A Study of Roughness in Modules of Fractions

The theory of rough sets is successfully applied in various algebraic systems (e.g. groups, rings, and modules). In this paper, the concept of roughness is introduced in modules of fractions with respect to its submodules. Hence, the notion of the lower and upper approximation spaces based on a submodule of the modules of fractions is introduced. Some fundamental results related to these approximation spaces are examined with examples. Moreover, this paper establishing several connections between the approximation spaces of two different modules of fractions with respect to the image and pre-image under a module homomorphism. This technique of building up a connection among the approximation spaces via module homomorphisms is useful to connect two information systems in the field of information technology.