Research On Some Properties Of Fuzzy Partially Ordered Sets And Fuzzy Union Algebra

Domain theory and quantale theory established in the early 1970’s and 1980’s,respectively,are two important branches of topologies on lattices.They developed independently,but they are based on order theory from the viewpoint of the com-mon mathematical foundation.Meanwhile,they make the close relationship with topology,algebra,category,logic and so on.Since the concept of fuzzy set was pre-sented by L.A.Zadeh in 1965,the development of fuzzy mathematics has changed rapidly.In 2000,Professor Fan Lei and others combined the Domain theory with the fuzzy mathematics,which greatly promoted the development of the classical Domain theory.This thesis is to research the free completions of fuzzy posets and the projective objects in the category of fuzzy sup-algebras.The structure of this thesis is organized as follows:Chapter One:Preliminaries.In this chapter,some basic concepts and rele-vant conclusions will be used in this paper are given.Chapter Two:Free completions of fuzzy posets.On the one hand,the free join-and meet-completions of fuzzy posets are built and characterized.The uni-versal property of free join-and meet-completions is studied.On the other hand,we identify the intermediate structure and △1-directed object,and prove that the△1-directed object coincides with the Dedekind-MacNeille completion of the inter-mediate structure in the bounded fuzzy lattice case.Chapter Three:The projective objects in the category of fuzzy sup-algebras.Firstly,the concept of K-flat projective objects in the category of fuzzy sup-algebras is introduced.We give some equivalent characterizations on the objects.Secondly,it is proved that the category of fuzzy sup-algebra is a reflective subcategory of the category of fuzzy pre-sup-algebra.At last,we introduce the notion of K-coherent fuzzy sup-algebra and study some properties about it.