In this paper, we consider a left quantale module represented by Q-module as a universal set and we introduce the notion of rough Q-submodule with respect to a Q-submodule of Q-module. Some results about homomorphic images of rough Q-submodules are also generalized and improved in the field of Q-modules. Next, the concepts of set-valued homomorphism and strong set-valued homomorphism of Q-modules are introduced, and related properties are investigated. The notions of generalized lower and upper approximation operators, by means of a set-valued mapping are defined.
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