?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=PENERAPAN+KONSEP+HIMPUNAN+ROUGH+PADA+STRUKTUR+IDEAL+SUATU+SEMIGRUP&rft.creator=LUTFIANA+%2C+SOFA&rft.subject=500+ilmu+pengetahuan+alam+dan+matematika&rft.description=Let+(U%2CR)+be+an+approximation+space+where+U+non-empty+set+and+R+is+an+equivalence+relation+on+U.+Equivalence+relation+is+a+relation+that+is+reflexive%2C+symmetric+and+transitive+which+will+form+separate+partitions+called+equivalence+class.+If+S+is+a+subset+of+U%2C+then+the+equivalence+class+will+form+the+upper+approximation+of+S+and+the+lower+approximation+of+S.+If+the+upper+approximation+of+S+and+the+lower+approximation+of+S+are+not+the+same%2C+then+S+is+called+a+rough+set.+If+a+binary+operations+*+are+defined%2C+then+%E2%8C%A9S%2C*%E2%8C%AA+will+form+a+rough+semigroup+if+it+meets+certain+conditions.+If+a+non-empty+set+I%E2%8A%86S%2C+then+I+is+called+a+rough+ideal+in+the+rough+semigroup++if+it+statisfies+the+conditions+for+rough+right+ideal+and+rough+left+ideal.+Futhermore%2C+we+give+some+examples+of+the+commutative+rough+semigroups+and+rough+ideals+on+a+finite+set.+In+addition%2C+we+provide+the+properties+of+the+rough+ideal.%0D%0AKeywords%3A+Approximation+space%2C+rough+set%2C+rough+semigroup%2C+rough+ideal.%0D%0A%0D%0ADiberikan+ruang+aproksimasi+(U%2CR)+dengan+U+himpunan+tak+kosong+dan+%0D%0AR+merupakan+relasi+ekuivalensi+pada+U.+Relasi+ekuivalensi+merupakan+relasi+yang+bersifat+reflektif%2C+simetris+dan+transitif+yang+akan+membentuk+partisi-partisi+yang+saling+lepas+yang+disebut+kelas+ekuivalensi.+Jika+diberikan+himpunan+bagian+S+di+U%2C+maka+kelas-kelas+ekuivalensi+akan+membentuk+aproksimasi+atas+dari+S+dan+aproksimasi+bawah+dari+S.+Jika+aproksimasi+atas+S+dan+aproksimasi+bawah+S+tidak+sama%2C+maka+S+disebut+himpunan+rough.+Jika+didefinisikan+operasi+biner+*+pada+S%2C+maka+%E2%8C%A9S%2C*%E2%8C%AA+merupakan+semigrup+rough+apabila+memenuhi+syarat-syarat+tertentu.+%0D%0AJika+diberikan+himpunan+tak+kosong++I%E2%8A%86S%2C+maka+I+disebut+ideal+rough+pada+semigrup+rough+jika+memenuhi+syarat+ideal+kanan+rough+dan+ideal+kiri+rough.+Selanjutnya+diberikan+contoh+konstruksi+semigrup+rough+dan+ideal+rough+komutatif+pada+himpunan+berhingga.+Selain+itu%2C+diberikan+sifat-sifat+ideal+rough+pada+semigrup+rough.%0D%0AKeywords%3A+Ruang+aproksimasi%2C+himpunan+rough%2C+semigrup+rough%2C+ideal+rough.%0D%0A&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM+&rft.date=2023-05-30&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F73323%2F1%2FABSTRAK.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F73323%2F2%2FSKRIPSI%2520FULL.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F73323%2F3%2FSKRIPSI%2520TANPA%2520BAB%2520PEMBAHASAN.pdf&rft.identifier=++LUTFIANA+%2C+SOFA++(2023)+PENERAPAN+KONSEP+HIMPUNAN+ROUGH+PADA+STRUKTUR+IDEAL+SUATU+SEMIGRUP.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM+%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F73323%2F