?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=KONSTRUKSI+MODUL+FAKTOR+ROUGH+ATAS+RING+ROUGH%0D%0A%0D%0AMENGGUNAKAN+KONSEP+KOSET&rft.creator=%09Aira%2C++Rahma+Gunawan+&rft.subject=500+ilmu+pengetahuan+alam+dan+matematika&rft.description=Given+an+ordered+pair+(U%2C+%CE%B8)+where+U+is+a+universal+set+and+%CE%B8+is+an+equivalence+re-%0D%0Alation+on+the+set+U+is+called+an+approximation+space.+The+equivalence+relation+%CE%B8+is%0D%0A%0D%0Aa+relation+that+is+reflexive%2C+symmetric%2C+and+transitive.+This+relation+will+partition+the%0D%0Aset+U+into+mutually+exclusive+classes%2C+namely+equivalence+classes.+If+the+set+X+%E2%8A%86+U%2C%0D%0Athen+we+can+determine+the+upper+approximation+of+the+set+X%2C+which+is+the+union+of%0D%0Aequivalence+classes+that+intersect+with+the+set+X%2C+denoted+by+Apr(X).+Next%2C+we+can%0D%0Adetermine+the+lower+approximation+of+the+set+X%2C+which+is+the+union+of+equivalence%0D%0Aclasses+contained+in+the+set+X%2C+denoted+by+Apr(X).+The+set+X+is+said+to+be+a+rough%0D%0Aset+on+(U%2C+%CE%B8)+if+and+only+if+Apr(X)%E2%88%92Apr(X)+%CC%B8%3D+%E2%88%85.+A+rough+set+X+is+a+rough+module%0D%0A%0D%0Aif+it+satisfies+certain+axioms.+This+paper+discusses+the+construction+of+a+rough+quo-%0D%0Atient+module+over+a+rough+ring+using+the+coset+concept+to+determine+its+equivalence%0D%0A%0D%0Aclasses+and+discusses+the+properties+of+a+rough+quotient+module+over+a+rough+ring%0D%0Arelated+to+a+rough+torsion+module.+Furthermore%2C+a+program+using+Python+is+made+to%0D%0Adetermine+whether+a+finite+set+is+a+rough+quotient+module+and+to+determine+rough%0D%0Asubmodules.%0D%0AKeywords%3A+Approximation+space%2C+rough+module%2C+rough+quotient+moduleover+rough%0D%0Aring%2C+rough+torsion+module.%0D%0ADiberikan+pasangan+berurutan+(U%2C+%CE%B8)+dengan+U+merupakan+himpunan+semesta+dan%0D%0A%0D%0A%CE%B8+ialah+relasi+ekuivalensi+pada+himpunan+U+disebut+ruang+aproksimasi.+Relasi+eku-%0D%0Aivalensi+%CE%B8+yaitu+suatu+relasi+yang+bersifat+refleksif%2C+simetris%2C+dan+transitif.+Relasi%0D%0A%0D%0Aini+akan+mempartisi+himpunan+U+menjadi+kelas-kelas+yang+saling+asing+yaitu+kelas%0D%0Aekuivalensi.+Jika+himpunan+X+%E2%8A%86+U%2C+maka+dapat+ditentukan+aproksimasi+atas+dari%0D%0A%0D%0Ahimpunan+X%2C+yaitu+gabungan+dari+kelas+ekuivalensi+yang+beririsan+dengan+him-%0D%0Apunan+X%2C+dinotasikan+dengan+Apr(X).+Selanjutnya%2C+dapat+ditentukan+aproksimasi%0D%0A%0D%0Abawah+dari+himpunan+X%2C+yaitu+gabungan+dari+kelas+ekuivalensi+yang+termuat+dalam%0D%0A%0D%0Ahimpunan+X%2C+dinotasikan+dengan+Apr(X).+Himpunan+X+dikatakan+himpunan+ro-%0D%0Augh+pada+(U%2C+%CE%B8)+jika+dan+hanya+jika+Apr(X)+%E2%88%92+Apr(X)+%CC%B8%3D+%E2%88%85.+Himpunan+rough+X%0D%0A%0D%0Amerupakan+modul+rough+jika+memenuhi+beberapa+aksioma+tertentu.+Pada+penelitian%0D%0A%0D%0Aini+dibahas+mengenai+konstruksi+modul+faktor+rough+atas+ring+rough+menggunak-%0D%0Aan+konsep+koset+dalam+penentuan+kelas+ekuivalensinya%2C+dan+membahas+sifat-sifat%0D%0A%0D%0Amodul+faktor+rough+atas+ring+rough+terkait+modul+torsi+rough.+Lebih+lanjut+dibuat%0D%0A%0D%0Aprogram+menggunakan+Python+untuk+menentukan+suatu+himpunan+berhingga+me-%0D%0Arupakan+modul+faktor+rough+dan+untuk+menentukan+submodul+rough.%0D%0A%0D%0AKeywords%3A+Ruang+aproksimasi%2C+modul+rough%2C+modul+faktor+rough+atas+ring+rough%2C%0D%0Amodul+torsi+rough.&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM+&rft.date=2024-03-21&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F83457%2F1%2F1.%2520ABSTRAK%2520-%2520Aira%2520Rahma%2520Gunawan.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F83457%2F2%2F2.%2520SKRIPSI%2520FULL%2520-%2520Aira%2520Rahma%2520Gunawan.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F83457%2F3%2F3.%2520SKRIPSI%2520TANPA%2520BAB%2520PEMBAHASAN%2520-%2520Aira%2520Rahma%2520Gunawan.pdf&rft.identifier=+++Aira%2C+Rahma+Gunawan+++(2024)+KONSTRUKSI+MODUL+FAKTOR+ROUGH+ATAS+RING+ROUGH+MENGGUNAKAN+KONSEP+KOSET.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM+%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F83457%2F