Research On Related Problems In Fuzzy Domain

Domain theory plays a fundamental role in the denotational semantics of program-ming languages.It is characterized by the close connection and interaction between orders and topologies,which makes it the common study field of both computer experts and mathematicians and having wide applications.Since 2000,the fuzzy set theory has been applied to Domain theory,forming the fuzzy Domain theory.At present,the theory has abundant theoretical achievements and the background of applications,and has been close to categorical theory,fuzzy topology theory,the formal concept analysis,rough set theory and the theory of computer science and so on.At the same time,it needs to be further study in many ways.This paper mainly studies fuzzy Z_L-algebraic poset,fuzzy Z_L-core complete poset and fuzzy Cut-stable mapping as well as the fuzzy polyadic formal concept analysis.Details are as follows:Chapter One:Preliminaries.This chapter reviews some preliminaries about several commonly used classes of lattice theory,fuzzy Domain theory as well as cate-gorical theory,which are necessary for the rest chapters.Chapter Two:Some results on fuzzy Z_L-algebraic poset.This chapter intro-duces the concepts of fuzzy Z_L-continuous(algebraic)poset,and study their properties.Then we give the definition of fuzzy Z_L-closure system and get that the sets of fuzzy Z_L-ideals on the sets of the compact elements of fuzzy Z_L-algebraic poset is fuzzy closure system,if,moreover,Z_L is union-complete,then it is fuzzy Z_L-closure system.More-over,we study the properties of fuzzy Z_L-morphism and fuzzy Z_L-comorphism and prove that every fuzzy Z_L-continuous poset can be embedded in a fuzzy Z_L-algebraic poset by a fuzzy Z_L-morphism.Chapter Three:Fuzzy Z_L-core complete poset and some properties of relevant categories.This chapter introduces the concepts of fuzzy Z_L-core complete poset,fuzzy Z_L-closed support,then we discuss their properties,mainly study the exten-sion property of fuzzy Z_L-core complete poset.On this basis,the definition of fuzzy Z_L-extension basis is studied.Futhermore,we discuss the relationships among the category of fuzzy poset,the category of fuzzy Z_L-core complete poset,the category of fuzzy Z_L-core poset,the category of fuzzy Z_L-complete poset.Chapter Four:Fuzzy cut-stable maps and its extension property.This chapter introduces the notions of fuzzy lower(upper)cut-continuous maps,fuzzy lower(upper)cut-stable maps,fuzzy residuated(residual)maps and fuzzy cut-preserving maps.The relationships among these maps are also discussed.Then,we obtain the extension property of fuzzy cut-stable maps on fuzzy posets,and prove that the category of fuzzy complete lattices with fuzzy weakly complete homomorphisms is a full reflective subcategory of the category of fuzzy posets with fuzzy weakly cut-stable maps.By the the extension property of fuzzy cut-stable maps,we prove that the category of fuzzy continuous lattices with fuzzy complete homomorphisms is a full reflective subcategory of the category of fuzzy precontinuous posets with fuzzy cut-stable maps.Chapter Five:Fuzzy weakly cut-stable maps.Based on Chapter Four,we give the definitions of fuzzy weakly lower(upper)cut-continuous maps,fuzzy weakly lower(upper)cut-stable maps and fuzzy weakly cut-preserving maps,and the relationships among them are discussed.Moreover,we obtain the extension property of fuzzy weakly cut-stable maps on fuzzy posets,and prove that the category of fuzzy complete lattices with fuzzy weakly complete homomorphisms is a full reflective subcategory of the category of fuzzy posets with fuzzy weakly cut-stable maps.Finally,we get an equivalent condition when the extended map of fuzzy weakly cut-stable map is an isomorphic map.Chapter Six:Fuzzy polyadic formal concept analysis.This chapter studies some questions of fuzzy polyadic formal concept analysis.Firstly,we define fuzzy triordered sets,fuzzy complete trilattices and prove that the set of fuzzy triadic formal concept is fuzzy complete trilattice.Then,we show the basic theorem of fuzzy triadic formal concept analysis,i.e.,each fuzzy complete trilattice is the fuzzy triadic concept lattice of some fuzzy triadic formal context.Finally,we discuss some properties of fuzzy n-adic formal concept analysis,and prove the basic theorem of fuzzy n-adic formal concept analysis,i.e.,each fuzzy complete n-lattice is the fuzzy n-adic concept lattice of some fuzzy n-adic formal context.