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This study assesses and models uncertainties in vector-based spatial processes and analyses in a Geographical Information System (GIS), including buffering, point-in-polygon query, overlay, and line simplification. GIS is a tool for spatial-related data processing and decision making. Handling decision making under uncertainty is a further extension of GIS functions. Therefore, it is of vital importance to study uncertainties in GIS and to decide the fitness of data to user's particular applications. Uncertainty in a vector spatial analysis is mainly introduced from (a) uncertainty of raw spatial data, (b) uncertainties propagated through various spatial analyses, and (c) uncertainty arising from a mathematical representation of the spatial analysis. Each spatial analysis has its own mathematical model to describe its mechanism. It is, therefore, impossible to obtain a generic uncertainty model for all spatial analyses. In this study, uncertainty models for vector buffer analysis, for vector overlay analysis, for point-in-polygon query, and for line simplification have been proposed, in order to provide uncertainty measures for the associated analyses. Current uncertainty models for line simplification are able to quantify uncertainty of the simplified line in a special case where the original line is free from uncertainty. The uncertainty of the initial line always exists; it is likely appropriate to consider an effect of the uncertainty of the original line on uncertainty of a simplified line. In order to overcome the problem of the current uncertainty model, we propose uncertainty models in a case where the uncertainty of the initial line exists and classify the uncertainty in line simplification into three types: propagated uncertainty, model uncertainty and overall processing uncertainty. Uncertainty measures for each uncertainty types can assess the uncertainty in line simplification in different situations. These uncertainty measures are potentially used to determine an optimal weed threshold of the Douglas-Peucker line simplification algorithm such that the simplified line satisfies a predefined acceptable level of accuracy. The significances of this research lie on two aspects: (a) contributing to the development of GIS by providing uncertainty analyses for vector-based spatial processes and analyses, and (b) contributing to the applications of GIS by providing data quality indices for GIS users. The first aspect can be exhibited in our theoretical uncertainty models while the second one can be demonstrated in our examples. Users can thus much efficiently decide the fitness of spatial data to their GIS applications according to the uncertainty level. (Abstract shortened by UMI.)