基于9-Intersection模型的模糊空间对象间的拓扑关系研究

本文将从地理认知的角度上分析并选择一个适合于在GIS中应用9-Intersection模型的模糊空间对象的边界定义,并构建一个能够采用9-Intersection模型精确判断模糊空间对象之间拓扑关系的模糊拓扑空间(CITfts),并进行相应的证明,最后建立简单模糊区域,采用empty/no-empty算子给出模糊空间对象之间的拓扑关系的表达形式。

Research on relationships between fuzzy spatial objects based on 9-Intersection matrix

The topological relationshi Pbetween spatial objects is one of the fundamental relationships in Geographic Information Science. By introducing the fuzzy objects into topological space, the topological relationshi Pbetween fuzzy objects has become a focus of nowadays research. Fuzzy sets are not complementary, considering the acquisition of fuzzy objects, the key part of judgment of relationshi Pbetween fuzzy objects using classical 9-Intersection matrix-the definition of boundary of fuzzy objects adopting cris Ptopological method, is not reasonable, which will lead to an inaccurate judgment of topological relations between fuzzy objects. The paper adopts a boundary definition that fits for GIS application, which is based on 9-Intersection matrix and analyzed from a cognition perspective firstly. Then it establishes a fuzzy topological space that can be used to judge the accurate topological relations by utilizing 9-Intersection matrix, and gives corresponding reasoning. Finally, it builds u Psimple fuzzy regions by the adoption of empty/no-empty operator to propose the expression of topological relationshi Pbetween fuzzy objects.