Fuzzy Reasoning about Geographic Regions

Reasoning about geographic regions, like forests, lakes, cities, etc., often involves uncertainty and imprecision. For example, when we talk about a region like the city of Auckland, we usually do not know exactly the boundaries of that region. Nevertheless, we are able to reason about such a region. Or if we hear on the radio that a cold front is moving in from Antarctica, we can estimate when it will reach New Zealand, although we might not be able to determine with certainty the exact relation between the area covered by the cold front and the one that is referred to as New Zealand.

Recently, the RCC theory has gained a particular interest in the AI research community as formalism to reason about regions. This first-order theory is based on a primitive relation, called connectedness, and uses eight topological relations, defined on the basis of connectedness, to provide a framework to reason about regions. Lehmann and Cohn have introduced an extension to the RCC theory, which deals with imprecision in spatial representations. Our work carries on from there by applying fuzzy sets to the RCC theory and introducing a uniform framework to reason about geographic regions under uncertainty and imprecision.