Study On Theory Of Fuzzy Countable Continuous Lattices

In the late 1960 s to 70 s, computer theorists D. Scott put forward Domain theory, it prepared the mathematic ground for semantics of computer theory.But, in the classic domain theory, the simply order relations can only express qualitative information between elements, and lack the quantitative information which is needed during the computing, that is, it can not reflect the amount of information which can be computed contained in the element. Nevertheless, the introductions of the fuzzy posets and the quantitative Domain have just made up for this shortfall.Therefore, in recent years, many scholars have paid much attention to the quantitative Domain and have made great progress. In this paper, the fuzzy countable way-below relation is given in approach of fuzzy countable directed subset, and based on it, the concept of fuzzy countable continuous lattices is introduced. Some properties of fuzzy countable continuous lattices relating to the basic theory and the order homomorphism are studied. The main contents are as follows:Firstly, we describe the background and research status of fuzzy partial order set, and give some preliminaries that related with classic domain theory, quantitative domain theory which we will be used throughout this paper.Secondly, we introduce a new fuzzy way-below relation——fuzzy countable waybelow relation. Based on it, the concept of fuzzy countable continuous lattices is given on fuzzy complete lattices, and some basic properties of fuzzy countable continuous lattices are discussed.Thirdly, we introduce fuzzy countable local basis and fuzzy countable basis, and give some basic properties and equivalent characterizations.Finally, we introduce fuzzy countable directed minimal set, and study the fuzzy order-homomorphism of fuzzy countable continuous lattices.