中文摘要：

鉴于已有模糊区域关系模型研究工作主要是针对二维空间中模糊区域间的拓扑关系，没有涉及三维立体空间中处于不同平面上的Vague区域间的不确定的拓扑关系，为了处理立体空间中复杂的Vague区域关系，基于Vague集对立体空间中的含核Vague区域之间的空间关系进行了详细的研究，给出了处于不同平面中的含核Vague区域关系的42种交集模型，进一步研究了处于同一平面和不同平面上的含核Vague区域关系的旋转对应性。研究成果可用于对立体空间中的含核Vague区域关系进行统一建模和数学分析，能较好地解决立体空间中的含核Vague区域关系的表示和分析问题。

英文摘要：

Considering that the existing research on fuzzy region relation models is mainly focused on the Vague region relations in the same plane instead of the Vague region relations in the different plane, to represent the complex Vague region relations in the three-dimensional space, the paper studies the Vague regions and the Vague region relations with kernel in the three-dimensional space in detail based on the Vague sets. The 42 intersection models in different planes are given. Furthermore, the revolution corresponding relations between the Vague region relations with kernel in the same plane and in different planes are also studied. The production of this work can be used to establish the mathematical model and conduct the mathematical description on the Vague region relations with kernel and can be used to represent and analyze the Vague region relations well in the three-dimensional space.