ABSTRACT
Surfaces are central to geographical analysis and their generation and manipulation a key component of geographical information systems (GISs). Geographical surface data are often not precise (errorless) since uncertainty is inherent in what is obtained — measurement uncertainty (position, instrument accuracy), method of data collection (satellite, sonar, LIDAR, altimeter, air photographs), the surface itself (ocean bottom, steep slope, terrain, wetlands, landforms — categories whose meanings combine several definitions or ideas), and methods of classification (dense forest, land cover/use — classifications, for example, defined via clustering algorithms). The uncertainty types
of interest to this presentation are: (i) finite ranges or intervals, for example, slope data are often given in 10-degree increments; (ii) transitional boundaries or fuzzy sets, for example, ocean to shore, grassland to shrubland; (iii) possibilistic values which are values that are known to exist, such as a 2000-meter isoline, but whose precise location is not since it is based on evidence arising from measurement and knowledge of the area, for example; and (iv) frequency or probability, for example, the daily temperature distribution over the last 100 years. It is emphasized that these four types of uncertainty are distinct from each other and must be handled correctly semantically and analytically. Data of types (i), (ii), (iii), and (iv) will be called in this study uncertainty data.
