The Order Homomorphism And Order Convergence On Fuzzy Partial Sequences

Domain theory, introduced in the1970s, has double background of theoretical computer science and pure mathematic research. Domain theory has built a founda-tion for the semantics of programming languages. The combination and interaction between order and topology is the essential character of domain theory, which has made domain theory to be a common interest for both computer science researchers and mathematic researchers from the time that domain theory was found. With the rapid development of computer science, the requirement for concurrent language is more and more. The binary order relation of domain theory can only express the qualitative information, but not express the quantitative information in gener-al. So quantitative domain theory (QDT for short) was generated for building a quantitative semantics model. QDT forms a new branch of domain theory and has undergone active research in the past three decades.From2000, the fuzzy domain theory has been formed with fuzzy poset theory applied to the research of QDT. Fuzzy poset, the foundation of fuzzy domain theory, is a generalization of classical poset. The main purpose of this thesis is to discuss the fuzzy order homomorphism and fuzzy order convergence of fuzzy poset. The structure is organized as follows:Chapter One:Preliminaries. This chapter gives some related concepts and results about lattice theory, logic algebra and fuzzy domain.Chapter Two:The basis and fuzzy homomorphism of fuzzy domain. Firstly, by introducing the concepts of a fuzzy directed minimal set and a basis of fuzzy dcpo, we prove that a fuzzy dcpo X is a fuzzy domain iff X has a basis iff for every element x of X, x has the fuzzy directed minimal set. Secondly, based on the fuzzy directed minimal sets and the bases of fuzzy domains, some properties of fuzzy order-homomorphisms of fuzzy domains are investigated. Lastly, we prove that the fuzzy order-homomorphisms from the basis of fuzzy domain X into fuzzy domain Y can be uniquely extended to the fuzzy order-homomorphisms from fuzzy domain X into fuzzy domain YChapter Three:The order convergence of L-filter on fuzzy poset. Firstly, we introduce the concept of doubly continuous fuzzy poset, and provide that fuzzy poset (X, e) is doubly continuous iff (X, e) and (X, eop) are continuous, and some related examples about doubly continuous fuzzy poset are given. Secondly, fuzzy order topology and fuzzy bi-Scott topology based on fuzzy poset are introduced, and the conclusion that fuzzy bi-Scott topology is coarser than fuzzy order topology is proved, and some properties of fuzzy order topology and fuzzy bi-Scott topology are studied. Finally, the fuzzy order convergence of L-filter is investigated, and the fact that fuzzy order convergence of L-filter on doubly continuous fuzzy poset is topological is proved.