中文摘要：

模糊区域的空间信息表示和区域关系处理在空间数据库、地理信息系统和人工智能等领域具有重要的意义．引入Vague集的概念和理论对含洞不规则Vague区域关系进行了系统的研究．基于Vague集给出了Vague区域、Vague洞和原子域等概念；将舍洞不规则Vague区域分成原子域，研究了原子域间的空间关系；联合原子域关系，给出了含洞不规则Vague区域关系．研究成果可较好地处理含洞不规则Vague区域内的模糊点不确定的隶属信息和复杂的含洞不规则Vague区域的空间关系的表示和分析等问题．

英文摘要：

Representing spatial information of the vague regions and handling the vague region relations are of great significance in spatial database, geographical information systems and artificial intelligence, etc. In real world, the vague information about the vague regions with holes is abounded. Whether the fuzzy points belong to the vague region with holes and the degree of the membership are often uncertain. The existing research on the vague regions can not represent roundly the idiographic vague information of the given points in the vague regions with holes and can not represent the complex region relations of the irregular vague regions with holes. In order to tackle the problem, the region relations of the irregular vague regions with holes are discussed based on vague sets. The conceptions of the vague regions, the vague holes and the atomic-regions are given based on the vague sets~ The irregular vague region with holes is divided into some atomic-regions and the spatial relations of the atomic-regions are studied systemically. Based on the spatial relations of the atomic-regions, the irregular vague region relations with holes could be presented. The result produced in this work can deal with the indeterminate membership information of the vague points in vague regions and the region relations of the irregular vague regions with holes.