Many valued lattices and their representations
This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P, the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak ohm-lattices and ohm-lattices, are introduced. It is shown that the notion of ohm-lattices coincides with that of lattice fuzzy orders of Belohlavek; and the notion of weak ohm-lattices coincides with that of vague lattices of Demirci. (c) 2007 Elsevier B.V. All rights reserved.
lattice fuzzy order vague lattice commutative unital quantale omega-category yoneda embedding omega-lattice weak omega-lattice