| Domain theory is the mathematical basis of computer functional programming language,which plays an important role in the theoretical calculation,and the quantitative study of that is the basis of application.So far,fuzzy Domain is the one of the basic framework of quantitative Domain and this theory provides a new method for the study of quantitative Domain.So this paper is based on fuzzy partial ordering relation and structure the continuity and the meet-continuity on fuzzy poset,then we deeply discuss the property of those.The composition and main content of this paper will be introduced.In first chapter,we introduce some basic concepts of poset and fuzzy poset,etc.In second chapter we study the continuity of fuzzy poset.The first,the generalized Scott topology on fuzzy directed complete poset is extended to fuzzy poset.Secondly,we set up fuzzy L-approximation relationship on fuzzy poset and structure the continuity of fuzzy poset by L-approximation relationship.Additionally,we study the category duality of fuzzy domain.In third chapter we study the meet-continuity of fuzzy poset.Firstly we prove the equivalence of generalized Scott closed set.Then according to the structural form of meet-continuity of classical Domain theory,we structure the meet-continuity on fuzzy poset and have some important conclusions.Such as continuity and meet-continuity on fuzzy poset about generalized Scott topology have the property of invariance and the hereditary.In fourth chapter,we structure a new fuzzy relation and define the concept of fuzzy lattice,fuzzy sub lattices under fuzzy relationship,then give the equivalent conditions of fuzzy lattice.On this basis we raise the concept and properties of fuzzy semiideal,fuzzy filter,as well as some related propositions. |
