?url_ver=Z39.88-2004&rft_id=2017031016&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=KARAKTERISASI+MODUL+FAKTOR+ROUGH+ATAS+RING+ROUGH+PADA%0D%0AHIMPUNAN+BERHINGGA&rft.creator=Lisa+%2C+Adelia&rft.subject=500+ilmu+pengetahuan+alam+dan+matematika&rft.subject=510+Matematika&rft.description=Diberikan+pasangan+berurutan+(U%2C+%CE%B3)+yang+disebut+sebagai+ruang+aproksimasi%2C+dengan%0D%0AU+merupakan+himpunan+semesta+dan+%CE%B3+yaitu+relasi+ekuivalensi+pada+himpunan%0D%0AU.+Relasi+%CE%B3+disebut+relasi+ekuivalensi+jika+relasi+%CE%B3+bersifat+refleksif%2C+simetris%2C+dan%0D%0Atransitif.+Relasi+ekuivalensi+membangun+partisi-partisi+yang+saling+asing+yaitu+kelas%0D%0Aekuivalensi.+Diberikan+B+%E2%8A%86+U.+Aproksimasi+bawah+dari+B%2C+dinotasikan+dengan%0D%0AApr(B)%2C+yakni+gabungan+dari+kelas-kelas+ekuivalensi+yang+termuat+di+dalam+himpunan%0D%0AB.+Aproksimasi+atas+dari+B+yaitu+gabungan+dari+kelas+ekuivalensi+yang%0D%0Amempunyai+irisan+dengan+himpunan+B%2C+dinotasikan+dengan+Apr(B).+Jika+Apr(B)%E2%88%92%0D%0AApr(B)+%CC%B8%3D+%E2%88%85+atau+Apr(B)+%CC%B8%3D+Apr(B)%2C+maka+himpunan+B+disebut+himpunan+rough%0D%0Apada+ruang+aproksimasi+(U%2C+%CE%B3).+Himpunan+B+merupakan+modul+rough+jika+B+memenuhi%0D%0Asyarat-syarat+tertentu.+Pada+penelitian+ini+dibahas+mengenai+konstruksi+ring%0D%0Afaktor+rough+dan+modul+faktor+rough+atas+ring+rough%2C+serta+membuat+program+untuk%0D%0Amenentukan+suatu+himpunan+berhingga+merupakan+modul+faktor+rough+atas+ring%0D%0Arough+menggunakan+Python.%0D%0A%0D%0AKata+Kunci%3A+Ruang+aproksimasi%2C+himpunan+rough%2C+modul+rough%2C+ring+faktor+rough%2C+modul+faktor+rough+atas+ring+rough.%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AABSTRACT%0D%0A%0D%0AGiven+an+ordered+pair+(U%2C+%CE%B3)+which+is+called+an+approximation+space%2C+where+U+is+a%0D%0Auniversal+set+and+%CE%B3+is+an+equivalence+relation+on+the+set+U.+A+relation+%CE%B3+is+called+an%0D%0Aequivalence+relation+if+the+relation+%CE%B3+is+reflexive%2C+symmetric%2C+and+transitive.+Equivalence%0D%0Arelations+build+mutually+separate+partitions+called+equivalence+classes.+Given%0D%0AB+which+is+a+subset+of+U%2C+the+lower+approximation+of+B+is+the+union+of+equivalence%0D%0Aclasses+contained+in+the+set+B%2C+denoted+by+Apr(B).+An+upper+approximation+of+B+is%0D%0Aa+union+of+equivalence+classes+that+have+intersections+with+B%2C+denoted+by+Apr(B).%0D%0AIf+Apr(B)%E2%88%92Apr(B)+%CC%B8%3D+%E2%88%85+or+Apr(B)+%CC%B8%3D+Apr(B)+then+the+set+B+is+called+a+rough+set%0D%0Ain+the+approximation+space+(U%2C+%CE%B3).+The+set+B+is+a+rough+module+if+B+meets+certain%0D%0Aconditions.+This+research+investigates+the+construction+of+the+rough+quotient+ring%0D%0Aand+the+rough+quotient+module+over+the+rough+ring.+In+addition%2C+we+build+a+program%0D%0Ato+determine+a+finite+set+is+a+rough+quotient+module+over+a+rough+ring+by+using%0D%0APython.%0D%0A%0D%0AKeywords%3A+Approximation+space%2C+rough+set%2C+rough+module%2C+rough+quotient+ring%2C+rough+quotient+module+over+rough+ring.&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM&rft.date=2024-03-20&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F79960%2F1%2FABSTRAK.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F79960%2F2%2FSKRIPSI%2520FULL.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F79960%2F3%2FSKRIPSI%2520TANPA%2520BAB%2520PEMBAHASAN.pdf&rft.identifier=++Lisa+%2C+Adelia++(2024)+KARAKTERISASI+MODUL+FAKTOR+ROUGH+ATAS+RING+ROUGH+PADA+HIMPUNAN+BERHINGGA.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F79960%2F