Quantale-valued fuzzy Scott topology

The aim of this paper is to extend the truth value table of lattice-valued convergence spaces to a more general case and then to use it to introduce and study the quantale-valued fuzzy Scott topology in fuzzy domain theory. Let (L; ∗; ε) be a commutative unital quantale and let ⊗ be a binary operation on L which is distributive over nonempty subsets. The quadruple (L; ∗;⊗; ε) is called a generalized GL-monoid if (L; ∗; ε) is a commutative unital quantale and the operation ∗ is ⊗-semi-distributive. For generalized GL-monoid L as the truth value table, we systematically propose the stratified L-generalized convergence spaces based on stratified L-filters, which makes various existing lattice-valued convergence spaces as special cases. For L being a commutative unital quantale, we define a fuzzy Scott convergence structure on L-fuzzy dcpos and use it to induce a stratified L-topology. This is the inducing way to the definition of quantale-valued fuzzy Scott topology, which seems an appropriate way by some results.