Studies On Some Theories Of Fuzzy Countable Semicontinuous Lattices

In the early of 1970 s, the domain theory was introduced. It attracted the attention of related domestic and foreign scholars and obtained the rapid development and a series of far-reaching results. But domain theory was not perfect in practice, so it could’t reflect the amount of information which be computed in the elements. Then Quantitative domain was proposed to solve the problem. In recent years, the research of Quantitative Domain was increasingly active and had also made a series of good conclusions. This thesis mainly studies the fuzzy countable semicontinuous lattices, fuzzy strongly countable semicontinuous lattices and homomorphisms of the consistently semicontinuous lattices and obtains a series of properties and conclusions about fuzzy domain theory.Fistly, we describe the background and research status of fuzzy partial order set,and give domain theory and fuzzy set theory will be used in the related knowledge and results.Secondly, we give a new fuzzy waybelow relation)fuzzy countable semiwaybelow relation by using fuzzy semiprime countable ideal. Based on it, the concept of fuzzy countable semicontinous lattices is given on the fuzzy complete lattices. Besides,we discuss some properties of fuzzy countable semicontinuous lattices and obtain equivalent characterizations of fuzzy countable semicontinous lattices which promotes the related literatures of fuzzy countable semicontinuous lattices.Thirdly, by giving the definition of fuzzy strongly countable semicontinuous lattices, we study the properties of fuzzy strongly countable semicontinous lattices and discuss the relation of fuzzy countable semicontinuous lattices and fuzzy strongly countable semicontinuous lattices.Finally, by giving the definition of compatible semiprime minimal set, we study the properties of homomorphisms of the consistently semicontinuous lattices and obtain some internal characterizations of the consistently semicontinuous lattices.