Nearness Modules

Abstract Near set theory, a generalization of rough set theory, constructs the universal set based on the properties of objects and the available information about these objects. Considering this fundamental property, the main aim of this paper is to introduce the concept of a nearness R -module, an algebraic structure containing objects with multiple properties, defined on a nearness ring R , based on near set theory. Additionally, we define nearness R -module homomorphisms and examine their basic properties.