The Research Of Completion On The L-fuzzy Poset

The classical Domain theory can't resolve the complicate fuzzy language efficiently. However,the fuzzy set and fuzzy order,to which the set and order in the classical Domain are generalized,solve that problem well.In this paper,based on the L-fuzzy poset introduced by[9],we establish a framework of theory of L-fuzzy poset's completion and obtain many equivalent characterizations about L-fuzzy Domain and related notions by the level cut sets in[3]-[6].Most of the theories we proposed are new and present a general framework for the study of the fuzzy data types,fuzzy relations and fuzzy approximation operators in information systems and database technology.The main results are:In chapter one,we introduce the background and the preliminary knowledge of Domain,fuzzy sets,and so on.In chapter two,the definition of L-fuzzy upper bound sets and propositions about L-fuzzy upper sets are given.Further,the definition of L-fuzzy complete lattices are given and the properties of L-fuzzy complete lattices are discussed.In chapter three,the L-fuzzy continuous lattices are defined,which is the generalization of the continuous lattices in the classical theory,and preserves some of its classical properties.By raising the ordinary mapping,the definition of an L-fuzzy Scott continuous mapping is obtained.Finally,we show equivalent characterizations of the L-fuzzy Scott closed subset by different cuts.In chapter four,firstly,we present some characterizations of L-fuzzy poser and their corresponding proofs.Then,we give the definition of an L-fuzzy upper set and prove its related properties.Next,we study the properties of L-fuzzy Co-Alexandrov topological spaces and equivalently characterize it which is a generalization of the Alexandrov topological spaces on a poset(X,e) in the classical topology theory. Finally,we establish the relationships of L-fuzzy poset,L-fuzzy upper set and L-fuzzy Co-Alexandrov topological spaces.The relationship between L-fuzzy poset and L-fuzzy upper set is that we can use them to construct the L-fuzzy Co-Alexandrov topological spaces.