W. Yao - Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang ۰۵۰۰۱۸, P.R. China
B. Zhao - Department of Mathematics, Shaanxi Normal University, Xi&#۰۳۹;an ۷۱۰۰۶۲, P.R. China

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame L. A definition of (strongly) completelydistributive L-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive L-orderedsets. The results in this paper establish close connections amongfuzzy-set approach of quantitative domains and fuzzy topology withmodified L-sober spaces and spatial L-frames as links. Inaddition, some mistakes in [K.R. Wagner, Liminf convergence in\Omega-categories, Theoretical Computer Science ۱۸۴ (۱۹۹۷)۶۱--۱۰۴] are pointed out.

Fuzzy DCPO, Fuzzy domain, Fuzzy Scott topology, (Spatial) L-frame, L-frame homomorphism, (Strongly) Completely distributive L-ordered set, Modified L-sober