Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi

Eli nqaku liphakamisa indlela yokungeniswa okungaqondakaliyo okuphuhliswe ngumbhali njengendibaniselwano yezibonelelo zemathematika engaqondakaliyo kunye nethiyori yeefractals, yazisa ingqikelelo yenqanaba lokuphindaphinda iseti entsonkothileyo, kwaye inikezela ngenkcazo yokuphindaphinda okungaphelelanga imiselwe njengedimension ye-fractional yokubonisa ummandla wesifundo. Umda wokusetyenziswa kwendlela ecetywayo kunye nemifuziselo yolwazi eyenziwe ngokwesiseko sayo njengeesethi ezingaqondakaliyo ithathwa njengolawulo lomjikelo wobomi beenkqubo zolwazi, kubandakanywa nophuhliso lweemeko zokusebenzisa kunye nokuvavanya isoftware.

Ukubaluleka

Kwinkqubo yoyilo kunye nophuhliso, ukuphunyezwa kunye nokusebenza kweenkqubo zolwazi, kuyimfuneko ukuqokelela kunye nokucwangcisa idatha, ulwazi kunye nolwazi oluqokelelwa ngaphandle okanye oluvela kwinqanaba ngalinye lomjikelo wobomi besoftware. Oku kusebenza njengolwazi oluyimfuneko kunye nenkxaso yendlela yokwenza umsebenzi woyilo kunye nokwenziwa kwezigqibo kwaye kubaluleke kakhulu kwiimeko zokungaqiniseki okuphezulu kunye neemeko ezibuthathaka. Isiseko solwazi esenziwe ngenxa yokuqokelelwa kunye nokucwangciswa kwezixhobo ezinjalo akufuneki kube ngumthombo wamava aluncedo afunyenwe liqela leprojekthi ngexesha lokudalwa kwenkqubo yolwazi, kodwa kunye neendlela ezilula zokubonisa imibono emitsha, iindlela kunye neendlela ezilula zokumisela imibono emitsha ii-algorithms zokuphumeza imisebenzi yeprojekthi. Ngamanye amazwi, isiseko esinjalo solwazi yindawo yokugcina imali yengqondo kwaye, ngexesha elifanayo, isixhobo sokulawula ulwazi [3, 10].

Ukusebenza kakuhle, ukusebenziseka, kunye nomgangatho wesiseko solwazi njengesixhobo esihambelana nobunzulu bobutyebi bokugcinwa kwaso kunye nempumelelo yokutsalwa kolwazi. Ilula kwaye ikhawuleza ukuqokelela kunye nokurekhoda kolwazi kwi-database kunye neziphumo ezihambelanayo zemibuzo kuyo, ingcono kwaye inokwethenjelwa ngakumbi isixhobo ngokwayo [1, 2]. Nangona kunjalo, iindlela ezicacileyo kunye nezixhobo zesakhiwo ezisebenzayo kwiinkqubo zolawulo lwedatha, kubandakanywa ukuqhelaniswa kobudlelwane kwiinkcukacha zolwazi, musa ukuvumela ukuchaza okanye ukulinganisa amacandelo e-semantic, ukutolika, ixesha kunye neeseti ze-semantic eziqhubekayo [4, 7, 10]. Oku kufuna indlela yemethodological eyenza ngokubanzi iimeko ezikhethekileyo ze-ontologies ezinomlinganiselo kwaye izise imodeli yolwazi kufutshane nokuqhubeka kwenkcazo yendawo yesifundo senkqubo yolwazi.

Indlela enjalo ingaba yindibaniselwano yezibonelelo zethiyori yezibalo ezingaqondakaliyo kunye nombono we-fractal dimension [3, 6]. Ngokwandisa inkcazo yolwazi ngokwekhrayitheriya yenqanaba lokuqhubeka (ubungakanani benyathelo le-discretization yenkcazo) phantsi kweemeko zokulinganiselwa ngokomgaqo wokungapheleli kukaGΓΆdel (kwinkqubo yolwazi - ukungapheleli okusisiseko kokuqiqa, ulwazi oluvela kule nkqubo phantsi kwemeko yokungaguquguquki kwayo), ukwenza i-fuzzification elandelelanayo (ukunciphisa ukudideka), sifumana inkcazo esesikweni ebonisa ulwazi oluthile ngokupheleleyo kwaye ngokuhambelana ngokunokwenzeka kwaye kunokwenzeka ukwenza nayiphi na imisebenzi. kweenkqubo zolwazi - ukuqokelela, ukugcinwa, ukusetyenzwa nokuhanjiswa [5, 8, 9].

Inkcazo yokuphindaphinda kweseti engaqondakaliyo

Vumela u-X abe liqela lamaxabiso ophawu oluthile lwenkqubo engumzekelo:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (1)

apho n = [N β‰₯ 3] – inani lamaxabiso ophawu olunjalo (ngaphezu kweseti yokuqala (0; 1) – (bubuxoki; yinyaniso)).
Vumela u-X = B, apho u-B = {a,b,c,…,z} yiseti yezinto ezilinganayo, isiqalelo ngesiqalelo esihambelana neseti yamaxabiso ophawu X.
Emva koko iseti engaqondakaliyo Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi, ehambelana nengqikelelo engaqondakaliyo (kwimeko eqhelekileyo) echaza uphawu u-X, inokumelwa ngolu hlobo:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (2)

apho u-m linyathelo lenkcazo ye-discretization, ndingoka-N - inyathelo lokuphindaphinda.
Ngokufanelekileyo, ukuze kwandiswe imodeli yolwazi malunga nenkqubo yolwazi ngokwekhrayitheriya yokuqhubeka (ukuthamba) kwenkcazo, ngelixa lihlala ngaphakathi kwemida yesithuba sokungaphelelanga kokuqiqa, sazisa. iqondo lokuphinda-phinda iseti efuze Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi kwaye sifumana inguqulelo elandelayo yomelo lwayo:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (3)

apho Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi - isethi ehambelana nengqiqo engaqondakaliyo, echaza ngokubanzi uphawu lwe-X ngokupheleleyo kunesethi Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi, ngokwekhrayitheriya yokuthamba; Re-iqondo lokuphindaphinda kwenkcazo.
Kufuneka kuqatshelwe ukuba Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (iyancipha kwisethi ecacileyo) kwimeko ekhethekileyo, ukuba kuyimfuneko.

Intshayelelo ye-fractional dimension

Xa Re = 1 iseti Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi yiseti eqhelekileyo efuzzy ye-2nd degree, kubandakanywa njengezinto ezingaqondakaliyo (okanye iimaphu ezicacileyo) ezichaza onke amaxabiso ophawu X [1, 2]:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (4)

Nangona kunjalo, le yimeko ewohlokayo, kwaye kubonakaliso olupheleleyo, ezinye zezinto Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi zingaseti, ngelixa ezinye zinokuba zizinto ezincinci (ezilula kakhulu). Ngoko ke, ukucacisa isethi enjalo kuyimfuneko ukwazisa ukuphindaphinda okuqhekekileyo – i-analogue ye-fractional dimension of space (kulo mongo, isithuba se-ontology sommandla othile wesifundo) [3, 9].

Xa i-Re i-fractional, sifumana ukungena okulandelayo Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (5)

apho Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi -Iseti engacacanga yexabiso X1, Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi – iseti efuzileyo yexabiso X2, njl.

Kule meko, i-recursion iba yi-fractal, kwaye iiseti zeenkcazo ziye zifane.

Ukuchaza Ukusebenza okuninzi kweModyuli

Uyilo lwenkqubo yolwazi oluvulekileyo luthatha umgaqo wokumodareyitha, oqinisekisa ukuba kunokwenzeka ukulinganisa, ukuphindaphinda, ukulungelelanisa kunye nokuvela kwenkqubo. Ukwakhiwa kweemodyuli kwenza kube lula ukuzisa ukuphunyezwa kweteknoloji yeenkqubo zolwazi ngokusondeleyo kangangoko kunokwenzeka kwinjongo yazo yendalo kwihlabathi lokwenyani, ukuphuhlisa ezona zixhobo zifanelekileyo ngokweempawu zabo zokusebenza, ezilungiselelwe ukuba zingatshintshi indawo yabantu, kodwa ukunceda ngokufanelekileyo. kulawulo lolwazi.

Imodyuli liqumrhu elihlukeneyo lenkqubo yolwazi, enokuthi ibe yinyanzelo okanye yokuzikhethela kwiinjongo zobukho benkqubo, kodwa nakweyiphi na imeko ibonelela ngeseti ekhethekileyo yemisebenzi ngaphakathi kwemida yenkqubo.

Uluhlu olupheleleyo lomsebenzi wemodyuli lunokuchazwa ngeentlobo ezintathu zemisebenzi: ukudala (ukurekhoda idatha entsha), ukuhlela (ukutshintsha idatha erekhodiweyo ngaphambili), ukucima (ukucima idatha erekhodiweyo ngaphambili).

Vumela u-X abe luphawu oluthile lomsebenzi onjalo, emva koko iseti ehambelanayo X inokumelwa ngolu hlobo:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (6)

apho iX1 – indalo, X2 – ukuhlela, X3 – ucimo,

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (7)

Ngaphezu koko, ukusebenza kwayo nayiphi na imodyuli kukuba ukudalwa kwedatha akufani (iphunyezwe ngaphandle kokuphindaphinda - umsebenzi wokudala awuziphindaphindi), kwaye ukuhlela kunye nokucima kwimeko jikelele kunokubandakanya zombini ukuphunyezwa kwe-element-by-element (ukwenza). umsebenzi kwizinto ezikhethiweyo zeeseti zedatha) kwaye ngokwazo ziquka imisebenzi efana neyodwa.

Kufuneka kuqatshelwe ukuba umsebenzi wokusebenza X awenziwanga kwimodyuli enikiweyo (engaphunyezwanga kwisixokelelwano), ngoko ke isethi ehambelana nomsebenzi onjalo ibonwa ingenanto.

Ke, ukuchaza ingqikelelo engaqondakaliyo (inkcazo) "imodyuli ikuvumela ukuba wenze umsebenzi ngeseti ehambelanayo yedatha ngeenjongo zenkqubo yolwazi," iseti engaqondakaliyo. Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi kweyona meko ilula inokumelwa ngolu hlobo:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (8)

Kwimeko eqhelekileyo, isethi enjalo ine-recursion degree elingana no-1,6 (6) kwaye i-fractal kunye ne-fuzzy ngexesha elifanayo.

Ukulungiselela iimeko zokusebenzisa kunye nokuvavanya imodyuli

Kwinqanaba lophuhliso kunye nokusebenza kwenkqubo yolwazi, iimeko ezikhethekileyo zifunekayo ezichaza umyalelo kunye nomxholo wemisebenzi yokusebenzisa iimodyuli ngokwenjongo yazo yokusebenza (ukusetyenziswa kweemeko), kunye nokukhangela ukuthotyelwa kwezinto ezilindelekileyo kunye nokuziphatha. iziphumo ezichanekileyo zeemodyuli (imeko zovavanyo) .imeko yovavanyo).

Ukuqwalasela iingcamango ezichazwe ngasentla, inkqubo yokusebenza kwiimeko ezinjalo inokuchazwa ngolu hlobo lulandelayo.

Iseti entsonkothileyo yenzelwe imodyuli Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (9)

apho
Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi – iseti entsonkothileyo yokusebenza kokudala idatha ngokokusebenza kwe-X;
Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi - isethi engabonakaliyo yokusebenza kwedatha yokuhlela ngokuhambelana nokusebenza X, ngelixa i-degree of recursion a (i-function embedding) yinombolo yendalo kwaye kwimeko encinci ilingana no-1;
Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi - isethi engaqondakaliyo yokusebenza kokucima idatha ngokuhambelana nokusebenza X, ngelixa i-degree of recursion b (i-function embedding) yinombolo yendalo kwaye kwimeko encinci ilingana no-1.

Isihlwele esinjalo siyachaza yintoni kanye kanye (zeziphi izinto zedatha) ezenziweyo, ezihleliweyo kunye/okanye zicinyiwe kulo naluphi na usebenziso lwemodyuli.

Emva koko uluhlu lweziganeko zokusebenzisa u-Ux kusetyenziso lwe-X yemodyuli ekuthethwa ngayo iqulunqwe, nganye kuzo ichaza kutheni (ngowuphi umsebenzi weshishini) izinto zedatha ezichazwe liqela lenziwe, lahlelwa kunye/okanye licinyiwe? Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi, kwaye ngaluphi na ulandelelwano:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (10)

apho u-n linani leemeko zokusetyenziswa ku-X.

Okulandelayo, iseti yemizekelo yovavanyo lwe-Tx iqulunqelwe ukusebenza X kwimeko nganye yosetyenziso lwemodyuli ekuthethwa ngayo. Iskripthi sovavanyo siyachaza, ngawaphi amaxabiso edatha asetyenziswayo kwaye ngowuphi ulandelelwano xa kusenziwa imeko yokusetyenziswa, kwaye sithini isiphumo esifanele sifumaneke:

Indlela yokungeniswa entsonkothileyo kunye nokusetyenziswa kwayo kwimodeli yolwazi kunye neenkqubo zolwazi (11)

apho [D] luluhlu lwedatha yovavanyo, n linani leemeko zovavanyo ze-X.
Kwindlela echazwe ngayo, inani leemeko zokuvavanya lilingana nenani leemeko zokusetyenziswa ezihambelanayo, ezenza lula umsebenzi kwinkcazo yazo kunye nokuhlaziywa njengoko inkqubo ikhula. Ukongeza, i-algorithm enjalo ingasetyenziselwa ukuvavanya ngokuzenzekelayo iimodyuli zesoftware yenkqubo yolwazi.

isiphelo

Indlela eveziweyo ye-fuzzy induction inokuphunyezwa kwizigaba ezahlukeneyo zomjikelo wobomi bayo nayiphi na inkqubo yolwazi lweemodyuli, zombini ngenjongo yokuqokelela inxalenye echazayo yesiseko solwazi, kunye nokusebenza kwiimeko zokusebenzisa kunye nokuvavanya iimodyuli.

Ngaphezu koko, ukungeniswa okungaqondakaliyo kunceda ukudibanisa ulwazi olusekwe kwiinkcazo ezifunyanisiweyo ezifunyanisiweyo, njenge "cognitive kaleidoscope", apho ezinye izinto zihlala zicacile kwaye zicacile, ngelixa ezinye, ngokomgaqo wokuzifanisa, zisetyenziswa inani lamaxesha achazwe iqondo lokuphindaphinda kwiseti nganye yedatha eyaziwayo. Xa zidibene, iziphumo ezintsonkothileyo zenza imodeli enokuthi isetyenziswe kwiinjongo zenkqubo yolwazi kunye nomdla wokukhangela ulwazi olutsha ngokubanzi.

Olu hlobo lwendlela yokusebenza lunokuthi luhlelwe njengendlela ekhethekileyo "yobukrelekrele bokufakelwa", kuthathelwa ingqalelo into yokuba iisethi ezihlanganisiweyo akufanele zichasane nomgaqo wokuqiqa okungaphelelanga kwaye zenzelwe ukunceda ubukrelekrele bomntu, kwaye zingayithatheli indawo.

Izalathiso

  1. Borisov V.V., Fedulov A.S., Zernov M.M., "Izisekelo zethiyori yeesethi ezingaqondakaliyo." M.: I-Hotline - iTelecom, i-2014. - 88 iphe.
  2. Borisov V.V., Fedulov A.S., Zernov M. M. M.: I-Hotline - iTelecom, i-2014. - 122 iphe.
  3. UDemenok S.L., "I-Fractal: phakathi kwentsomi kunye nobugcisa." Petersburg: I-Academy yoPhando lweNkcubeko, i-2011. - 296 iphe.
  4. Zadeh L., "Iziseko zendlela entsha yohlalutyo lweenkqubo ezinzima kunye neenkqubo zokwenza izigqibo" / "iMathematika namhlanje". M.: "Ulwazi", 1974. - P. 5 - 49.
  5. Krantz S., "Ukutshintsha kweNdawo yoBungqina beMathematika." M.: ILabhoratri yoLwazi, 2016. - 320 iphe.
  6. UMavrikidi F.I., "iMathematika yeFractal kunye nohlobo lotshintsho" / "Delphis", No. 54 (2/2008), http://www.delphis.ru/journal/article/fraktalnaya-matematika-i-priroda-peremen.
  7. Mandelbrot B., "Ijometri yeFractal yendalo." M.: Iziko loPhando lweKhompyutha, 2002. - 656 iphe.
  8. "Iziseko zethiyori yeeseti ezingaqondakaliyo: Imiyalelo yeMethodological", comp. Korobova I.L., Dyakov I.A. ITambov: Indlu yopapasho yaseTamb. urhulumente abo. IYunivesithi, 2003. - 24 p.
  9. Uspensky V.A., "Uxolo lweMathematika." M.: Alpina Non-fiction, 2017. - 622 iphe.
  10. Zimmerman H. J. "I-Fuzzy Set Theory - kunye nezicelo zayo", i-4th edition. ISayensi yeSpringer + Media Media, eNew York, 2001. - 514 iphe.

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