对区间值模糊集的边界的研究

When we study the interval-valued fuzzy sets, it is found that, the order on the interval-valued fuzzy sets is determined by the boundary of the sets to a large extent. For example, the uncompleteness of the lattice on the interval-valued fuzzy sets is originated by the properties of the lower boundary. As a result, in this research, we will attempt to study the relations between the boundary of the sets and the lattices on the sets. Firstly, we will study the properties of the boundary, as a part of the whole sets. Then, we will study the connection between the order on the sets and the boundary of the sets, and clarify how the boundary influence of the order.

在对区间值模糊集进行研究时，发现其边界的形式对该集合的序结构有着很大的影响。比如，该集合序结构的不完备性，很大程度上是由于其下边界的性质导致的。因此，在本项目中，我们将对区间值模糊集的边界与该集合序结构的关系展开研究。首先，我们将对该集合的边界本身的性质展开探究，发掘其作为整个区间值模糊集一部分在整个集合中的性质。进而，通过连续变换等方式，对区间值模糊集的序结构与该集合边界的关系展开研究，以明确该集合的边界对该集合本身的性质的影响。

本项目基本按照预计展开研究，基本完成了预想的工作，并取得了一定的理论成果。研究了一般模糊集上的弱统一模等基本运算，对区间值模糊集的边界性质进行了的探讨，并通过弱化边界，提出了双函数模糊集和一种新的格。并在此基础上，对这两种集合的性质展开了探讨。