Vague集的包含度

Vague inclusion degree

Vague集是Zadeh模糊集的一种推广形式,同样Vague集的包含度也是模糊集包含度的一种扩展。针对现有文献涉及到的Vague集的包含度只是属于[0,1]区间的一个模糊值的问题,根据Vague集理论的基本思想拓展了Vague集的包含度,提出一种新的Vague集的包含度定义,以体现Vague集的拓展意义。提出并验证了四类Vague集的包含度的计算公式,同时给出此Vague集包含度与模糊集包含度之间关系的定理。

Vague set is one of generalizations of Zadeh’s fuzzy set,and Vague inclusion degree is also an extension of fuzzy inclusion degree.For the definition of Vague inclusion degree existed in present references is only a fuzzy value,this paper proposes a new definition of Vague inclusion degree to reflect the expansion meaning of the Vague set.This new Vague inclusion degree based on the notion of vague set extends the conception of Vague inclusion degree and fully expresses the advantage of Vague set.Four classes of Vague inclusion degree formulas are proposed and verified,a theorem about the relationship between Vague inclusion degree and fuzzy inclusion degree is given.