Construction of the Rough Quotient Modules over the Rough Ring by Using Coset Concepts - Rahma, Aira; Fitriani, Fitriani; Faisol, Ahmad (Diponegoro University, 2025)
Given an ordered pair (U, θ) where U is the set universe and θ is an equivalence relation on the set U is called an approximation space. The equivalence relation θ is a relation that is reflexive, symmetric, and transitive. If the set X U, then we can determine the upper approximation of the set X, denoted by Apr(X), and the lower approximation of the set X, denoted by Apr(X). The set X is said to be a rough set on (U, θ) if and only if Apr(X)-Apr(X) ≠ . A rough set X is a rough module if it satisfies certain axioms. This paper discusses the construction of a rough quotient module over a rough ring using the coset concept to determine its equivalence classes and discusses the properties of a rough quotient module over a rough ring related to a rough torsion module.