The Expansion Of Fuzzy (subset) Ideals

The poset theory plays a significant role in the study of mathematics,logic and computer science.Therefore,it has been closely concerned by scholars at home and abroad,and has developed into a relatively perfect theoretical system.But with the rapid development of information technology,the qualitative information provided by the binary order relations in the classical poset can’t satisfy the needs of research,especially the needs of research for calculating the quantitative differences between information.In this context,fuzzy poset theory has been proposed and developed rapidly.At present,under the joint efforts of numerous mathematical researchers,the framework of fuzzy poset theory has been basically formed,but there is still a lot of work to be done in terms of content.In this paper,we study the extensions of fuzzy ideals and the extensions of L-subsets.Based on the above description,this thesis is arranged as follows:Chapter One:Preliminaries.In this chapter,some basic concepts and relative conclusions about lattice theory,category and fuzzy poset theory will be used in this paper are given.Chapter Two:The extensions of fuzzy ideals on fuzzy poset.In first part of this chapter,we introduce the concepts of the extensions of fuzzy ideals,and study the properties of these extensions.In second part,a number of examples of the extensions of fuzzy ideals are given.The third part,by the properties of these extensions,the equivalent characterization for prime(distributive)fuzzy poset is given.Chapter Three:The extensions of L-subsets on fuzzy poset.In this chapter,we consider two different kinds of extensions of L-subsets,and then by these extensions prove that the category CFPos is a fully reflective subcategory of the category FPos.