Abstract: 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. hhc region relations of the vague region with kernel and the Vaguchole region were discussed detailedly based on Vague sets. hhc conceptions of the Vague region with kernel, the Vague-hole region and the region partition were given based on the Vague sets. The region relations of the Vague region with kernel and the Vagucholc region in the different plane were discussed respeclively. The implication theorem and the implication algorithm for the relations of the Vague sub-regions were also given. Furthermore, the analysis of an instance was also given. The production in this work can deal with the indeterminate membership information of the Vague points in the Vague regions with kernel and the Vaguchole regions, and the region relations of the vague region with kernel and the Vague-hole region can be determined well.

Key words: Vague sets, Vague region with kernel, Vagucholc regions, Vague region relations