Quantitative domains via fuzzy sets: Part II: Fuzzy Scott topology on fuzzy directed-complete posets

This paper pursues an investigation on quantitative domains via fuzzy sets initiated by the first author. This time we define an L-topology, called the fuzzy Scott topology, on fuzzy dcpos and investigate its properties. Scott convergence of stratified L-filters is also defined and studied. We show that a fuzzy dcpo (X,e) is continuous if and only if for any stratified L-filter on X, Scott convergence coincides with the convergence with respect to the fuzzy Scott topology. At last, we show that the category of fuzzy dcpos with fuzzy Scott continuous maps is Cartesian-closed.