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Yunita Septriana Anwar
Program Studi Pendidikan Matematika Universitas Muhammadiyah Mataram
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Journal : Integra: Journal of Integrated Mathematics and Computer Science

 1 
On the Construction of Rough Quotient Modules in Finite Approximation Spaces Adelia, Lisa; Fitriani; Faisol, Ahmad; Anwar, Yunita Septriana
Integra: Journal of Integrated Mathematics and Computer Science Vol. 2 No. 1 (2025): March
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20252116

Abstract

Let S be a set and φ an equivalence relation on S. The pair (S, φ) forms an approximation space, where the relation φ partitions S into mutually disjoint equivalence classes. For any subset B' ⊆ S, the lower approximation Apr(B') is defined as the union of all equivalence classes entirely contained in B', while the upper approximation Apr(B') is the union of all equivalence classes that have a non-empty intersection with B'. The subset B' is called a rough set in (S, φ) if Apr(B') ≠ Apr(B'). If, in addition, B' satisfies certain algebraic conditions, it is termed a rough module. This paper investigates the construction of rough quotient rings and rough quotient modules within such approximation spaces. The approach is developed using finite sets to facilitate the algebraic formulation and analysis of these rough structures.
Algebraic Construction of Rough Semimodules Over Rough Rings Trisnawati, Evi; Fitriani; Faisol, Ahmad; Anwar, Yunita Septriana
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241219

Abstract

Let (℧, µ) be an approximation space, where ℧ is a non-empty set and µ is an equivalence relation on ℧. For any subset H ⊆ ℧, we can define the lower approximation and the upper approximation of H . A set H is called a rough set if its lower and upper approximations are not equal. In this study, we explore the algebraic structure that emerges when certain binary operations are defined on rough sets. Specifically, we investigate the conditions under which a subset H forms a rough semimodule over a rough semiring. We present several key erties of this structure and construct illustrative examples to support our theoretical results.
Co-Authors Abdillah Abdillah Abdillah Abdillah Adelia, Lisa Ahmad Faisol Ahmad Febrian Rusdiansyah Apriliani, Nova Baidowi Baidowi Baidowi Baidowi1 Budi Surodjo Dewi Kartika Sari Dewi Pramita Dewi Pramita Farapatana, Elsa Fitriani I Putu Yudi Prabhadika Indah Emilia Wijayanti Islahudin Kurniati Kurniati Laranisa, Sri Mahsup Mahsup Muzili, Sukron NURUL HIKMAH Putri Andriani Rizki, Heru Tri Novi Rizki, Heru Tri Novi Sirajuddin Sirajuddin Sirajudin Sirajudin Sri Wahyuni Sripatmi ., Sripatmi Sripatmi Sripatmi Sripatmi Sripatmi Suhaedi, Saefudin Suhaedi, Saefudin Trisnawati, Evi Vera Mandailina, Vera