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Rahmawati, Rara Gusti
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The Properties of Rough Submodule over Rough Ring Rahmawati, Rara Gusti; Fitriani, Fitriani; Faisol, Ahmad
Jurnal Matematika Integratif Vol 20, No 2: Oktober 2024
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v20.n2.55570.185-196

Abstract

A pair of non-empty set $U$ and equivalence relation $R$ on $U$, denoted as $(U,R)$, is called approximation space. Furthermore, equivalence classes form the construction of lower approximation and upper approximation. Let $X\subseteq U$, the lower approximation of $X$ denoted by $\underline{X}$ and the upper approximation of $X$ denoted by $\overline{X}$. A pair $Apr(X)=(\underline{X},\overline{X})$ is a rough set if $\underline{X}\neq \overline{X}$. $Apr(X)$ is rough module if $Apr(X)$ satisfies some conditions. In this research, we investigate some characteristics of the rough module and rough submodule over rough ring. Furthermore, we construct examples of the rough module and the rough submodule on approximation space $(U,R)$.
Co-Authors Ahmad Faisol Fitriani