A theory of vague lattices based on many-valued equivalence relations-II: complete lattices

As a continuation of Part I, two sorts of vague lattices called complete vague lattices and ordinarily complete vague lattices, both of which correspond to the generalization of complete lattices based on many-valued equivalence relations, are introduced, and some of their elementary properties are presented in this paper. Furthermore, the representations and the constructions of (ordinarily) complete vague lattices are studied in details.