Research On Several Problems Of Quantitative Domains

Domain theory is an interdiscipline of theoretical computer science and mathematics.To describe the degree of approximation between information is the idea of quantitative domain.Fuzzy domain is one of the research directions of quantitative domain,which combines the approximation step-by-step in domain theory and the degree expression in fuzzy mathematics organically.Applying the method of combining topologies and orders,this paper discusses some problems in fuzzy domain theory under the case of taking the lattice value as the unit closed interval.The main results of this paper are listed as follows.(ⅰ)Under certain conditions,the two definitions of continuous fuzzy domain in references are equivalent.(ⅱ)The two fuzzy topologies in two references are closely related: each set of a fuzzy Scott open set is defined by Yao is a Scott open set defined by Zhang.(ⅲ)The fuzzy Scott topology and the metric topology on an ultrametrical space(which can be considered as a fuzzy partial order set)agree.(ⅳ)The ideal completion of an ultrametrical space(viewed as a fuzzy poset)is an ultrametric completion of the space.(ⅴ)The fuzzy induced topology on an ultrametrical space is the semi-fuzzy Scott topology.