Logical operations on vague sets

By defining a partial ordering relation on the Vague domain of unit interval I, a definition of Vague sets on a lattice V(I) was given. Applying the classic extension principle, the corresponding Vague logical operators defined on V(I) were constructed with continuous fuzzy triangular norms, negator and continuous fuzzy implicators. The representations of the generalized intersection/union, complementary operation and implications on Vague sets were introduced in the context. Some basic properties of Vague logical operations were summarized. It enriches the conceptual framework of Vague sets, and will enlarge its applications on such fields as logic, linguistic and inference, as well as the information representation and processing.