Researches On The Z-semicontinuous Domain And The Z-fuzzy Semicontinuous Domain

In recent years,the continuous domains were generalized to various classes of ordered structures for different motivations.The semicontinuous domain and the fuzzy semicontinuous domain were introduced by D.Guo.Based on them,the concepts of Z-semicontinuous domain and Z-fuzzy semicontinuous domain are introduced,and their some properties are studied.We show that such a Z-semicontinuous domain and Z-fuzzy semicontinuous domain is a generalization of a semicontinuous domain and the fuzzy semicontinuous domain.Based on the domain theory and the fuzzy domain theory were learned.Moreover,some relevant literature are searched and researched.The structure of this thesis is organized as follows:Chapter One,introduction.we briefly introduce the history and the current research situation on domain theory and fuzzy domain theory,and give a clean reins of them.Through citing and analyzing numerous works in this field,we also give some preliminaries that related with domain theory and fuzzy domain theory which we will be used throughout this paper.Chapter Two,Z-semicontinuous domain.Firstly,the concept of Z-semicontinuous domain is introduced,we show that the Z-continuous domain?the Z-semicontinuous domain and the strongly Z-continuous domain is different from an article,and its some properties are studied.Secondly,the concept of Z-semibasis?locally Z-semibasis and Z-semiweight on a Z-semicontinuous domain are introduced,and its some properties are studied.In particular,some characterizations of Z-semicontinuous domain with the help of Z-semibasis and locally Z-semibasis are given.Thirdly,the concept of character and density on a Z-semicontinuous domain with the help of locally Z-semibasis are given,and its some properties are studied.Finally,the concept of Z-subspace in Z-Domain is given,it is proved Z-SemiScott open sets and Z-SemiScott closed sets are Z-subspace.The concept of Z-semicontinuous subspace is also given,it is proved Z-semicontinuous domain is hereditary for closed Z-subspace.Chapter Three,Z-fuzzy semicontinuous domain.Firstly,the concept of generalized fuzzy subset systems?Z-fuzzy semicontinuous domain and Z-fuzzy strongly continuous domain are given and examined,and its some properties are studied.Secondly,the defination of Z-fuzzy SemiScott open sets and Z-fuzzy SemiScott Topology are given,more over some equivalent characterizations of Z-fuzzy semicontinuous domain and Z-fuzzy strongly continuous domain with the help of Z-fuzzy SemiScott open sets and Z-fuzzy SemiScott Topology are given.Thirdly,Z-fuzzy semiprime minimal set is defined and then a characterization of homomorphisms of the Z-fuzzy semicontinuous domain.Finally,two extended theorems on the Z-fuzzy semicontinuous domain are also obtained.