Algebraic Construction of Rough Semimodules Over Rough Rings - Trisnawati, Evi; Fitriani; Faisol, Ahmad; Anwar, Yunita Septriana (Magister Program of Mathematics, Universitas Lampung, 2024)
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.