Z-fuzzy Semicontinous Lattices

This thesis further expands fuzzy domain theory and the main con-tents are the properties of Z-fuzzy semicontinuous lattices, fuzzy semicontinuous lat-tices and special element. The thesis mainly includes four chapters:Chapter one: Foreword and preliminaries knowledge. In this chapter, we firstlynarrate the developing history and researching status of fuzzy poset sets. At thesame time, we give out some preliminaries that related with classic domain theory,quantitative domain theory which we will be used throughout this thesis.Chapter two: Z-fuzzy semicontinuous lattices. Firstly, the generalized fuzzyideal sub-systems is defined, and though it, the Z-fuzzy semiwaybelow relation canbe introduced. Then Z-fuzzy semicontinuous lattice can be obtained. Based onthe above definitions, we discussed the primary properties of Z-fuzzy semicontinuouslattice. Secondly, characters of Z-fuzzy semiscott topology are discussed. And someequivalent characterizations of Z-fuzzy semiscott topology are also given. Finally, thecharacters of function space on Z-fuzzy semiscott lattice are studied.Chapter three: The generalized semiscott topology on fuzzy semi-continuouslattices. Firstly, we generalize semiscott open sets are defined, and some propertiesof it are discussed. Based on it, we prove that the family consistent with generalizedsemiscott open sets are generalized semiscott topology. Secondly, the definition offuzzy semiscott continuous function is introduced and it’s equivalent characterizationis obtained.Chapter four: The special element of fuzzy poset sets. In the first place, somespecial elements of fuzzy poset sets are defined. Next, the relations of various kindsof special elements are discussed.Chapter five: Weak continuous join-irreducible elements and some applications.In this chapter, weak continuous join-irreducible elements are defined. In addition,some properties of it are discussed, and some conclusions are obtained.