Vague(模糊)线形变换及其“表示”

Vague linear shift and its representation

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”、“Vague线性变换”等一系列概念 ,并在此基础上 ,严格证明了“Vague关系”和“Vague线性变换”之间一一对应的关系 。

Vague sets and the operations of them are introduced by analyzing the insufficiency of the existing theory of Fuzzy sets. Concepts such as broad sense relationship and its projection and truncation, Vague relationship and its projection and truncation are well defined in this paper, on the basis of which the one-to-one correspondence between Vague relationship and Vague linear shift is demonstrated fully in detail. What has been presented in this paper provides theoretical bases for Fuzzy decision-making problems.