The decision making in the real world is inevitably characterized with vagueness, and imprecision due to incomplete knowledge. To this end, we combine the information set with the rough set theory to represent both the vagueness and imprecision at the same time. We term the proposed structure as rough information set that has information sets based on fuzzy equivalence relations as its building blocks. The usefulness of the proposed structure is demonstrated through a case study in credit scoring analysis, and a biometrics application on knuckle-based recognition. © 1993-2012 IEEE.