Study On Theory Of Fuzzy Uniform Posets

Domain theory was put forward by Mathematician and computer theorist D.S.Scott.In Domain theory,the relation between two elements can express by order.With the development of modern computer network,the traditional binary order relation can not express the quantitative difference between the calculated amount of information.Quantitative Domain proposed to make up for this gap.Therefore,in recent years,the research on quantitative Domain is in full swing,and many good results have been obtained.In this paper,the concept of fuzzy uniform posets is introduced by using the concept of uniform posets and fuzzy posets.And then,the definition of fuzzy uniform continuous posets is given.The bases theory of fuzzy uniform continuous posets are studied.The main contents are as follows:1.This paper introduces the development of fuzzy posets and Domain theory.Also some basic knowledge needed in this dissertation.2.By using the concept of the uniform posets and the properties of the fuzzy directed sets,the concept of the fuzzy uniform posets are studied,and the definitions of the fuzzy uniform complete posets,the fuzzy uniform continuous posets and the fuzzy uniform minimal posets are given.The related properties and some equivalent characterizations of them are studied.3.On the basis of fuzzy uniform continuous posets,the concepts of fuzzy uniform bases and fuzzy uniform local bases are proposed,and some properties of fuzzy uniform bases and fuzzy uniform local bases are discussed.4.The definitions of preserving fuzzy uniform way-below and fuzzy ordered homomorphism mapping are given.and the related properties of fuzzy uniform minimal posets,fuzzy uniform bases and fuzzy uniform local bases are discussed under fuzzy ordered homomorphism.Some equivalent characterizations of fuzzy uniform local bases and an ordered homomorphism extension theorem of fuzzy uniform bases are obtained.Secondly,the concept of fuzzy uniform Scott open sets is introduced,and the related properties of fuzzy uniform Scott open sets are discussed.