Region Relations of the Irregular Vague Regions with Holes Based on Vague Sets

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.