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All Journal Jurnal Sains dan Seni ITS IPTEK The Journal for Technology and Science Journal of the Indonesian Mathematical Society UNEJ e-Proceeding Limits: Journal of Mathematics and Its Applications International Journal of Computing Science and Applied Mathematics Pattimura Proceeding : Conference of Science and Technology
Subiono -
Departemen Matematika, Institut Teknologi Sepuluh Nopember
Agriculture, Biological Sciences & Forestry Arts Humanities Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Education Energy Engineering Materials Science & Nanotechnology Mathematics Physics

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Journal : UNEJ e-Proceeding

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APROKSIMASI PADA GRUP Dian Winda Setyawati; Subiono Subiono
UNEJ e-Proceeding 2022: E-Prosiding Seminar Nasional Matematika, Geometri, Statistika, dan Komputasi (SeNa-MaGeStiK)
Publisher : UPT Penerbitan Universitas Jember

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Abstract

A non-empty set with binary operations on a set is called a group if the set satisfies the associative property, the existence of an identity, and the existence of an inverse for each element of the set . A normal subgroup in group can partition group into equivalence classes so that a lower approximation and an upper approximation can be formed from the non-empty set corresponding to the normal subgroup . Let be a non-empty subset of , the lower approximation of corresponding to the normal subgroup is defined as the set of elements in where the equivalence class of the element is a subset of while the upper approximation of corresponding to the normal subgroup is defined as the set of elements in where the equivalence class of the element intersects the set . In this paper, we will give more general properties regarding the relationship between the upper approximation and the lower approximation by involving two different normal subgroups of group and two different sets that are subsets of group . Furthermore, we will show the corollary of these properties if we use one normal subgroup and one subset of group . Keywords: equivalence classes, lower approximation, upper approximation
Co-Authors Desi Indriyani Dian Winda Setyawati Farah Azizah Heri Purnawan HESTY IRNA AULIA Mohammad Jamhuri Mufid, Muhammad Syifa’ul Muhammad Syifa’ul Mufid Rif`an Amrozi Soleha Soleha