A theory of vague lattices based on many-valued equivalence relations-I: general representation results

The present work introduces a new and general theory of ordering relations and lattices based on many-valued equivalence relations under the name vague ordering relations and vague lattices, respectively. Representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper, and various desirable results in this direction are established. Furthermore algebraic characterizations of vague lattices are studied.