| Real world, in which there are lots of complex relations between phenomena and processes, is an infinitive complex and huge system, and also a continuous and natural real model. However, GIS, in which spatial data are managed, analyzed and processed, is a finite and discrete system, and the digital model stored in GIS is discrete through cognition, abstract and presentation steps. The differences between the infinite and the finite, the continuous and the discrete and the natural and the cognition result in the uncertainty of spatial data, analysis models, process methods and visualization. On the one hand, impacted by the uncertainty of data, cognition and methods, spatial relations are also uncertain. On the other hand, there always exist differences between the concepts described by existing methods of describing spatial relations and spatial language often used by human. Because existing methods of describing spatial relations are certain and can not describe that uncertainty and differences, the relations between two spatial objects computed by existing methods are inconsistent with the ones among entities in real world, which makes the results got from query and process based on spatial relations are clearly different with real relations or not the expected ones. Based on above points, the fuzzy methods for describing spatial relations and a model for describing and reasoning direction relations are proposed, and the works covering the issues of theoretic consideration, technology development, and application prototypes are presented. The fuzzy methods can describe the uncertainty of spatial relations, while the detailed direction relations can process the spatial relations in natural language, therefore can decrease the differences between the concepts expressed by existing methods and spatial language .The main contents of this dissertation include following points.(1) The three sources of the uncertainty of spatial relations, including the uncertainty of spatial data, the fuzziness of cognition and the uncertainty of process of spatial relations, are proposed. In addition, these three sources must be processed in a united method, not in different methods.(2) The fuzzy morphological operators processing fuzzy data are proposed. The basic operators of crisp mathematical morphology based on classic sets are extended to fuzzy operators based on fuzzy set. Therefore, the fuzzy operators can process fuzzy data.(3) First, the impacts of uncertainty of position and attribute upon topological relations are analyzed. Second, the fuzzy membership functions of dividing topological space and describing topological relations are proposed. Third, a fuzzy 9-intersection model is formed based on the fuzzy membership functions. The fuzzy 9-intersection model can describe the topological relations between fuzzy objects and crisp objects in a united framework, and deal with the impact of uncertainty ofposition and attribute on topological relations. Finally, the vector and raster algorithms of fuzzy 9-intersection model are researched. The vector algorithms have better precision and computation speed than raster ones.(4) Introducing the methods of rough set into the description of direction relations, the rough methods of reasoning direction relations are proposed. Both fuzzy objects and crisp objects can be expressed by two rough sets, down and up rough sets, and the difference set between up and down rough set shows the uncertainty of spatial data. In the same way, the direction relations also can be approximated by a down and an up rough set, the difference between these two rough sets express the uncertainty of direction relations. The reasoning of direction relations is described by two rough sets, and the difference set represents the uncertainty of reasoning direction relations.(5) After analyzing the impacts of uncertainty of position, attribute and cognition upon direction relations, first, the fuzzy membership functions of direction relations and there similarities are presented; seco...
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