The category theoretic approach of Obtulowicz to Pawlak's rough sets has been reintroduced in a somewhat modified form. A generalization is rendered to this approach that has been motivated by the notion of rough membership function. Thus, a link is established between rough sets and L-fuzzy sets for some special lattices. It is shown that a notion of indistinguishability lies at the root of vagueness. This observation in turn gives a common ground to the theories of rough sets and fuzzy sets.
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