Vague集的映射定理及其证明

从分析现有模糊集的不足入手，引入Vague集，规定了Vague集之间的运算，依次定义了“广义关系”、“广义关系的投影与截影”、“Vague关系”、“Vague关系的投影与截影”、“Vague映射”等一系列概念，并在此基础上，严格证明了“vague关系”、“Vague映射”之间一一对应的关系，丰富了模糊集理论，为模糊决策问题提供了初步的理论基础。

The map theory and its demonstration of Vague sets

Vague sets and the operation of them are introduce by analyzing the insufficiency of the existing theory of Fuzzy sets. Concepts such as broad sense relationship and its projection and gruncation, Vague relationship and its projection and gruncation are well defined in this paper, on the basis of which the one-to-one correspondence between Vague relationship and Vague map is demonstrated fully in detail. What has been presented in this paper enriches Fuzzy sets theory and provides a preliminary theoretical basis for Fuzzy decision-making problems.