中文摘要：

空间关系及其尺度变化建模，一直是地理信息科学基础理论的重要前沿领域之一。本文全面总结了该领域在理论、方法和应用方面的最新进展。首先，详细阐述了关系表现与几何表现的特点和差异，提出了关系表现的尺度问题，尤其是与制图综合的关系。然后，分别结合形状化简、面对象合并、属性归纳、空间维数退化等制图综合算子，论述了拓扑和方向关系尺度变化规律的推导和建模方法。最后，结合多尺度空间关系变化模型，提出了基于关系的多尺度数据分析技术框架，并重点阐述了基于关系的多尺度数据一致性检测和多尺度数据查询的概念及解决方法，且用实例分析证明了它们的有用性。详细而具体地研究不同综合算子对拓扑和方向关系尺度变化的影响及建模方法，对于分析和理解多尺度空间数据，具有重要意义。

英文摘要：

Modeling spatial relations and their scale changes has been one of the important topics in GIS science. This paper discussed the geometric-based and relational-based representation of geographic information. The first representation aims to store, manage, and analyze geometric data with coordinates, and concentrates on the geometric locations, shapes and distributions of spatial objects, thus it is termed as geometric representation. The latter uses symbols to qualitatively represent, communicate and infer spatial relationships between spatial objects based on people＇ s cognition and understanding, thus it is termed as relational representation. This paper mainly focused on summarizing the latest progress in theories, methods and applications about the relational representa- tion. First, the above-mentioned two representations were compared and their scale changes were highlighted. It is discovered that the geometric representations of same geographic entities vary at different spatial scales, so do the relational representations vary between geographic entities. This type of changes in relational representations strongly associates with cartographic generalization operators, which affects the changes of shapes, sizes and structures of spatial objects. Second, the influences of the generalization operators, which include shape simplifi- cation, merging of areal objects, attribute induction and spatial dimension reduction, on spatial relations were an- alyzed, and related methods were presented for deriving and modeling the scale changes of topological and direc- tional relations which was caused by the four operators. Third, combined with multi-scale spatial relations, a technological framework for analyzing multi-scale datasets was presented. We also illustrated the concepts and solutions for detecting the consistency of multi-scale data, and tested them practically with case studies to dem- onstrate their efficiency. Finally, it can be concluded that the generalization operators and modeling methods play impo