Abstract: The normal definition of the similarity degree between Vague sets（or elements） is proposed based on some present methods.Moreover，the boundary condition is worked out through the investigating on the differences and relationships between the distance and the similarity，and an example concerned with the similarity between classical sets helps to clarify the boundary condition.Knowing the boundary condition，the blindness in constructing and choosing a proper similarity measure is surely reduced.Finally，a new method based on Hausdorff distance is established，and the case of continuous or discrete universe of discourse is considered，respectively.

Key words: Vague set, similarity measure, boundary condition, Hausdorff distance

摘要： 基于对现有Vague集（值）之间相似度度量方法的分析，给出了基本相似度和强相似度的定义，引入了能反映相似度与距离内在联系的边界条件，减少了相似度选取与构造的盲目性与随意性。基于Hausdorff距离给出了一种相似度度量新方法，并将该方法应用于离散论域及连续论域，得到了若干对应的加权相似度的计算公式。为解决基于Vague集的模式匹配和决策分析等问题作了理论上的准备，也为吸收和利用Fuzzy集、Rough集理论的相关结果和思想提供了方便。

关键词: Vague集, 相似度, 边界条件, Hausdorff距离