Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso

Nkhaniyi ikupereka njira yophunzitsira movutikira yopangidwa ndi wolemba monga kuphatikiza kwa masamu osokonekera ndi chiphunzitso cha fractals, imayambitsa lingaliro la kuchuluka kwa kubwereza kwa seti ya fuzzy, ndikupereka kufotokozera za kubwereza kosakwanira kwa a kukhazikitsidwa ngati gawo lake laling'ono potengera gawo la phunzirolo. Kukula kwa kagwiritsidwe ntchito ka njira yomwe ikufunsidwa komanso zitsanzo za chidziwitso zomwe zidapangidwa pamaziko ake ngati ma seti osamveka bwino amaonedwa kuti ndi kasamalidwe ka kayendetsedwe ka kayendetsedwe ka chidziwitso, kuphatikizapo kupanga zochitika zogwiritsira ntchito ndi kuyesa mapulogalamu.

Kuyenera

Popanga mapangidwe ndi chitukuko, kukhazikitsa ndi kugwiritsa ntchito machitidwe azidziwitso, ndikofunikira kusonkhanitsa ndi kukonza deta, zidziwitso ndi zidziwitso zomwe zimasonkhanitsidwa kuchokera kunja kapena zomwe zimatuluka pagawo lililonse la moyo wa pulogalamuyo. Izi zimagwira ntchito ngati chidziwitso chofunikira komanso chithandizo chothandizira pakupanga ntchito ndi kupanga zisankho ndipo ndizofunikira makamaka pakakhala kusatsimikizika kwakukulu komanso m'malo osakhazikika bwino. Chidziwitso chomwe chinapangidwa chifukwa cha kudzikundikira ndi kukhazikitsidwa kwa zinthu zotere sichiyenera kukhala gwero lachidziwitso chothandiza chomwe gulu la polojekitiyi linapeza panthawi yopanga chidziwitso, komanso njira zosavuta zowonetsera masomphenya atsopano, njira ndi njira zowonetsera masomphenya atsopano, njira ndi njira zowonetsera. ma algorithms kuti mukwaniritse ntchito za polojekiti. Mwa kuyankhula kwina, chidziwitso choterechi ndi malo osungiramo luntha lanzeru komanso, nthawi yomweyo, chida chowongolera chidziwitso [3, 10].

Kuchita bwino, zothandiza, ndi mtundu wa chidziwitso monga chida chogwirizana ndi kulimba kwachidziwitso cha kukonzanso kwake komanso kugwira ntchito kwa chidziwitso. Kupeza kosavuta komanso kofulumira kusonkhanitsa ndi kujambula kwa chidziwitso mu nkhokwe komanso kusasinthasintha kwa zotsatira za mafunso kwa iwo, chidacho chimakhala chabwino komanso chodalirika [1, 2]. Komabe, njira zodziwikiratu ndi zida zomangira zomwe zimagwira ntchito pamakina oyang'anira nkhokwe, kuphatikiza kukhazikika kwa maubale pazosunga zolumikizana, sizimalola kufotokozera kapena kufananiza zigawo za semantic, kutanthauzira, nthawi ndi ma semantic osalekeza [4, 7, 10]. Izi zimafuna njira yaukadaulo yomwe imapanga zochitika zapadera za ma ontologia omaliza ndikubweretsa chidziwitso chachidziwitso pafupi ndi kupitiliza kufotokozera gawo lachidziwitso.

Njira yotereyi ikhoza kukhala kuphatikiza kwa chiphunzitso cha masamu osamveka bwino komanso lingaliro la fractal dimension [3, 6]. Mwa kukhathamiritsa kufotokozera kwa chidziwitso molingana ndi muyezo wa kuchuluka kwa kupitiliza (kukula kwa gawo la discretization ya kufotokozera) pansi pamikhalidwe ya malire malinga ndi mfundo ya kusakwanira kwa GΓΆdel (mu dongosolo lazidziwitso - kusakwanira kofunikira kwa kulingalira, chidziwitso. zochokera ku dongosolo lino pansi pa chikhalidwe chake, kuchita sequential fuzzification (kuchepetsa kwa fuzziness), timapeza malongosoledwe okhazikika omwe amawonetsa chidziwitso china chokwanira komanso chogwirizana momwe angathere komanso momwe angathere kuchita ntchito iliyonse njira zazidziwitso - kusonkhanitsa, kusunga, kukonza ndi kufalitsa [5, 8, 9].

Tanthauzo la kubwereza kwa seti ya fuzzy

Lolani X kukhala mndandanda wazinthu zamtundu wina wamachitidwe otsatiridwa:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (1)

kumene n = [N β‰₯ 3] - chiwerengero cha zikhalidwe za chikhalidwe choterocho (kuposa zoyambira (0; 1) - (zabodza; zoona)).
Lolani X = B, pomwe B = {a,b,c,…,z} ndi seti ya zofanana, element-by-element yolingana ndi seti ya mikhalidwe ya X.
Ndiye fuzzy anakhala Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso, lomwe limafanana ndi lingaliro losamveka (nthawi zambiri) lofotokoza mawonekedwe a X, limatha kuimiridwa motere:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (2)

pamene m ndi sitepe yofotokozera discretization, ndine wa N - kuchulukitsa kwa sitepe.
Momwemo, kuti muthe kukulitsa chidziwitso cha chidziwitso cha dongosolo lachidziwitso molingana ndi kupitiliza (kufewa) kwa kufotokozera, tikukhalabe m'malire a danga la kusakwanira kwa kulingalira, timayambitsa. digiri ya kubwereza kwa seti yosamveka Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso ndipo timapeza mawonekedwe awa oyimira:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (3)

kumene Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - seti yofananira ndi lingaliro losamveka, lomwe limafotokozera mawonekedwe a X mokwanira kuposa momwe adakhazikitsira Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso, malinga ndi muyezo wofewa; Kubwereza - digiri ya kubwereza kwa kufotokozera.
Izo ziyenera kudziΕ΅ika kuti Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (ochepetsedwa ku seti yomveka bwino) muzochitika zapadera, ngati kuli kofunikira.

Chiyambi cha gawo laling'ono

Pamene Re = 1 set Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso ndi seti wamba yosamveka bwino ya digiri ya 2, kuphatikiza ngati zinthu zosokonekera (kapena mapu awo omveka bwino) omwe amafotokoza zachikhalidwe X [1, 2]:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (4)

Komabe, ichi ndi vuto lonyozeka, ndipo pakuyimira kwathunthu, zina mwazinthu Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso ikhoza kukhala seti, pamene zina zonse zingakhale zazing'ono (zosavuta kwambiri) zinthu. Chifukwa chake, kutanthauzira kuyika kotere ndikofunikira kuyambitsa kubwereza pang'ono - analogue ya gawo laling'ono la danga (m'nkhaniyi, danga la ontology la phunziro linalake) [3, 9].

Pamene Re ndi fractional, timapeza zotsatirazi Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (5)

kumene Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - Zosawoneka bwino za mtengo wa X1, Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - Zosawoneka bwino za mtengo wa X2, ndi zina.

Pankhaniyi, kubwereza kumakhala kocheperako, ndipo mafotokozedwe ake amakhala ofanana.

Kufotokozera Zochita Zambiri za Module

Mapangidwe a dongosolo lachidziwitso lotseguka amalingalira mfundo ya modularity, yomwe imatsimikizira kuthekera kwa makulitsidwe, kubwerezabwereza, kusinthasintha ndi kutuluka kwa dongosolo. Kumanga modular kumapangitsa kuti zitheke kubweretsa kukhazikitsidwa kwaukadaulo kwa njira zazidziwitso pafupi kwambiri ndi zomwe zikuchitika mdziko lenileni, kupanga zida zosavuta kwambiri potengera zomwe zimagwira ntchito, zomwe zidapangidwa kuti zisalowe m'malo mwa anthu, koma kuti zithandizire bwino. iwo mu kasamalidwe ka chidziwitso.

Module ndi gawo lapadera lachidziwitso, chomwe chingakhale chovomerezeka kapena chosankha pazifukwa za kukhalapo kwa dongosolo, koma mulimonsemo umapereka ntchito zapadera mkati mwa malire a dongosolo.

Mitundu yonse ya magwiridwe antchito amatha kufotokozedwa ndi mitundu itatu ya magwiridwe antchito: kulenga (kulemba zatsopano), kusintha (kusintha zomwe zidalembedwa kale), kufufutidwa (kufufuta zomwe zidalembedwa kale).

Lolani X kukhala mawonekedwe enaake a magwiridwe antchito, ndiye kuti X yofananira ikhoza kuyimiridwa monga:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (6)

kumene X1 - chilengedwe, X2 - kusintha, X3 - kuchotsa,

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (7)

Kuphatikiza apo, magwiridwe antchito a gawo lililonse ndikuti kupanga deta sikufanana (kukhazikitsidwa popanda kubwereza - ntchito yolenga siibwerezanso), komanso kusintha ndi kufufutidwa nthawi zambiri kungaphatikizepo kukhazikitsa zonse ziwiri-ndi-chinthu (kuchita). opareshoni pa zinthu zosankhidwa za seti ya data) ndipo iwonso amaphatikiza ntchito zofanana ndi iwowo.

Zindikirani kuti ngati ntchito yogwiritsira ntchito X siichitidwa mu gawo linalake (lomwe silinagwiritsidwe ntchito mu dongosolo), ndiye kuti seti yofanana ndi opaleshoni yotereyi imatengedwa kuti ndi yopanda kanthu.

Chifukwa chake, pofotokoza lingaliro losavuta (chiganizo) "gawo limakupatsani mwayi wochita opareshoni ndi seti yofananira ya data pazolinga zachidziwitso," gulu losamveka bwino. Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso m'njira yosavuta ikhoza kuyimiridwa motere:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (8)

Nthawi zambiri, seti yotereyi imakhala ndi digiri yobwereza yofanana ndi 1,6 (6) ndipo imakhala yosasunthika komanso yosamveka nthawi yomweyo.

Kukonzekera zochitika zogwiritsira ntchito ndi kuyesa gawoli

Pamagawo a chitukuko ndi magwiridwe antchito azidziwitso, pakufunika zochitika zapadera zomwe zimalongosola dongosolo ndi zomwe zikugwiritsidwa ntchito pogwiritsira ntchito ma module malinga ndi ntchito yawo (zochitika zogwiritsira ntchito), komanso kuyang'ana kutsatiridwa kwa zomwe zikuyembekezeredwa ndi zotsatira zenizeni za ma modules (zoyeserera) .test-case).

Poganizira malingaliro omwe afotokozedwa pamwambapa, njira yogwirira ntchito pazochitika zoterezi ingafotokozedwe motere.

Seti yosamveka imapangidwira gawolo Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (9)

kumene
Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - seti yosamveka bwino yopangira data malinga ndi magwiridwe antchito a X;
Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - seti yosamveka bwino yogwiritsira ntchito kusintha kwa data malinga ndi magwiridwe antchito a X, pomwe kuchuluka kwa kubwereza (kuphatikiza ntchito) ndi nambala yachilengedwe ndipo m'malo ocheperako ndi ofanana ndi 1;
Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso - seti yosamveka bwino yochotsa deta molingana ndi magwiridwe antchito a X, pomwe kuchuluka kwa recursion b (kuyika ntchito) ndi nambala yachilengedwe ndipo muzochitika zazing'ono ndi zofanana ndi 1.

Khamu loterolo likufotokoza ndi chiyani kwenikweni (zomwe zinthu za data) zimapangidwira, kusinthidwa ndi / kapena kuchotsedwa pakugwiritsa ntchito module iliyonse.

Kenako mndandanda wa zochitika zogwiritsa ntchito Ux pa magwiridwe antchito X pa gawo lomwe likufunsidwa limapangidwa, chilichonse chomwe chimafotokoza. chifukwa chiyani (pantchito yanji yabizinesi) ndi zinthu za data zomwe zimafotokozedwa ndi seti zopangidwa, kusinthidwa ndi/kapena kufufutidwa? Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso, ndipo mu dongosolo lanji:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (10)

kumene n ndi chiwerengero cha zochitika zogwiritsira ntchito X.

Kenako, seti ya mayeso a Tx amapangidwa kuti agwire ntchito X pamutu uliwonse wogwiritsa ntchito gawo lomwe likufunsidwa. Test script ikufotokoza, ndi ma data ati omwe amagwiritsidwa ntchito komanso momwe angagwiritsire ntchito nkhaniyo, ndi zotsatira zotani zomwe ziyenera kupezedwa:

Njira yosavuta yophunzitsira komanso kugwiritsa ntchito kwake pakutengera chidziwitso ndi machitidwe azidziwitso (11)

kumene [D] ndi mndandanda wa data yoyesera, n ndi chiwerengero cha mayesero a X.
M'njira yomwe tafotokozayi, kuchuluka kwa zochitika zoyeserera kumafanana ndi kuchuluka kwa momwe amagwiritsidwira ntchito, zomwe zimathandizira ntchito pakulongosola kwawo ndikuwongolera momwe dongosolo likukulira. Kuphatikiza apo, algorithm yotereyi ingagwiritsidwe ntchito poyesa kuyesa ma module a pulogalamu yazidziwitso.

Pomaliza

Njira yowonetsedwa yophunzitsira movutikira imatha kukhazikitsidwa pamagawo osiyanasiyana amoyo wamtundu uliwonse wa chidziwitso chodziwikiratu, ndicholinga chopeza gawo lofotokozera lachidziwitso, komanso pogwira ntchito zogwiritsa ntchito ndikuyesa ma module.

Kuphatikiza apo, kulowetsedwa movutikira kumathandizira kuphatikizira chidziwitso kutengera zomwe zapezedwa, monga "cognitive kaleidoscope", momwe zinthu zina zimakhala zomveka bwino komanso zomveka bwino, pomwe zina, molingana ndi lamulo lodzifananiza, zimagwiritsidwa ntchito kuchuluka kwa nthawi zomwe zafotokozedwa mlingo wa kubwereza kwa seti iliyonse ya deta yodziwika. Kuphatikizidwa pamodzi, zotulukapo zosamveka bwino zimapanga chitsanzo chomwe chitha kugwiritsidwa ntchito pazolinga zachidziwitso komanso pofunafuna chidziwitso chatsopano.

Njira yamtunduwu imatha kufotokozedwa ngati mawonekedwe apadera a "nzeru zopangira", poganizira kuti zida zophatikizika sizitsutsana ndi mfundo yamalingaliro osakwanira ndipo zidapangidwa kuti zithandizire luntha laumunthu, osati m'malo mwake.

Zolemba

  1. Borisov V.V., Fedulov A.S., Zernov M.M. M.: Hotline - Telecom, 2014. - 88 p.
  2. Borisov V.V., Fedulov A.S., Zernov M.M., β€œFundamentals of theory of fuzzy logical inference.” M.: Hotline - Telecom, 2014. - 122 p.
  3. Demenok S.L., "Fractal: pakati pa nthano ndi zaluso." St. Petersburg: Academy of Cultural Research, 2011. - 296 p.
  4. Zadeh L., "Zofunikira za njira yatsopano yowunikira machitidwe ovuta komanso njira zopangira zisankho" / "Mathematics Today". M.: "Chidziwitso", 1974. - P. 5 - 49.
  5. Kranz S., "Kusintha Kwa Umboni Wa Masamu." M.: Laboratory ya Chidziwitso, 2016. - 320 p.
  6. Mavrikidi F.I., β€œFractal mathematics and the nature of change” / β€œDelphis”, No. 54 (2/2008), http://www.delphis.ru/journal/article/fraktalnaya-matematika-i-priroda-peremen.
  7. Mandelbrot B., "Fractal geometry of Natural." M.: Institute of Computer Research, 2002. - 656 p.
  8. "Zofunikira za chiphunzitso cha seti zopusa: Malangizo", comp. Korobova I.L., Dyakov I.A. Tambov: Nyumba yosindikizira ya Tamb. boma izo. Univ., 2003. - 24 p.
  9. Uspensky V.A., "Apology for Mathematics." M.: Alpina Non-fiction, 2017. - 622 p.
  10. Zimmerman HJ "Fuzzy Set Theory - ndi Ntchito Zake", kope lachinayi. Springer Science + Business Media, New York, 4. - 2001 p.

Source: www.habr.com

Kuwonjezera ndemanga