Research On The Key Theory Of The Spatial Relations In The Spatial Database

The spatial relations are the relations between the spatial objects with some spatial characteristics, such as the topological relation, the direction relation and the distance relation etc. They are the basis of the spatial data organization, query, analysis and the spatial reasoning. The uncertainty of the spatial relations are diversity and complexity because of the uncertainty of the spatial data, the uncertainty of cognitive and the uncertainty of the spatial analysis. The representation of the indeterminate spatial relations and the construction of the spatial model are great difficult. To deal with the spatial relations between the ambiguous regions with the uncertain membership values of the point in the regions and to analyze the complex ambiguous regions and the ambiguous region relations, this paper described and analyzed the complex region relations between the ambiguous regions with the uncertain information based on the Vague set and the intersection model matrix. The existing research on the spatial relations of the spatial objects were mainly about the representation of the spatial relations and the spatial reasoning of the spatial point objects, line objects and region objects and the research on the spatial network were mainly about the relations of the moving objects in the spatial network, the structure and the properties of the network and the query of the moving objects in the network. The research achievement of the previous work can not deal with the representation, analysis and spatial reasoning of the complex spatial networks. To remedy the defects of the existing research, this paper discussed systemically the representation and the reasoning for the spatial network relations.To the uncertain complex ambiguous region relations and the spatial network relations, the innovation work were mainly as follows:Firstly, The conceptions of the Vague regions, Vague region partitions, Vague hole regions, Vague direction points and dynamic implicative relations were defined based on the Vague sets. This paper discussed the Vague region representation and the Vague region relations about the Vague regions with kernel and without kernel in the same plane and in the different plane based on the Vague sets. The dynamic transformation relations for the Vague regions with kernel and without kernel were studied, the algorithm and the theorem of the relation reasoning for the Vague subregions were also given.Secondly, The region relations of the irregular Vague regions with holes were discussed detailedly based on Vague sets. The irregular Vague region with holes was divided into some atomic-regions and the spatial relations of the atomic-regions were studied systemically, the algorithm and the theorem of the relation reasoning for the Vague subregions were also given. Based on the spatial relations of the atomic-regions, the irregular Vague region relations with holes could be presented.Thirdly, The Vague region relations and the direction relations were systematically analyzed based on the Vague sets which can deal with a great deal of uncertainty information. Based on the Vague sets, the intersection matrices and the representation model of the Vague regions were given. To handle the uncertainty of the direction relations which is caused by the ambiguity of the Vague regions, the Vague direction points and the Vague direction space were defined based on the Vague sets and the the intersection matrices of the direction relations were studied. The dynamic adjacency table of the Vague direction space were given and the related reasoning of the Vague region relations and the Vague direction relations were studied also.Fourthly, Representation and reasoning of the spatial network relations are focus of research on the spatial database. The representation of the predication and the intersection model for the spatial network relations were discussed systemically. The characteristic-condition-formulas and the implication-condition-formulas were also presented, furthermore, the theorem and the corollary to distinguish the spatial network relations were given.Fifthly, To forecast the spatial relations, the transform diagrams of the spatial network relations were also presented. The methods of the reasoning for the spatial network relations were studied systemically. The reasoning excluded rules and the implication rules were discussed detailedly. Based on the rules, the reasoning composite tables were also presented.The production in this paper lay the foundation for the applications and research of the Vague region relations and the spatial network relations in the spatial database.