Vagueness in Spatial Data

This entry examines aspects of vagueness in spatial data from the perspective of a spatial database used to support a geographic information system (GIS). A spatial database is a collection of data concerning objects located in some reference space that attempts to model some enterprise in the real world. The real world abounds in uncertainty, and any attempt to model aspects of the world should include some mechanism for incorporating uncertainty. There may be uncertainty in the understanding of the enterprise or in the quality or meaning of the data. There may be uncertainty in the model, which leads to uncertainty in entities or the attributes describing them. And at a higher level, there may be uncertainty about the level of uncertainty prevalent in the various aspects of a database.

Many operations are applied to spatial data under the assumption that features, attributes, and their relationships have been specified a priori in a precise and exact manner. However, inexactness often exists in the positions of features and the assignment of attribute values and may be introduced at various stages of data compilation and database development. Models of uncertainty have been proposed for spatial information that incorporate ideas from natural-language processing, the value-of-information concept, nonmonotonic logic and fuzzy set, and evidential and probability theory. Thus, in the modern GIS, there is a need to more precisely model and represent the underlying uncertain spatial data. The major aspects of spatial data description to focus on for uncertainty considerations include spatial region descriptions, spatially related attributes, and spatial relationships.

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Spatially Related Properties

Next, consider spatially related properties such as soil types, which might be described in linguistic terms such as

Such linguistic terms are commonly modeled as fuzzy sets. So soil classification might be assessed as belonging to the fuzzy set “sandy” with a membership value of 0.8. It is also possible to allow numeric as well as scalar values. For example, a fuzzy number such as “about 3 cm” of rainfall at a location could be used.

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