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

Abstract

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.