关键词: Vague集, 相似度, 边界条件, Hausdorff距离

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