Fuzzy Meet-Semicontinous Lattice And Its Relevant Problems

In recent years, the continuous lattices were generalized to various classes of ordered structures for different motivations. The semicontinuous lattice was introduced by D. Zhao. The meet-semicontinuous lattice was introduced by Wu Xiuhua, and its some properties were studied. Based on it, the concept of fuzzy meet-semicontinuous lattice is introduced and its some properties are studied. We show that such a fuzzy meet-semicontinuous lattice is a generalization of a meetsemicontinuous lattice. Based on the classic domain theory, continuous lattice theory,quantitative domain theory, topological structure and so on are learned. Moreover,some relevant literature are searched and researched. The structure of this thesis is organized as follows:In the first part, we briefly introduce the history and the current research situation on Domain theory and fuzzy poset, and give a clean reins of them. Through citing and analyzing numerous works in this field, we also give some preliminaries that related with classic domain theory, quantitative domain theory and category theory which we will be used throughout this paper.In the second part, Firstly, the fuzzy meet-semiwaybelow relation is defined. We show that the fuzzy meet-semiwaybelow relation, the fuzzy semiwaybelow relation and the fuzzy waybelow relation is different from an article. Based on it, fuzzy meetsemicontinuous lattice are defined, and its some properties are studied. Secondly,fuzzy meet-semicontinuous minimal set is defined and then a characterization of homomorphisms and two extended theorems on the fuzzy meet-semicontinuous lattice are also obtained. Finally, the fuzzy meet-semibase and the fuzzy local meet-semibase are defined on the fuzzy complete lattice. Some basic properties of the fuzzy meetsemibase and the fuzzy local meet-semibase are disscused, more over some equivalent characterizations of the fuzzy meet-semibase and the fuzzy local meet-semibase are also obtained.In the third part, the concept of fuzzy meet-semicontinuous on dcpo are introduced, some basic properties of the fuzzy meet-semicontinuous dcpo is disscused.