòå òàêèõ ðàññóæäåíèé ÑÏÏÐ ìîæåò áûòü âûáðàíà ñèòóàöèÿ ' ~ k s , áëèçêàÿ ê òðåáóå- ìîé ' k s . Äàííîå îáñòîÿòåëüñòâî òðåáóåò èñïîëüçîâàíèÿ ñïåöèàëüíûõ ñðåäñòâ îöåíêè ìåðû áëèçîñòè (èëè ïîäîáèÿ [3]) ñèòóàöèé. 0xlWm/--@"][cʲ14`3#(&[lcN7Ȓ-~c+º+(C̡8@yڇǧ/?irs=ss3OD2E"sFd DI]C_Iۓla"ds}P1gp9S\7k9S\t v&* 9&LRȭR*2*yڭ:u{?^:[ЩEtӈNt36JX?p 3LCNn+9݈cGekM~_u?DF-lC(T2ql3Eb'S/cx}hIȿ.et[q2Tj<\^fb4Y ezO};nTK,8xJT8]Wi:s|ޝ-]14ɲy<%+ufr19S UHOBmG.UW">2ӏ_F{ּPH̿`ńIyZM}+[Ys?pNHMo/DKcgCm pa ;6^ ߏYÞ8a*1nG}ʼnls#,39U~w.Rڻ[܅'|z۝/[wt;ez;a|2Iv`ky~СlJrkP~X_un X~|{|:Qc< e}= ʅ8?syԾCp*p, }6?,>yyFں7*c7[S~mWmx Y]StOco )FA9_o6b/@ZEad 8̌ o4t8:VR55 ~AMyVNX:h}/|NA:LzҌbv,:8Qu^ʫl;ZM6dIZIz]F {w; ^ Ѥ$/Uij |<Ճ`^Zx)UDemQ1 vA 1lȏ.px7՜=ok=hYl>^՗%*2/&xW}+i$ִvLJ2S{"3VfsG.m1ui|mfSB{;t/_ɳ `\^nok4;$_SO`s }DVԳdQL!Hih5=<;164tM7`/6qt$o0Gʵ|`y$y;|ȿ N)Ue}&hur^U昴q;i/fl/}ৡ1aYv)LMFBnvr;W`Ӯ4{;o`=5Oqx~6g =_硇>m4vzC܍z'̃FRvJ5%Ct]'˜*7{dO[O3Ķ2y_M'JZ鯗 ݄ +Ï2ԃ^YdtoB} @{/fFrwtfl;LnA71[_u]갤oE}=ףe9x?ʲBFAD<7pde z?n>h%4xGc?2־rwx-3/h >_#OArܞB[]\ž&]cZ_I&j\ߒQ|SvzWTж-FFT^BV/ zF5^v޻A7Ֆ}꘾2:~^l![W{si}۲}O<7UMƢdݨ1}(+o(} 5g>=()tòW:|ݎ[̷abFS^o3A~TE1Em'طg4Qkuo>|zWߍl;j?{RPFCX6Wq#G @8q"h8q#G @#*Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:31:40  p =`h(160>2f>/ev1S 4{0lxŜ{]G}&$% /&n x4P:mT JӦ$"ϊD ZPG+F4j)EDUiT^J+WM՛:ů6q3w{N&k̜{fp 3MΤl??;̷5͆ۛf4L󪛛=' Tۿ/?i M. _]߼7m ~-waS])??_p'i KcRø+oRN>%ۜ|lWژ+<%]4#iuxfZ̕@F[ShҴ\׋K՜ەRWfQQskA>r[3VۛBQ]gyߞyoԼޟoqϹKL:8wVZӯ?e+߾mv;Yܴ/ޘ;wW;W/\-Ç/|>\&]͆|iZʨ Wt}K{ҹ͕nzc[KN;l^F-?8zDwO"+^+hӴ׎w}k^ 2ɖޭq@_ #c$oVj|ksKsGĔ*\`dgOMpj\|Ά7aSEm]/'?m:6S'asɟm~6c&4DꪶgBWIH9&mJ*ipھ C|s,eGi$?=́<4-p]Lhf,|jv8tm}'-3lXKnK: u!F8ԅӆެ'78b!m=mn9pφL"|3y_1m_K6i:m9i?4/8ݜl..䏯``X4O-' @sQ8?Y' |9=l˘'rcz\#r+#lF^I?m/OҶcoq111>qiw܎plcG1X ୁNxa4|Gj{b#6޺ZO_ϷſK -|s<60K#*<z+@Vȇ9#&eXtC_WYWy>X?a6lvn: Za=l탸=J : Z=X JRrP_9!g`R^P,^]M_>XZ광CZy8OCCrl5x g](X7l̾t o߲G6vR O^dk%E :0OR-Z>l%eRWeC+=)=_,y+J:i:_I/gOߌGcVSvjL]Dbv[ =Ar@ 싘'21G$":3~B7DOIeڤN$ڨey6<ܟ$Bo:sOW[kF{(^:Zo3:ՁuyI9pa[sCW1('IkI:'AWnZpQNmSC_pI[&> ~7}8;5:[GeG^}C<}+R>8\G?l~\XOp%;.y;Z vyc8sEȌe#o'?mN}k~H+_yjk/pv -0x?pCo]?[@t8&fOu>W(Tyb/mp,ciŊYͷ[@b1e씩2?)[brGzqm:b j{_wƶCO]Rϡq 3?vs\XӶju;`&nJ`?O,'mh:#$QPgʞ83ӎlU[6 /F$^Z}j#}O`k}Y] j7Oc Ixi-|F'z|k= >Yd|]C_)ssx+"x\n?!.X=f =>lK.WQb4]!QGdW찎_yT=VN0Z.z-_ʦ'UI?-ڷ9#q>^~ AҖ$2^OT/XWb4ڃgtK=aoS`ׄ~GRWIAӜ˲+'ūUr*ۧ+lՁ,µo[+zT=\W!#D=[nϤ\\?r`§.5''O 9 L;1uPX+s{>#sYqƅӜXZ}{|q7wȤWV =xL 7R3 /\|ry5Ox9F3ONM݁jeoVV{(D{OxrWؿL]!aG}yzO| &)3ԲmIM#0p^|."m'pze$h0/i}Oku>x#/x,gqea,ync΃\P>OҎ9f>ĬyH`kw: D1dd?w,Ϋ^4įmSFȒL#Hk)Og۟6}t'p#/0azW;LrKzrN`Wf?ގ=c]p]q$IsEs r4YXhx{c unt9W?=[W¬\u xl%>kWIĥجK^sY9><})w$ ؈mWvM`Vǜo[oʹs9*+%,+ N9-% E߷F/عarDf $, o$=/K+cuF$vh#=t}u/`ol{p~w3hx4bޅo +%9M?N-k8^P> [S,(' Ns'cS #Fk:(&ZP{*G{Y-r\K9ǁw͟}S}Y]>ױI/.9I)X7%~ Db\=?9V)[gGsr-q8i,w8w{9z}j*'字DU,(v}#qu%ޕa?fR8]-~a{Q__YpLYy('mn>usu~ܺ/tv:<`\qn[;4'h<'˞=Z Ұu ,b7b]os9tI Ocw%?J^ >Oɻ xMڸ'`3rTlXY=B ]|:ݶ4‰wsvQhyPr/0ZK2F^륖bll7Q&#krci^cݗ|Uwا> >Qk'c|NI&Sڕhu\ED:;wc>ߞkg-թO s&`H̟ļNb\VYЏ)wՁ9} omP=7upuua Qǹ v; ݣdw[Tt+0{>gMx_i˛JUSd ȃ8L݁|A`OPlycї9'~WQ}3>.vy>{wOC{&1'Z夁߿NG#qYD:=(-^~۽)(Qs޽yQy0wru#~B6li&r\?VA#?Kk[Е8/;fײs&g ǚo؁?~ |LgJ_W麼?p x2sv.qBIU{,Pbm}KLeljӆ2%nN'm=ꁺ0튶z,ЯcЯ Mpi_OԺ,ϊ&k:b?2?V١'qse_ ;&uʛ7jJZ_n;&SGȓl#3a[\d,L Ȗ\k|ۅ m`><}R^kt|}Ϫ7zeo< sgo. iFE)o)ր|CG o-:O?M }1WmN+#ȮnǿyPOu69A~ xGphv2p&Z$qs[ҭ3'}3-MfSͭYʹ(L$?7Ӯ9|{\>7 'f_&L{AhfǶ|7Ӑ7}~4}k5|/{^wx]~gK+_͑Sǖz>ϟd,xmNw{VkFz7*C% /=qQ9D.CKN>C<# ~qߙae~}!Bvx4_  O8WZu+_l`;~w ?O= {8#$1{8 l//𗷦9Ȋ%]dDo_<_\Sm~ rUȧhluY ohSO]9i" zyQO}x~1v}~}\[C?>icjMOrI§E:˹v TcOluKK,Z\R. 3t'd+_tAyR<10O|Y>ȡ-@ X7>>S#0إf_O6{(ou?O$˧> O}='d.AWnxI$0>$yHOn  p?Zg?p+l%ʖ_5 \e={gʍ唐roJ; dhCȣepN;t*D[1 cN/`3QO߬ص{ôq^6/e+7;j˗e_=:ƿ m.O<ߏ.a_b8 99ٯgtO| w?edDBfQN׸_yʟ\p-C[v|xϚegt G)RۧKUMӆˉ=$w}YWO_;÷1P enXGg8彟r3\'s~\a}eMN;<Ak|ҮOKkI%*/i/:>G/΁to͊?}/ |987bu3־]CC9w)sebM|wE 66X9/y*rƹA; F9vC8c 9"/pas" 801G:e֥#w,c.8ѧx\׮Nןd`k/tYVv-D3f]coR~=~YSRΔxs@Z="?ꔕ ~:FH|ɡW6h1^J8m}|w{t?ϏdoV$$=u>ʒFZq>K>~)%+rcʛ22vo+:er(2>䯝@x9k7|>k$_`n}y{_%݋w8'9? 4Ox9,,62  ñâÿçè ñ ñóùåñòâåííîé íåïîëíîòîé èíôîðìàöèè îòíîñèòåëüíî ïàðàìåòðîâ î÷àãà âîçãîðàíèÿ, íåèçáåæíî ïðèñóòñòâóþùåé â ðåàëüíûõ óñëîâèÿõ, öåëåñîîá- ðàçíî èñïîëüçîâàòü ñòðàòåãèþ ïîèñêà ïëàíîâ, îñíîâàííóþ íà âûÿâëåíèè õàðàê- òåðíûõ ïðèçíàêîâ ðàñïðîñòðàíåíèÿ î÷àãà âîçãîðàíèÿ è ñîïîñòàâëåíèÿ ñ íèìè ñîîòâåòñòâóþùèõ ëîêàëüíûõ ñòðàòåãèé, õðàíèìûõ â áàçå çíàíèé. Ïðîöåññ ïîèñêà îáùåãî ïëàíà îñóùåñòâëÿåòñÿ ñ èñïîëüçîâàíèåì ìîäåëè ðàñ- ñóæäåíèé íà îñíîâå ïðåöåäåíòîâ (Case-based reasoning, CBR). Ïðèìåíåíèå ïî- äîáíûõ ìîäåëåé â èíòåëëåêòóàëüíûõ ÑÏÏÐ ïîçâîëÿåò ïîâûñèòü ýôôåêòèâíîñòü ïðèíÿòèÿ ðåøåíèé ïðè âîçíèêíîâåíèè ïðîáëåìíûõ ñèòóàöèé. Äëÿ ýòîãî ïðîèçâî- äèòñÿ ïîèñê è àäàïòàöèÿ ïðèíÿòûõ ðàíåå ðåøåíèé äëÿ ïîäîáíûõ ïðîáëåìíûõ ñèòóàöèé, ñîõðàíåííûõ â ôîðìå ïðåöåäåíòîâ â ñïåöèàëüíî ïîñòðîåííîì èíôîð- ìàöèîííîì õðàíèëèùå — õðàíèëèùå ïðåöåäåíòîâ. Ìåòîäû CBR óñïåøíî ïðèìå- íÿþòñÿ äëÿ ðåøåíèÿ øèðîêîãî êðóãà çàäà÷ êëàññèôèêàöèè, äèàãíîñòèêè, ïðîãíî- çèðîâàíèÿ, ïðåäñêàçàíèÿ, ïëàíèðîâàíèÿ è ïðîåêòèðîâàíèÿ â ðàçëè÷íûõ ïðåä- ìåòíûõ îáëàñòÿõ (íàïðèìåð, äëÿ îáíàðóæåíèÿ ìîøåííè÷åñòâà â ôèíàíñîâîé ñôåðå, ïëàíèðîâàíèÿ ìàðøðóòîâ â òðàíñïîðòíûõ ñèñòåìàõ, ðàçðàáîòêè ïðî- ãðàììíîãî îáåñïå÷åíèÿ). Èñïîëüçîâàíèå ïðåöåäåíòíûõ ñèñòåì ðàññóæäåíèé â óñëîâèÿõ âûñîêîé äèíà- ìèêè è íåîïðåäåëåííîñòè âîçíèêàþùèõ ñèòóàöèé, ÷òî õàðàêòåðíî äëÿ ÑÏÏÐ â ÷ðåçâû÷àéíûõ ñèòóàöèÿõ, íå âñåãäà âîçìîæíî èç-çà íåâûñîêîé ýôôåêòèâíîñòè ïðîöåññà ôóíêöèîíèðîâàíèÿ ñèñòåìû, îñíîâàííîé íà îáùåïðèíÿòûõ ìåòîäàõ ïîñòðîåíèÿ õðàíèëèùà ïðåöåäåíòîâ.  òî æå âðåìÿ ìîäåëè ïðèíÿòèÿ ðåøåíèé, îñíîâàííûå íà ïðåöåäåíòàõ, ÿâëÿþòñÿ íàèáîëåå ïîäõîäÿùèìè äëÿ äàííîé ïðåä- ìåòíîé îáëàñòè. Êëþ÷åâîé îñîáåííîñòüþ ïðåöåäåíòíûõ ñèñòåì ÿâëÿåòñÿ âûâîä çàêëþ÷åíèé íà îñíîâå ïîäîáèÿ òåêóùåé ñèòóàöèè íåêîòîðîé àíàëîãè÷íîé ñèòóàöèè, ïðîèñøåä- øåé ðàíåå (ïðåöåäåíòó), ñîõðàíåííîé â õðàíèëèùå ïðåöåäåíòîâ. Ïðîöåññ ïðèíÿ- òèÿ ðåøåíèÿ íà îñíîâå ïðåöåäåíòîâ, êàê ïðàâèëî, ñîñòîèò èç ÷åòûðåõ ôàç: – ïîèñêà è èçâëå÷åíèÿ ïîäîáíûõ ïðåöåäåíòîâ; – âûðàáîòêè ðåøåíèÿ; – ïåðåñìîòðà è ìîäèôèêàöèè ïðèíÿòîãî ðåøåíèÿ; – ñîõðàíåíèÿ âíîâü ñôîðìèðîâàííîãî ïðåöåäåíòà. Íà ïåðâîé ôàçå èñïîëüçóþòñÿ ìîäåëè ïîäîáèÿ ñèòóàöèé [3], íàèáîëåå ÷àñòî ïðèìåíÿåòñÿ îòíîøåíèå íå÷åòêîãî (èëè ïðèáëèæåííîãî) ñòðóêòóðíîãî ïîäîáèÿ. Îòîáðàííûå íà ýòîé ôàçå ïðåöåäåíòû âìåñòå ñ òåêóùåé ñèòóàöèåé äàëåå ðàñ- ñìàòðèâàþòñÿ ñîâìåñòíî. Íà âòîðîé ôàçå äëÿ ïðèíÿòèÿ ðåøåíèÿ î âûáîðå òîãî èëè èíîãî âîçìîæíîãî ïëàíà äåéñòâèé èñïîëüçóåòñÿ ìîäåëü ðàçâèòèÿ ïîæàðà [7], ïðèâÿçàííàÿ ê ïðî- ñòðàíñòâåííîé ìîäåëè, ðåàëèçîâàííîé ñðåäñòâàìè ãåîèíôîðìàöèîííîé ñèñòåìû. Òàêîå ðåøåíèå ïîçâîëÿåò ðàññìàòðèâàòü ïðåöåäåíòû íå êàê ñàìîñòîÿòåëüíûå åäèíèöû çíàíèé, à âíóòðè ïîñòðîåííîé ìîäåëè, ÿâëÿþùåéñÿ äëÿ ïðåöåäåíòîâ êîíòåêñòîì. Êîíòåêñò ìîæåò ïðåäñòàâëÿòü ñîáîé ïîâåðõíîñòíóþ èëè ãëóáèí- íóþ ìîäåëü çíàíèé.  ïåðâîì ñëó÷àå ñèìáèîç ñèñòåìû, îñíîâàííîé íà ïðåöåäåí- òàõ, ñ ñèñòåìîé, îñíîâàííîé íà ìîäåëè, ïîçâîëÿåò äîáèòüñÿ ïîñòåïåííîãî óòî÷íå- íèÿ ìîäåëè ïóòåì ðåàëèçàöèè èíäóêòèâíûõ, àáäóêòèâíûõ è òðàäóêòèâíûõ [5, 6] ìåõàíèçìîâ ðàññóæäåíèé îòíîñèòåëüíî òåêóùåé ñèòóàöèè. Îäíèì èç íàèáîëåå ñóùåñòâåííûõ íàïðàâëåíèé äàëüíåéøåãî ðàçâèòèÿ ñèñòå- ìû E-Plans ÿâëÿåòñÿ ðåàëèçàöèÿ ïðåäìåòíî- è ïðîáëåìíî-çàâèñèìûõ îãðàíè÷å- íèé è óïðîùåíèé, ïîçâîëÿþùèõ ñíèçèòü âðåìÿ, òðåáóþùååñÿ äëÿ ïåðåáîðà èìåþùèõñÿ âîçìîæíûõ ïëàíîâ. Íà òðåòüåé ôàçå ïðîèçâîäèòñÿ êîíòðîëü ïðàâèëüíîñòè ïðèíÿòîãî ðåøåíèÿ, ïðè÷åì åñëè ïðèíÿòîå ðåøåíèå î äàëüíåéøèõ äåéñòâèÿõ ïîâëåêëî èñêîìûé ðåçóëüòàò, ôîðìèðóåòñÿ íîâûé ïðåöåäåíò, ñîñòîÿùèé èç òåêóùåé ñèòóàöèè è ïëàíîâ åå ïðåîäîëåíèÿ, è ïåðåäàåòñÿ íà ÷åòâåðòóþ ôàçó íåïîñðåäñòâåííî. *xaheϳ6ﶻ;MjyZ"D(m_l2TPg4jd-'sk+f2Xz]h_9 K1e"R0BaxY%!>S"k4$nOfdNY @~&Ch9 XZXj4Ci>Gcp:Z+ĞtAVc7uͫ2Z8C {c[3͐I/UTP_ 62 oFF[e\#xr3R,RhDZ䟣?̔y&SZbl!,?~Y9j/O^J^ ĕ1;c3_O/᧨5O=p)=^ Et0Ԑ[wN)Lm㨳 {:vw3{{PDko>ko5LEfK/Ygy^ _L|mZB8/>^*|-vB{HG%c>4j;sTbz^be0n\VaB=.*j,\?g:G{gnyz[ snnsEރugq?Rj}ۊ[Ͽ |^ʱ`15p~ o gX~ G_Ao<>g}X?xZ>ET~>O8i>kʿ1>t|udUZB <%}]h<."WmG\yiM4kXpNAǨ/oM"37_'>zGcQƓ뛧oz2ߔ/ |{M?| ^u%9ʙRLp}gRoJ/&}Vs|yssoIh?xnp|mËSC=#}6p{J]LZ9x;Rox'(g6[=*ۧԶ/?&>y_> ZڨSZYߵg؞ޤ V<2Ycްڟ kMŠ7Ms?}Xp )wE_DPx͉ɘu})W'YնRf^xiѷvھ~x}A t/){wʱ!Ǜ}O,p('qs8}?p`Q@|8 oNi5Ot8D$};:^tI\$ǻչ<^[9K^R/P.uk_^r;dl ^/ κ7vOt~k,I˻ V8qcS?_+_>Hp >(IV+СXmĮC0'7:vxx4ړ=O;Je{WcH:G+iלsVЭydmNyiG6ܼ~yHbo'|]6o=v [˽wT7̃^Pi$?׷؍hcM={ o]\iox oQuL?]Ctp >\FOR~r뮷_/Y?ޜ%n޾ԟg?lwn}CxgboǦnbԈJN<2`c=ߗ]TmV+ܦdz1W6mЋk;ϼnj}sfmwv߿g?wŶo~dd jלBp߻Y*ߴf\c\>v%WyW+s틦CIX+u1[B/;6Nݭti._)h^n̕ƮiV1f ͫ5hYySfX{o1fQz;}'elt\=&-ӗ S8g9Y̨Ǝιeq;og}?G]-r;ꅮu+mݹ+W-WxP(pO3_uk3O}i}]ɳ;_xD|Ws'jݙmw~[ϦgS}ƮƗ'n[7ځ^:͗?8yxyNd˷{k_<M1+k:3|:׹cjW)<FXɋ۪yk=iDFiߤx*O0.O/ͷWcgná>9S}ûwA"ӽ|ʹ{ﳒۍqlM-yۍ.j =b(zoyk[7xu*K)2ڏ/0ѴmX9ҹI?u!N_+ 76,zo,ɿHnw{4XmӤ¸U;"ȰOL+.qg E[E>X˪ætS=K^孜/Osk*m<_y|xN:}C<.=e|"Ņnݭc1)~o 7k>>XGHqVtb~+]-ZJs S/ᤧcnQV7orA~iF>qx_;=c;OػX}"O;XO\QZQV=XD7c׸X@ptѱ;C(~{փ?;P7թyWGv۝M~·ʓ⁛rEvFΜ/q >^mk͡u/Y=al\#;>OwˍufsΜvV\~˵\{#G ѺeZ *q^9<}@/MNr3|OE+ 1Hhcnvnw?KXN{h;q;?x4rZ꜎vQT ǯlN⯞\FKkS3s^{=iH6.rѕw._ۀ>'\봝ʫ7xbk?On m}|,Cj؜s}ap7FY s[Nc;b;0vmƛ,fu{#qٻefYv;^'^plkCk< +v\4rWEUw+yL<ŕ? dd~0j%ӳdg:E#&0ǃt&rj>XzNo_s{qCgF[ӭCNSs?0}~ZzWwdn+|ϱw;o[ C~ !xiy׷O~)Pœ.-Me۽Լ_NPձ){pҘxW\!8foq}ٰ3'εg]0Ow`==|6bxWu|4^zo<kBJ Vi*-/}ɷNcu[^{.N})W.~yg~)GkWx|u:Rƅk,]~^s'~yO|p'z.;3=aOf/i-}썉0Oyӳ)N箾 hi8st3T?<z39}l)|wp'-G_Q9A>#A.@U~%<~p`qp/ 5g=$6hk5l8"NL7wtSS>k۽F}_tU{m`Z⡧t@O6hʫ5 ) 5շӎAy엜teucO=5 /=i;`}S:i`?;IwS`;I}?jk@^8?YS=EM>v{{'I>tp헒n{?m+>߹+~n҇k7MnmvMv{xvp9x{O;vēm>5ՙշ"gLq1z !_caM^Wƙ64ciY}[a"z\odCs7/I>/[~~c҇L~.m~Ns;7q>|mh| 3Iy+yc;P|y*8>qewVn\N3ඍ e|ci{So~6s|}gQ'߹}q`GvҫrUM.RF:s{K_ãP{PȗVz+6ZO}RRzdh,]d/@;?@ƹ<1VYC{Ϟ7 _+iPe}]p}s}ힸ|_oǃÿ⋳`Hؙd]!&l_c6޽z|շ@M7o<hYxKd޴gl>#Cc?6fkCW7xT)D#ӽ6ׅ cd'u{L7fHZ2.6Q.]L_Dbݫ҇3)m/]\<'O.M:qtq鋳N+~iGS9#`,eJk}eU1d7&Ɖf~Wh8_ڱ _OtqXyd Q}u»? m'<oD[;Nkkm; 8HE}4zpUu ^? ;C{ʃr*jڸ?u{F;Ic]~n}D_rw/=jog8@Wsl}؝Oh~Y0|qĺl}F;?-kI~!Oj\1rd|q';-I}O{qx]ٍCukX}+5>dwϪ/Wc]/x@Oy-zFNQĿ}?HV3Nά7&ݜ}[8P\lJtaϥxG j!cPkۦ ^$M 8/\Q_o%8s79_뒬8O_\(s%Yw,._IQG6&} e:hż\~8ƌG%O??=?zxKhpexC|]睙_gۻ h7"B/қ2'_`y ?^ ׫ȀtG>{IW^wPOߤ)W6uyy[,,oINt~WǮ*h\NkXb|ˀq7\Rs~oSBhhnvϻOlO}I7%蜲Nɍ2{'q_9|ѵa_#-?>`G鷾7hsd>hs. mH+_W)Ԏ|6 ޕ4]>+mv}mhc`[G7K٠e~8-{t'17ǧƴ׆6 {]_dyqd4ݫ:#%8;YE;7yL6$[O.8׾w,û/ohM{ [XNJ \ݡK]1OϭqG^;mZ{'+cѵ7^҅wlum{. k`0߭q~4?>O}hiμ/v/&S<qgoD}v 8exccg)g m,ޚg}s-Suc_sݭUC>ʐ'cSWy/򣟳*['8pq0Ҹ47ޖ?iŷ0)=hָ7X|wȿҶKzxg_Z }|MC@}\ȜW鿱ϓAvȪ\[/l}_JpeƳZ*g(ɸM;_o<=^iK4=o7 :KлtWS'9xIrP}ǃ&UV_@q-=moy{\WnvswGbߓM$+ӎb^yT7~?2nyImnKhDښa3䐧V.yA]6e';|)j'@B$Wd̺NF2r'+?A&p=e%qY 6wLixve5Ό7{7̅m/ߙww_◳ߊW7/TnxU&iO~&$[|}(ߓ)W_{MZ~ErZʮT茮ހ8Ch ~8G<6 ՎZo׼3'cppWS_ ]\k&>!.}S~e} ͗Wr'|S}j:w̢\Ͻ !GwZObݱSq~v8v~ifQ{UúzQ~g `at1v1i=VWzkZmA9섟سmO>>HmmޱWx` »B뻭uHgL,ϲ~weHwXdΣ6[~T+Ո0vيU@-']xtM}i<{t_`pݡ#AGMbGtЎ}Oc Ù'y&gC2{;"<\}[The=صG3OEքFOmzƞD0o1ܡb":c2^*3]sW]2Wsm{9yʍ~o_}Qg& j_]Um'Bߥ+>u77+8p66ormM9]mk[g/_lNy;E^=Զս2wTgfU~:|Kh=ȡîϵ)vG!@ቺZW={#+nd˛gߕ+Z=<%rg"ݓٵo؟} 4Ԩg-ϘKW~+ŧ\pPʀCpꗧgavgi>{3%s]5g`z{cﰜp\_|xAw)7+Ynpc2PyL6RU]Q7Oۖ]޶Unt/Onw"ۻ2C:5.m1ֹ[z([cWum`)K{ߴ㭽>ܵm7%5'2E3@>HoCtv7fs,,)63 Åñëè æå îòìå÷åíî ðàñõîæäåíèå ìåæäó èñêîìûì è ïîëó÷åííûì ðåçóëüòàòîì, ïðîèçâîäèòñÿ íåîáõîäèìàÿ ìîäèôèêàöèÿ (êîððåêöèÿ) ïîñòðîåííîãî ïëàíà ëèáî âûáîð èíîãî èç âîçìîæíûõ, ïîñòðîåííûõ íà âòîðîé ôàçå ïëàíîâ, ïðè÷åì íà ÷åòâåðòóþ ôàçó ïåðåäàåòñÿ ïðåöåäåíò íåóñïåøíîãî (èëè íåòî÷íîãî) ðåøåíèÿ òåêóùåé ñèòóàöèè. Äëÿ îáåñïå÷åíèÿ âûñîêîé ýôôåêòèâíîñòè êîíòðîëÿ èñïîëíåíèÿ ïëàíîâ â ñèñòåìå E-Plans èñïîëüçóåòñÿ ïîäñèñòåìà ìîíèòîðèíãà [1], îñíîâîé êîòîðîé ÿâëÿåòñÿ èíòåëëåêòóàëüíàÿ ñèñòåìà èçâëå÷åíèÿ çíàíèé èç áàç äàííûõ è íå- ñòðóêòóðèðîâàííûõ èñòî÷íèêîâ èíôîðìàöèè [6]. ×åòâåðòàÿ ôàçà ïðåäíàçíà÷åíà äëÿ ñîõðàíåíèÿ âíîâü îáðàçîâàííîãî ïðåöå- äåíòà â õðàíèëèùå, äëÿ ÷åãî â ñèñòåìå E-Plans èñïîëüçóåòñÿ ìîäåëü êîìïåòåíò- íîñòè ïðåöåäåíòîâ. Ïðèìåíåíèå â ñèñòåìå E-Plans èíòåëëåêòóàëüíîãî ïîëüçîâàòåëüñêîãî èíòåðôåéñà îáåñïå÷èâàåò íåîáõîäèìûé óðîâåíü óäîáñòâà ðàáîòû îïåðàòîðà, è â öåëîì ñïîñîá- ñòâóåò ïîâûøåíèþ ýôôåêòèâíîñòè ïðîöåññà âçàèìîäåéñòâèÿ ñ íèì, ÷òî îñîáåííî âàæíî â ñëó÷àå âîçíèêíîâåíèÿ ×Ñ.  îñíîâó ôóíêöèîíèðîâàíèÿ òàêîãî èíòåðôåéñà ïîëîæåíà êîíöåïöèÿ ñèòóàöèîííîãî óïðàâëåíèÿ äèàëîãîì ïóòåì àíàëèçà ìîäåëè ïîëüçîâàòåëÿ è ìîäåëè âçàèìîäåéñòâèÿ [1]. Ãðàôè÷åñêàÿ âèçóàëèçàöèÿ ñîñòîÿíèÿ îáúåêòîâ îáåñïå÷èâàåò öåëîñòíîñòü âîñïðèÿòèÿ äèñïåò÷åðîì ñèòóàöèè â çîíå ×Ñ, ÷òî ñíèæàåò âåðîÿòíîñòü âûáîðà îøèáî÷íîé ñòðàòåãèè ïî åå ëèêâèäàöèè. Äðóæå- ñòâåííîñòü, èíôîðìàòèâíîñòü è ãèáêîñòü âåäåíèÿ äèàëîãà îáåñïå÷èâàåòñÿ èñïîëüçî- âàíèåì èíòåëëåêòóàëüíîãî ïîìîùíèêà (èíòåðôåéñíîãî àãåíòà). Ôóíêöèîíèðîâàíèå èíòåðôåéñíîãî àãåíòà [2] îñóùåñòâëÿåòñÿ â ôîíîâîì ðåæè- ìå, ãåíåðàöèÿ ñîîáùåíèé-ðåêîìåíäàöèé ïðîèñõîäèò òîëüêî â ñëó÷àå íåîáõîäèìîñ- òè. Ïðè ýòîì ïðåäóñìàòðèâàåòñÿ âîçìîæíîñòü âêëþ÷åíèÿ äîïîëíèòåëüíîãî çâóêî- âîãî îïîâåùåíèÿ îá èçìåíåíèè ñèòóàöèè íà îáúåêòå, ÷òî ñíèæàåò îáùóþ èíôîðìà- öèîííóþ íàãðóçêó íà äèñïåò÷åðà è ïîâûøàåò îïåðàòèâíîñòü åãî ðåàãèðîâàíèÿ â ñëó÷àå íåîáõîäèìîñòè îäíîâðåìåííîãî êîíòðîëÿ ñîñòîÿíèÿ íåñêîëüêèõ îáúåêòîâ. Ñïèñîê ëèòåðàòóðû: 1. Õîäàêîâ Â.Å., Øåðñòþê Â.Ã., Áåíü À.Ï. Àäàïòèâíîå ïëàíèðîâàíèå â èíôîðìàöèîííûõ ñèñòåìàõ ïðåäïðèÿòèé è ó÷ðåæäåíèé // Ñá. íàó÷. òð. II Ìåæä. íàó÷. êîíô. “ Èíôîðìàöèîííàÿ èíôðàñòðóêòóðà âûñøèõ ó÷åáíûõ çàâåäåíèé ” . Õåðñîí: ÕÄÏÓ. 2000. T.2 Ñ. 259–263. 2. Áåíü À.Ï. Îñîáåííîñòè ðàçðàáîòêè àäàïòèâíûõ èíòåëëåêòóàëüíûõ èíòåðôåéñîâ èíôîðìàöèîííûõ ñèñòåì// Ñá. íàó÷. òð. II Ìåæä. íàó÷. êîíô. “ Èíôîðìàöèîí- íàÿ èíôðàñòðóêòóðà âûñøèõ ó÷åáíûõ çàâåäåíèé ” . Õåðñîí: ÕÄÏÓ. 2000. T.2 Ñ. 69–73. 3. Õîäàêîâ Â.Å., Øåðñòþê Â.Ã., Êîçóá Í.À., Äèäûê À.À. Ïðèëîæåíèå òåîðèè íå÷åòêîãî ïîäîáèÿ ê ïðåäñòàâëåíèþ çíàíèé â èíòåëëåêòóàëüíûõ ñèñòåìàõ // Âåñòíèê ÕÃÒÓ, ¹2(2), Õåðñîí, 1998. Ñ. 138-141. 4. Õîäàêîâ Â.Å., Øåðñòþê Â.Ã., Ñòåïàíñêèé Ê.Ã., Äèäûê À.À., Ìàðòûíîâ À.Í. Ìåòîäû îöåíêè ðåëåâàíòíîñòè èíôîðìàöèîííûõ ñòðóêòóð â áàçàõ çíàíèé // Ïðîáëåìû áèîíèêè. 1998. Âûï. 49. Ñ. 186-195. 5. Øåðñòþê Â.Ã. Èçâëå÷åíèå çíàíèé êàê âûáîðî÷íîå âûÿâëåíèå òåîðèé â êîíòåêñòíîé ëîãèêå // Âåñòíèê ÕÃÒÓ, ¹3(6), Õåðñîí, 1999. Ñ. 163-167. 6. Õîäàêîâ Â.Å., Øåðñòþê Â.Ã., Äèäûê À.À., Êîçóá Í.À., Ñòåïàíñêèé Ê.Ã. Ìîäåëèðîâàíèå èíäóêòèâíûõ ðàññóæäåíèé â ñèñòåìàõ èçâëå÷åíèÿ çíàíèé êîðïîðàòèâíûõ èíôîðìàöèîííûõ ñèñòåì // Âåñòíèê ÕÃÒÓ, ¹1(3), Õåðñîí, 1998. Ñ. 21-25. 7. Èñêóññòâåí- íûé èíòåëëåêò.  3-õ êí./ Ïîä ðåä. Ý.Â. Ïîïîâà. Ì.: Ðàäèî è ñâÿçü, 1990. 464ñ. 8. Waern A. Recognizing Human Plans: Issues for Plan Recognition in Human-Computer Interaction// PhD Thesis, Swedish Institute of Computer Science, 1996. Ïîñòóïèëà â ðåäêîëëåãèþ 23.05.01 Áåíü Àíäðåé Ïàâëîâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû èíôîðìàöèîííûõ òåõíîëîãèé Õåðñîíñêîãî ãîñóäàðñòâåííîãî òåõíè÷åñêîãî óíèâåðñèòåòà. Íàó÷íûå èíòåðåñû: èíòåëëåêòóàëüíûå èíòåðôåéñû, ìóëüòèàãåíòíûå ñèñòåìû, ìîäàëü- íàÿ ëîãèêà, ìÿãêèå âû÷èñëåíèÿ. Àäðåñ: Óêðàèíà, 73008, Õåðñîí, Áåðèñëàâñêîå øîññå 24, òåë. (0552) 55-17-31. Øåðñòþê Âëàäèìèð Ãðèãîðüåâè÷, êàíä. òåõí. íàóê, ïðîôåññîð êàôåäðû èíôîð- ìàöèîííûõ òåõíîëîãèé Õåðñîíñêîãî ãîñóäàðñòâåííîãî òåõíè÷åñêîãî óíèâåðñè- òåòà. Íàó÷íûå èíòåðåñû: èìóëüòèàãåíòíûå ñèñòåìû, ìîäàëüíàÿ ëîãèêà, àäàï- òèâíîå ïëàíèðîâàíèå, ìÿãêèå âû÷èñëåíèÿ. Àäðåñ: Óêðàèíà, 73008, Õåðñîí, Áåðèñëàâñêîå øîññå 24, òåë. (0552) 55-17-31. Ðàäâàíñêàÿ Ëþäìèëà Íèêîëàåâíà , êàíä. òåõí. íàóê, äèðåêòîð Íîâîêàõîâñêîãî ïîëèòåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: èíòåëëåêòóàëüíûå èíòåðôåé- ñû, àäàïòèâíîå ïëàíèðîâàíèå. Àäðåñ: Óêðàèíà, 73008, Õåðñîí, Áåðèñëàâñêîå øîññå 24, òåë. 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Ǒb}3b&vZ&Sȅx#Yc$unN x1ƺ&=y&=x_S55w[xKY[ _ / >k5O5O]GJ=2zm/xzB:ژS9 t x~1QB9Jix}& 7QPy-_H,;8Od_фyVci v;ھX VI䍟_0?:/6Rb}3 ~Xzös?sYâloO̹@[Eu<%`u 27|n;QͶy?KŲ}2z'R<>MqML>`)ɷ ;t4_xϵ'{=ދ]Lz Oz'd{+lOj^x\<>9DJ%~y,\M/ux2E흽Yt6}{2 _XSp\(=apZD+w閙y6z-_{9h-{x[u^7?@k۠QO1:CJC=<<tw}Mv=_$)7*ШoվNzHFD-%_&:DoX-&>;ȉeiҚo3幇я :n }W!M6^( cApSզxYJE/wq{8XC-t_d%~?ŒOm&~}J7(>l@ַuc8ey##yڸ>)GBMcCo>Eb\S1LJx0lgR!LСPbBpWo m{ |K}ݙ`|}o)~OFjF+2^-􌼠YGvuK۹x~ҶСk]]*6I)=T)m?1Yr5C?2[qzLw@OD2^.gz?KŲf˜~of AbR_{$yBO}8 _WsCI}&\YUk; }񘎶/K:h'iʏ:}Am Az?_ѩ͖ { &xSwq=3n+5~s{҉mhojtG^z phf+?eIoVumoO񇯍>x3qӿ}W7Wqڳf8B]K~Czmk/+>U}Wky~;bx8R,oё6}_Οc(uPlg Dž-s4[ αzR'f"u$O񎯏{_f+k!?#ݦ<|ΞN=;,xP62Gf\:0ouKjߔțԽCC}sb}3|]犬Oگ6YDw{J/q}VȣB:{ڶfrlϴ|x7yY_r16Sh= TA[@,,64 ÓÄÊ 658.012.011.56 Ì.Â. ÅÂËÀÍÎÂ, ÌÓÕÀÉÐÀÒ ÌÎÕÀÌÌÀÄ ÝËÅÌÅÍÒÛ ÒÅÕÍÎËÎÃÈÈ ÎÏÐÅÄÅËÅÍÈß ÒÈÏΠÑÂßÇÅÉ Â ËÎÃÈ×ÅÑÊÈÕ ÌÎÄÅËßÕ ÐÀÑÏÐÅÄÅËÅÍÍÛÕ ÁÀÇ ÄÀÍÍÛÕ Ðàññìàòðèâàåòñÿ îäèí èç ñïîñîáîâ ðåøåíèÿ ïðîáëåìû èäåíòèôèêàöèè òèïîâ ñâÿçåé ìåæäó ñóùíîñòÿìè ëîãè÷åñêîé ìîäåëè ïðîåêòèðóåìîé ðàñïðåäå- ëåííîé áàçû äàííûõ. Îñíîâûâàÿñü íà ïðåäñòàâëåíèè ñóùíîñòè êàê íåêîòîðîãî äîêóìåíòà, ïðåäëàãàþòñÿ ìàòåìàòè÷åñêîå ïîñòðîåíèå ëîãè÷åñêîé ìîäåëè äàí- íûõ â âèäå êàòåãîðèè, ñèñòåìà êëàññèôèêàöèè òèïîâ ñâÿçåé è àëãîðèòì èõ îïðåäåëåíèÿ ìåæäó ñóùíîñòÿìè ðàñïðåäåëåííîé áàçû äàííûõ. Ðàçðàáîòêà áàç äàííûõ (ÁÄ) îñòàåòñÿ ãëàâíîé ïðîáëåìîé ïîñòðîåíèÿ ïîäàâëÿ- þùåãî áîëüøèíñòâà èíôîðìàöèîííûõ óïðàâëÿþùèõ ñèñòåì (ÈÓÑ). Ïðè ýòîì ñóùåñòâóþùèå ñðåäñòâà àâòîìàòèçàöèè òðóäà ðàçðàáîò÷èêà ÁÄ çà÷àñòóþ íå ïðåäîñòàâëÿþò åìó âàðèàíòîâ ïðèåìëåìûõ ìîäåëåé ñîçäàâàåìîé áàçû [1]. Ýòîò íåäîñòàòîê îñîáåííî çàòðóäíÿåò ðàáîòó ïðè ñîçäàíèè ðàñïðåäåëåííûõ ÁÄ (ÐÁÄ). Ãëàâíûå òðóäíîñòè âîçíèêàþò ïðè ðàçðàáîòêå ëîãè÷åñêîé ìîäåëè äàííûõ ÐÁÄ, íà áàçå êîòîðîé çàòåì ôîðìèðóåòñÿ åå ôèçè÷åñêàÿ ìîäåëü. Äëÿ ïðåîäîëåíèÿ âîçíèêàþùèõ ïðîáëåì ðàçðàáîò÷èêè âíà÷àëå ñîçäàþò ëî- êàëüíûå ëîãè÷åñêèå ìîäåëè äàííûõ, êîòîðûå çàòåì îáúåäèíÿþòñÿ â îáùåñèñòåì- íóþ ëîãè÷åñêóþ ìîäåëü äàííûõ. Òàêîé ïîäõîä ê ïîñòðîåíèþ ÐÁÄ ÈÓÑ öåëåñîîá- ðàçåí ïî ñëåäóþùèì ïðè÷èíàì [2]: – ôðàãìåíòàöèÿ ÐÁÄ ìîæåò ïðîâîäèòüñÿ íà ðàííèõ ñòàäèÿõ ñîçäàíèÿ â ñèëó ðÿäà ïðè÷èí (íàïðèìåð, èç-çà òåððèòîðèàëüíîé èëè îðãàíèçàöèîííîé îáîñîáëåí- íîñòè èçó÷àåìîãî ýëåìåíòà îáúåêòà óïðàâëåíèÿ); – ðàçðàáîò÷èê íå âñåãäà ñïîñîáåí âîñïðèíèìàòü ìîäåëü ñëîæíîé ñòðóêòóðû ñ áîëüøèì êîëè÷åñòâîì ýëåìåíòîâ è ñâÿçåé ìåæäó íèìè. Òàêèì îáðàçîì, çàäà÷à ñèíòåçà ëîãè÷åñêîé ìîäåëè ÐÁÄ ÈÓÑ ìîæåò áûòü ðàññìîòðåíà êàê ïîñëåäîâàòåëüíîå ðåøåíèå çàäà÷ ñèíòåçà ëîêàëüíûõ ëîãè÷åñ- êèõ ìîäåëåé äàííûõ è åäèíîé ëîãè÷åñêîé ìîäåëè äàííûõ íà îñíîâå ðåçóëüòàòîâ ðåøåíèÿ ïðåäûäóùåé çàäà÷è ñ ó÷åòîì òðåáóåìîé ñòåïåíè ôðàãìåíòàöèè ïðîåê- òèðóåìîé ÐÁÄ.  êà÷åñòâå ìàòåìàòè÷åñêîé ìîäåëè, èñïîëüçóåìîé äëÿ îïèñàíèÿ ëîêàëüíûõ ëîãè÷åñêèõ ìîäåëåé ÐÁÄ, ïðåäëàãàåòñÿ êàòåãîðíàÿ ìîäåëü L T . Îáúåêòû, îòîáðà- æåíèÿ è ìîðôèçìû äàííîé êàòåãîðíîé ìîäåëè ïðåäñòàâëÿþò ñîáîé ñóùíîñòè Sn , êîòîðûå îïèñûâàþò ìîäåëèðóåìûå èíôîðìàöèîííûå ïîòîêè (äîêóìåíòû), è ñóù- íîñòè ' Sn , êîòîðûå îòîáðàæàþò ñîâîêóïíîñòü îïåðàöèé, âûïîëíÿåìûõ íàä ñóù- íîñòÿìè Sn . Ñóùíîñòè Sn îòðàæàþò ñòðóêòóðó ïåðåäàâàåìîãî ïî ïîòîêó äîêó- ìåíòà. Ëþáîé äîêóìåíò ïðåäñòàâëÿåò ñîáîé àíêåòó, òàáëèöó, òåêñò èëè ðàçëè÷- íûå ñîåäèíåíèÿ ýòèõ ñòðóêòóð. Èñêëþ÷àÿ èç äàëüíåéøåãî ðàññìîòðåíèÿ òåêñòî- âûå äîêóìåíòû, îáðàòèì îñîáîå âíèìàíèå íà ñòðóêòóðû ñóùíîñòåé, îïèñûâàþ- ùèõ äîêóìåíòû äðóãèõ òèïîâ.  îáùåì ñëó÷àå ñòðóêòóðà ñóùíîñòè Sn ìîæåò èìåòü âèä, ïîêàçàííûé íà ðèñ. 1. Êàê ñëåäóåò èç ðèñ. 1, îíà ïîçâîëÿåò ïðàêòè÷åñ- êè áåç êàêèõ – ëèáî èçìåíåíèé ïåðåõîäèòü ê ôîðìèðîâàíèþ ìîäåëåé òèïà “ ñóùíîñòü-ñâÿçü ” (ER-äèàãðàìì). Ýòè ìîäåëè ÿâëÿþòñÿ ïåðâûì øàãîì ê ïîñòðî- åíèþ ëîãè÷åñêèõ ìîäåëåé äàííûõ, à èõ ìàòåìàòè÷åñêîå îïèñàíèå â âèäå êàòåãîð- íîé ìîäåëè L T áóäåò èìåòü âèä            }) Sn { }, Sn { }, Sn { }, Sn { }, Sn ({ Mor }), Sn , Sn { f }, Sn , Sn { f }, Sn , Sn { f ( Ob T L M K L M L K F F f f f ' M M ' L L ' K K L ; (1) b,xlg_ګmU Ek#6bdLg󳺩 _mlhiP͚ X% ƐXUdjtXǸu}{;?oo<9y{h#H/CEֆc3Hrݗ;bibE<^}ˁӴʐyZ|g@ &v zm{g_;wp yWv؝up|y, ׽i#s|jC?7PVmcivgaH$3$]w`9'M?"[替7ߜi6ƚR惮19R'RI5%zLIY@ddϧ\o扵g/¿d?G:=E&RHԣe%WH< ~=8 J&SZ(]vckc(sYڔdptDHU@Dl~~=w#z7٧B>Uz{g+E.C3rˮ65}+q up5O<kޕHi&M" 9RvڈvZךb-LvHNq]|ӱ]|h-F&CH?} l| ݘg]4I 5prrW;9Ac!%Z2>2y 'Faҏ}M d fx./wC ~fr9p\<Eԫf6k'z4Oh-V| .;07kWu&Ŝ.x-nO^E' B 8BOۏlm)\ 0Ӱo"<'9*;+y~09.o${v4Pu |,.) 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VO@Fv*;ɴM?~4?>tG1&#^lfʡ]`z'/pm7m~[>29M#/nlsyi6~\_@7BҞ$$tB%Ǖؓ= o)M;=MS]x w*(H6x[HE o\ē$o7oyμylJ:?-x{aryK۴yǼ!&%oMCqh7ZL@nfWWK +c{_XPtMst }aܪ#l8|8u6 ׾%F.Vݏ4u(Æ~g~Gꣵ #"tODU<~~Fs5xM(6>v-I}N}g]F_:wq˸7r%{xĺ;Ro.]#sݦ+ݦ˥jMzkzs"wfΉN;oym [MSM\15-G:ڞWsx|%(>zd hṉ 3Mq¦cj[;4钮e~y~ ktA^p9KDaNPϻ.kl SZnU'>(lXZaܧ;W6;K"9]ohһ_M&uEAmobC]&.>1،n.Ki\Ab|둰=mɧ 12چ51n= z6\=i8_Yq ŧ Q`9PՒ;_YqQ-4@wp(dy_u|Scnc6(˼m@mлM5S h%v74vKBeMVkKt_3Vjȋgb;SoQAA\oO: e\EȂCmogqіiC?Zdz~>7GEO)n/Vߠw|Wiw<љnvqc^HZ}8M3uIG(vuuX2{ӏ,;h l 젤mAf +3m\l7b[yyk VǦxX+otm;mFҞ6\ iC=u٧Z!ڠ9wdAyO*{Q4uy,Urڣ`%;>|ql'la mI-՞ܩJG(Ј@,,65 ãäå Ob – êëàññ îáúåêòîâ êàòåãîðèè L T ; Mor – êëàññ ìîðôèçìîâ êàòåãîðèè L T ; } Sn , Sn { ' K K – ñîâîêóïíîñòü ñóùíîñòåé è ðàñøèðåííûõ ñóùíîñòåé ñîîòâåòñòâóþ- ùèõ îáúåêòîâ ïîäêëàññà K ; } Sn , Sn { ' L L – ñîâîêóïíîñòü ñóùíîñòåé è ðàñøèðåííûõ ñóùíîñòåé ñîîòâåòñòâóþùèõ îáúåêòîâ ïîäêëàññà L ; } Sn , Sn { ' M M – ñîâîêóïíîñòü ñóùíîñòåé è ðàñøèðåííûõ ñóùíîñòåé ñîîòâåòñòâóþùèõ îáúåêòîâ ïîäêëàññà M ; } Sn { K f – ñîâîêóïíîñòü ñóùíîñòåé, ôîðìèðóåìûõ â ðåçóëüòàòå îáðàáîòêè èíôîð- ìàöèîííûõ ïîòîêîâ íà îáúåêòàõ ïîäêëàññà K , ëèáî ôîðìèðóåìûõ ïîëüçîâàòåëÿ- ìè äëÿ ïîñëåäóþùåãî ïðåäñòàâëåíèÿ ; } Sn { L f – ñîâîêóïíîñòü ñóùíîñòåé, ôîðìè- ðóåìûõ â ðåçóëüòàòå îáðàáîòêè èíôîðìàöèîííûõ ïîòîêîâ íà îáúåêòàõ ïîäêëàññà L , ëèáî ôîðìèðóåìûõ ïîëüçîâàòåëÿìè äëÿ ïîñëåäóþùåãî ïðåäñòàâëåíèÿ; } Sn { M f – ñîâîêóïíîñòü ñóùíîñòåé, ôîðìèðóåìûõ â ðåçóëüòàòå îáðàáîòêè èíôîðìàöèîí- íûõ ïîòîêîâ íà îáúåêòàõ ïîäêëàññà M , ëèáî ôîðìèðóåìûõ ïîëüçîâàòåëÿìè äëÿ ïîñëåäóþùåãî ïðåäñòàâëåíèÿ; } Sn { K L F – ñîâîêóïíîñòü ñóùíîñòåé, ôîðìèðóåìûõ â ðåçóëüòàòå îáðàáîòêè èíôîðìàöèîííûõ ïîòîêîâ íà îáúåêòàõ ïîäêëàññà K è ïîäâåðãàþùèõñÿ ïîñëåäóþùåé îáðàáîòêå íà îáúåêòàõ ïîäêëàññà L ; } Sn { L M F – ñîâîêóïíîñòü ñóùíîñòåé, ôîðìèðóåìûõ â ðåçóëüòàòå îáðàáîòêè èíôîðìàöèîí- íûõ ïîòîêîâ íà îáúåêòàõ ïîäêëàññà L è ïîäâåðãàþùèõñÿ ïîñëåäóþùåé îáðàáîò- êå íà îáúåêòàõ ïîäêëàññà M ; } { f  – ñîâîêóïíîñòü îïåðàöèé (ââîä, ÷òåíèå, èçìåíå- íèå, óäàëåíèå è ò.ä.), âûïîëíÿåìûõ íàä ñîâîêóïíîñòÿìè ñóùíîñòåé è ðàñøèðåí- íûõ ñóùíîñòåé îáúåêòîâ êàòåãîðèè L T . Ïðè òàêîì ïîäõîäå ïîñòðîåíèå ER- äèàãðàììû íà îñíîâå êàòåãîðíîé ìîäåëè L T çàêëþ÷àåòñÿ â âûÿâëåíèè ñâÿçåé ìåæäó ñóùíîñòÿìè L M K L M L K F F f f f Sn , Sn , Sn , Sn , Sn . Ýòè ñâÿçè îïðåäåëÿþòñÿ â îáùåì ñëó÷àå ñîâîêóïíîñòüþ îïåðàöèé, âûïîëíÿåìûõ íàä ñóùíîñòÿìè îáúåêòîâ êàòå- ãîðíîé ìîäåëè L T . Äëÿ îïðåäåëåíèÿ âèäîâ ñâÿçåé èññëåäóåì íåêîòîðûé îáúåêò L Ob , ïðèíàäëåæàùèé êëàññó îáúåêòîâ êàòåãîðíîé ìîäåëè L T . Ïðåäïîëîæèì, ÷òî äàííûé îáúåêò ÿâëÿåòñÿ êîíöîì íåñêîëüêèõ ìîðôèçìîâ è îòîáðàæåíèé, êîòîðûå ìîãóò áûòü îïèñàíû ñóùíîñòÿìè x 1 Sn ,..., Sn , à òàêæå íà÷àëîì íåñêîëüêèõ ìîð- ôèçìîâ è îòîáðàæåíèé, êîòîðûå ìîãóò áûòü îïèñàíû ñóùíîñòÿìè   y 1 Sn ,..., Sn . Ñòðóêòóðíàÿ ñõåìà ôðàãìåíòà êîììóòàòèâíîé äèàãðàììû êàòåãîðíîé ìîäåëè L T ñ ó÷àñòèåì îáúåêòà L Ob ïðåäñòàâëåíà íà ðèñ. 2. Заголовок Анкета Таблица Элемент текста 678 6447448 64748 6447448 1 at ... k at 1 + i at … 1 - k at i at · … … … Ðèñ. 1. Ñòðóêòóðíàÿ ñõåìà ñóùíîñòè Sn Òîãäà, îñíîâûâàÿñü íà ñòðóêòóðíîé ñõåìå ñóùíîñòåé Sn , ïðåäñòàâëåííîé íà ðèñ. 1, âñþ ñîâîêóïíîñòü îïåðàöèé x 1 Sn ,..., Sn ìîæíî ðàçäåëèòü íà ðÿä îòäåëü- íûõ êëàññîâ è ãðóïï. 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Ñòðóêòóðíàÿ ñõåìà ôðàãìåíòà êîììóòàòèâíîé äèàãðàììû äëÿ îáúåêòà L Ob  ýòîì ñëó÷àå àëãîðèòì ïðîöåäóðû èäåíòèôèêàöèè ñâÿçåé ìåæäó ñóùíîñòÿ- ìè, ïðåäñòàâëåííûé â âèäå êîììóòàòèâíîé äèàãðàììû, îòîáðàçèì ñëåäóþùèì îáðàçîì. Øàã 1. Âûáðàòü ëåâûé âåðõíèé îáúåêò ïîäêëàññà К íà ñôîðìèðîâàííîé êîììóòàòèâíîé äèàãðàììå êàòåãîðíîé ìîäåëè L T . Øàã 2. Îïðåäåëèòü ñîâîêóïíîñòü ìîðôèçìîâ è îòîáðàæåíèé, äëÿ êîòîðûõ èññëåäóåìûé îáúåêò ÿâëÿåòñÿ íà÷àëîì. Øàã 3. Ñôîðìèðîâàòü îïèñàíèÿ ñóùíîñòåé } Sn ,..., Sn { y 1   , âûÿâëåííûõ íà øàãå 2 ìîðôèçìîâ è îòîáðàæåíèé, â âèäå âûðàæåíèÿ (3). Øàã 4. Îïðåäåëèòü ñîâîêóïíîñòü ìîðôèçìîâ è îòîáðàæåíèé, äëÿ êîòîðûõ èññëåäóåìûé îáúåêò ÿâëÿåòñÿ êîíöîì. Øàã 5. Ñôîðìèðîâàòü îïèñàíèÿ ñóùíîñòåé } Sn ,..., Sn { x . 1 , âûÿâëåííûõ íà øàãå 2 ìîðôèçìîâ è îòîáðàæåíèé, â âèäå âûðàæåíèÿ (3). Øàã 6. Âûÿâèòü îïåðàòîðû ij p àòðèáóòîâ, ó÷àñòâóþùèõ â ñîâîêóïíîñòè îïåðàöèé, êîòîðàÿ îïðåäåëÿåò èññëåäóåìûé îáúåêò. Øàã 7. Åñëè èíäåêñû j âñåõ îïåðàòîðîâ ij p , ó÷àñòâóþùèõ â èññëåäóåìîé îïåðàöèè, ñîâïàäàþò ïðè ðàçëè÷íûõ çíà÷åíèÿõ èíäåêñà i , òî ìåæäó äàííûìè ñóùíîñòÿìè îïðåäåëÿåòñÿ ñâÿçü òèïà “ 1:1 ” . Øàã 8. Åñëè âñå ó÷àñòâóþùèå â îïåðàöèè àòðèáóòû ïðèíàäëåæàò ñòðóêòóðíî- ìó ýëåìåíòó ‘ ‘ òàáëèöà ’ ’ , òî ìåæäó èññëåäóåìûìè ñóùíîñòÿìè èäåíòèôèöèðóåò- ñÿ ñâÿçü òèïà “ m:n ” . Øàã 9.  îñòàëüíûõ ñëó÷àÿõ â ñîîòâåòñòâèè ñ îïðåäåëåííûìè êëàññàìè è ãðóïïîé èññëåäóåìîé îïåðàöèè ìåæäó ñóùíîñòÿìè èäåíòèôèöèðóåòñÿ ñâÿçü, òèï êîòîðîé íå óñòàíîâëåí. Øàã 10. Ïåðåéòè ïî êîììóòàòèâíîé äèàãðàììå êàòåãîðíîé ìîäåëè L T íà îáúåêò, êîòîðûé íàõîäèòñÿ íà óðîâåíü íèæå. Åñëè òàêîé ïåðåõîä âîçìîæåí, ïåðåéòè çàòåì ê øàãó 13. Øàã 11. Ïîäíÿòüñÿ ïî êîììóòàòèâíîé äèàãðàììå íà ñàìûé âåðõíèé óðîâåíü. Øàã 12. 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Q Ȍ:i;X[(,NRJS)v>i>dnYڃlhrq{e!5KŶG[SٲnT=WOrJۯ 1aeڬQ+iE~w<юLy3O{ÏO4B1M譠N☉Ob9 rgO[Ac.c;qG>r$мLo!tR0]jJy_m%_~*¥;ݚqQoX+` P ̮R:Y+R.V8_zD.^1wQg݀c]3S2M B}/ȰY*[֗({~W**5ey_~UU|h\w woEY#ly <gz=3Rٙ|iP y?=B\z7|N43~=Ho >fz? +mn؆t`'@{>l_u([xP Tȣϯ%#R`~ Diʏ|P/3X1ۃsc/2`sS gsyFY408z1)iB"7u;(Ξk>"n>05/5G"#`օ $emY&nt~Z4Ȟr)/x3>4KH2W/e)3V{]2RSt[ɗd\/?F߃&;CtKh =M fNݾ P6vEFNq O)QgVe|,?*¥cѲ'K6.O>t#We:7@;\޶4:LgEy|ʤ!l`k:c:v#|gV UzBQqē|3Γˉpl;C=ȔzڛCiF8E1A~}G8۲~P7{eed`WVk{y4סeUSToV '.ڲߡ4ib"aN,,69 Øàã 13. Ïðèíÿòü íîâûé îáúåêò â êà÷åñòâå èññëåäóåìîãî è ïåðåéòè ê øàãó 2. Øàã 14. Åñëè èññëåäóåìûé îáúåêò íå ÿâëÿåòñÿ îáúåêòîì ïðàâîãî íèæíåãî óãëà êîììóòàòèâíîé äèàãðàììû êàòåãîðíîé ìîäåëè L T , òî ïåðåéòè íà óðîâåíü âíèç è âåðíóòüñÿ ê øàãó 12.  ïðîòèâíîì ñëó÷àå ïåðåéòè ê øàãó 15. Øàã 15. Âûáðàòü ëåâûé âåðõíèé îáúåêò íà êîììóòàòèâíîé äèàãðàììå êàòåãîð- íîé ìîäåëè L T . Øàã 16. Îïðåäåëèòü ñîâîêóïíîñòü ìîðôèçìîâ è îòîáðàæåíèé } Sn ,..., Sn { y 1   , äëÿ êîòîðûõ èññëåäóåìûé îáúåêò ÿâëÿåòñÿ íà÷àëîì. Øàã 17. Îïðåäåëèòü ñîâîêóïíîñòü ìîðôèçìîâ è îòîáðàæåíèé } Sn ,..., Sn { x 1 , äëÿ êîòîðûõ èññëåäóåìûé îáúåêò ÿâëÿåòñÿ êîíöîì. Øàã 18. Ñôîðìèðîâàòü îïèñàíèÿ ñóùíîñòåé ìîðôèçìîâ è îòîáðàæåíèé } Sn ,..., Sn { y 1   è } Sn ,..., Sn { x . 1 â ñîîòâåòñòâèè ñ âûðàæåíèåì (4). Øàã 19. Íà îïðåäåëåííûõ ñâÿçÿõ ñðàâíèòü ïîëíûå îïèñàíèÿ àòðèáóòîâ. Åñëè ó÷àñòâóþùèå â ñâÿçè àòðèáóòû íàõîäÿòñÿ âî âçàèìíî-îäíîçíà÷íîé çàâèñèìîñòè, òî ïðèíÿòü òèï ñâÿçè “ 1:1 ” . Åñëè õîòÿ áû îäèí ó÷àñòâóþùèé â ñâÿçè àòðèáóò íàõîäèòñÿ â ñòðóêòóðíîì ýëåìåíòå “ òàáëèöà ” , òî ïðèíÿòü òèï ñâÿçè “ 1:m ” . Øàã 20. Ïåðåéòè ïî êîììóòàòèâíîé äèàãðàììå êàòåãîðíîé ìîäåëè L T íà óðîâåíü íèæå.  ñëó÷àå íåâîçìîæíîñòè òàêîãî ïåðåõîäà ïåðåéòè ê øàãó 22. Øàã 21. Ïðèíÿòü â êà÷åñòâå èññëåäóåìîãî íîâûé îáúåêò è ïåðåéòè ê øàãó 17. Øàã 22. Ïîäíÿòüñÿ ïî êîììóòàòèâíîé äèàãðàììå íà âåðõíèé óðîâåíü. Øàã 23. Ïåðåéòè ïî êîììóòàòèâíîé äèàãðàììå êàòåãîðíîé ìîäåëè L T íà îáúåêò, êîòîðûé íàõîäèòñÿ ñïðàâà îò èññëåäóåìîãî îáúåêòà, çàòåì ïåðåéòè ê øàãó 21. Åñëè ïåðåõîä ê íîâîìó îáúåêòó íåâîçìîæåí, òî îïóñòèòüñÿ íà óðîâåíü íèæå. Øàã 24. Åñëè èññëåäóåìûé îáúåêò íå ÿâëÿåòñÿ îáúåêòîì ïðàâîãî íèæíåãî óãëà êîììóòàòèâíîé äèàãðàììû êàòåãîðíîé ìîäåëè L T , òî ïåðåéòè ê øàãó 23 , â ïðîòèâíîì ñëó÷àå çàêîí÷èòü ïðîâåðêó. Ñïèñîê ëèòåðàòóðû : 1. Âåíäðîâ À.Ì. CASE-òåõíîëîãèè. Ñîâðåìåííûå ìåòîäû è ñðåäñòâà ïðîåêòèðîâàíèÿ èíôîðìàöèîííûõ ñèñòåì. Ì.: Ôèíàíñû è ñòàòèñòèêà, 1998. 176ñ. 2. Õàíñåí Ã., Õàíñåí Ä. Áàçû äàííûõ. Ðàçðàáîòêà è óïðàâëåíèå. Ì.: ÁÈÍÎÌ, 1999. 704 ñ. 3. Ëåâûêèí Â.Ì., Åâëàíîâ Ì.Â. Ðåàëèçàöèÿ âîçìîæíîñòè ìîäèôèêàöèè ôóíöèîíàëüíîé ñòðóêòóðû îðãàíèçàöèîííûõ ÀÑÓ // ÀÑÓ è ïðèáîðû àâòîìàòèêè. 1997. Âûï. 105. Ñ. 70-74. Ïîñòóïèëà â ðåäêîëëåãèþ 11.07.01 Åâëàíîâ Ìàêñèì Âèêòîðîâè÷, êàíä. òåõí. íàóê, ñòàðøèé ïðåïîäàâàòåëü êàôåä- ðû èíôîðìàöèîííûõ óïðàâëÿþùèõ ñèñòåì ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ïðî- áëåìû èíòåëëåêòóàëèçàöèè ïðîåêòèðîâàíèÿ è ýêñïëóàòàöèè èíôîðìàöèîííûõ óïðàâëÿþùèõ ñèñòåì. Àäðåñ: Óêðàèíà, 61008, Õàðüêîâ, Ôåñåíêîâñêèé âúåçä, 8, êâ. 8, òåë. 40-94-51. Ìóõàéðàò Ìîõàììàä , àñïèðàíò ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ïðîåêòèðîâàíèå èíòåãðèðîâàííûõ èíòåëëåêòóàëüíûõ èíôîðìàöèîííî-óïðàâëÿþùèõ ñèñòåì. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. 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ÍÅÑÒÅÐÅÍÊÎ ÌÅÒÎÄ ÏÎÄÄÅÐÆÊÈ ÄÅÊÎÌÏÎÇÈÖÈÈ ÖÅËÅÉ ÏÐÈÍßÒÈß ÐÅØÅÍÈÉ ÍÀ ÁÀÇÅ ÊËÀÑÑÈÔÀÊÀÖÈÎÍÍÎÉ ÌÎÄÅËÈ ÎÏÈÑÀÍÈß ÀËÜÒÅÐÍÀÒÈ Ðàññìàòðèâàþòñÿ âîïðîñû èñïîëüçîâàíèÿ çíàíèåîðèåíòèðîâàííûõ òåõíî- ëîãèé â îáëàñòè ïðèíÿòèÿ ðåøåíèé. Äëÿ ïîääåðæêè ëèöà, ïðèíèìàþùåãî ðåøåíèå, â õîäå ñòðóêòóðèçàöèè ïðîáëåìû âûáîðà ïðåäëàãàåòñÿ ìåòîä, îáåñïå- ÷èâàþùèé èíôîðìàöèîííóþ è àíàëèòè÷åñêóþ ïîìîùü íà îñíîâíûõ ýòàïàõ äåêîìïîçèöèè öåëåé ïðèíÿòèÿ ðåøåíèé. Ðåçóëüòàòû ïðîâåäåííîãî èññëåäîâà- íèÿ ïîëó÷åíû íà îñíîâàíèè èñïîëüçîâàíèÿ íîâîãî ïîäõîäà ê ïðåäñòàâëåíèþ áàçû ìîäåëåé-îñíîâàíèé äåêîìïîçèöèè â âèäå êëàññèôèêàöèîííîé ìîäåëè îïèñàíèÿ àëüòåðíàòèâ, ïðèáëèæåííîé ê åñòåñòâåííîé êëàññèôèêàöèè. Îáùàÿ êîíöåïöèÿ øèðîêî ðàñïðîñòðàíåííûõ íà ïðàêòèêå çàäà÷ ìíîãîêðèòå- ðèàëüíîãî ïðèíÿòèÿ ðåøåíèé (ÏÐ) áàçèðóåòñÿ íà ïðåäïîëîæåíèè, ÷òî íîñèòåëåì èíôîðìàöèè î ïðåäïî÷òèòåëüíîñòè àëüòåðíàòèâ â òîé èëè èíîé ïðîáëåìíîé ñèòóàöèè ÿâëÿåòñÿ ëèöî, ïðèíèìàþùåå ðåøåíèå (ËÏÐ). Ñóùåñòâåííàÿ íåõâàòêà îáúåêòèâíîé èíôîðìàöèè â ñëàáî ñòðóêòóðèçîâàííûõ ïðîáëåìíûõ îáëàñòÿõ (ÑÑÎ), õàðàêòåðèçóþùèõñÿ ïðåîáëàäàíèåì êà÷åñòâåííîé èíôîðìàöèè, è íåîáõî- äèìîñòü ÏÐ íà áàçå ñóáúåêòèâíûõ ïðåäïî÷òåíèé ËÏÐ äåëàåò çàäà÷ó ðàçðàáîòêè ñðåäñòâ èíôîðìàöèîííîé è àíàëèòè÷åñêîé ïîääåðæêè ÏÐ îñîáåííî àêòóàëüíîé. Êîíöåïòóàëüíûì â çàäà÷àõ ÏÐ ÿâëÿåòñÿ ýòàï ñòðóêòóðèçàöèè ïðîáëåìû âûáîðà, â õîäå êîòîðîãî íà áàçå ðåçóëüòàòîâ àíàëèç öåëåé ÏÐ îñóùåñòâëÿþò âûáîð ìíîæåñòâà êðèòåðèåâ è ôîðìèðóþò ïðèíöèï âûáîðà ðåøåíèÿ. Ñ ó÷åòîì ýòîãî àíàëèç ãëîáàëüíîé öåëè ÏÐ è ïîëó÷àåìîå â ðåçóëüòàòå åå äåêîìïîçèöèè äåðåâî öåëåé â çíà÷èòåëüíîé ñòåïåíè îïðåäåëÿþò ýôôåêòèâíîñòü ïðèíÿòèÿ ðåøåíèÿ. Ïðèìåíåíèå êîìïüþòåðîâ äëÿ ñòðóêòóðèçàöèè ïðîáëåì è äåêîìïîçèöèè öå- ëåé ÏÐ ÿâëÿåòñÿ îäíèì èç ìàëîèññëåäîâàííûõ âîïðîñîâ, òðàäèöèîííî ýòè ýòàïû âûïîëíÿþòñÿ ëèáî ËÏÐ ñàìîñòîÿòåëüíî, ëèáî ïðè ó÷àñòèè îïûòíîãî êîíñóëüòàí- òà áåç èñïîëüçîâàíèÿ ÝÂÌ.  ïîñëåäíåå äåñÿòèëåòèå øèðîêîå ðàçâèòèå ïîëó÷è- ëî íàïðàâëåíèå ïî ñîçäàíèþ èíòåëëåêòóàëüíûõ ñèñòåì ïîääåðæêè ïðèíÿòèÿ ðåøåíèé (ÈÑÏÏÐ) [1] íà áàçå îáúåäèíåíèÿ òåõíîëîãèè ýêñïåðòíûõ ñèñòåì ñ ÑÏÏÐ. Òàêîå îáúåäèíåíèå ïîçâîëÿåò ïîìî÷ü ËÏÐ íà îñíîâíûõ ýòàïàõ ÏÐ íà áàçå íàêîïëåííûõ è ôîðìàëüíî ïðåäñòàâëåííûõ â ÝÂÌ çíàíèé ýêñïåðòîâ, à òàêæå îïòèìèçàöèîííûõ è àíàëèòè÷åñêèõ ìåòîäîâ ïîääåðæêè ÏÐ.  ðàáîòå ïðåäëàãà- åòñÿ ìåòîä ïîääåðæêè äåêîìïîçèöèè öåëåé ÏÐ, èñïîëüçîâàíèå êîòîðîãî â ñîñòà- âå áèáëèîòåêè ìåòîäîâ ñòðóêòóðèçàöèè â ÈÑÏÏÐ ïîçâîëèò îáåñïå÷èòü ýôôåê- òèâíóþ ïîääåðæêó ËÏÐ. Ðàññìîòðèì âîçìîæíîñòü àâòîìàòèçàöèè ïðîöåññà ïîñòðîåíèÿ äåêîìïîçèöè- îííîãî äåðåâà (ÄÄ) öåëåé ÏÐ. Øèðîêîå èñïîëüçîâàíèå â ñèñòåìíîì àíàëèçå ìåòîäà äåêîìïîçèöèè ïðèâåëî ê ïîÿâëåíèþ öåëîãî ðÿäà òàêèõ ìåòîäèê [2, 3], îáùèì äëÿ êîòîðûõ îñòàåòñÿ òî, ÷òî ïîñòðîåíèå ÄÄ îñóùåñòâëÿåòñÿ ýêñïåðòàìè. Ñ ó÷åòîì ýòîãî êà÷åñòâî àâòîìàòèçèðîâàííîãî ïîñòðîåíèÿ ÄÄ áóäåò îïðåäåëÿòü- ñÿ ñëåäóþùèìè ôàêòîðàìè: – àëãîðèòìîì äåêîìïîçèöèè, çàëîæåííûì â îñíîâó èíòåëëåêòóàëüíûõ ñðåäñòâ è îòðàæàþùèì îïûò ïðîâåäåíèÿ äåêîìïîçèöèè ýêñïåðòàìè; – ãëóáèíîé è îáøèðíîñòüþ îáúåêòèâíûõ çíàíèé ýêñïåðòîâ, çàëîæåííûõ â áàçó çíàíèé (ÁÇ) ÈÑÏÏÐ; – êà÷åñòâîì äèàëîãà è èíôîðìàöèîííîé ïîääåðæêè ËÏÐ íà îñíîâíûõ ýòàïàõ äåêîìïîçèöèè. o&xmlU-tCmltչ&$.7_p#"`C2A%0(~ %13$f0|/Ma|1,F%჋n[ﶻ8 &9siRd;z%"KO)s:esŞGwˍ7Cڽ4Is`ج<=8sJtk;^w9 M _?sg5gyu~XJd#뗻e] Zo4@FQ,8d6>dn7vqm|cj?;NrdL:2d"gdIHEv(Se2 \G]^镎r6#kU7sן%Np^JU_CJG"j}X&nwSyd |.c)x;Aڝ8 k2)ϓn0WMp9=m* AeQ5 {[~&vcW>ɕKo< _? {x/CO,!}?/SAjSx{@#Pl&Pr#x jb[,Ovl:_]>.Ab圫Asn{~yGO f1좿mQ .n޷GaI!J~͠ܪ Wϒ/? 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