ABSTRACT
Most GISci are traditionally designed on the basis that the represented spatial objects, such as rivers, roads, trees, and buildings, are error free. As has been indicated in Chapter 2, this assumption may not always be true, owing either to vagueness or fuzziness in the definition or identification of spatial objects or randomness during the measuring process. For example, it is impossible to describe a fuzzy boundary between urban and rural areas using crisp lines, without uncertainty, as has been the practice in traditional GIS representations. It has become obvious that there is a need to enhance the currently used GIS functions by introducing a means to describe single objects. Such descriptions would include any uncertainty present and, also, enable the description of fuzzy topological relationships between such uncertain spatial objects. On this basis, it could be concluded that descriptions of objects with crisp boundaries using the classical set theory (Apostol, 1974), is possibly no longer suitable (Wang, Hall, and Subaryono, 1990). However, it is likely that fuzzy set theory could be used to describe fuzzy uncertain objects in GISci. In addition, fuzzy topology provides a theoretical basis for modeling fuzzy topological relationships between spatial objects.
