A generalization of the Chen-Wu duality into quantale-valued setting

With the unit interval [0,1] as the truth value table, Chen and Wu presented the concept of possibility computation over dcpos. Indeed, every possibility computation can be considered as a [0,1]-valued Scott open set on a dcpo. The aim of this paper is to study Chen-Wu's duality on quantale-valued setting. For clarity, with a commutative unital quantale $L$ as the truth value table, we introduce a concept of fuzzy possibility computations over fuzzy dcpos and then establish an equivalence between their denotational semantics and their logical semantics.