Boundaries

Where shape or size of areas matter, the notion of a boundary comes into play. This concerns geographic objects but also the constituents of a discrete geographic field. Location, shape and size are fully determined if we know an area’s boundary, and thus the boundary is a good candidate for its representation. This especially applies to areas with naturally crisp boundaries. A crisp boundary is one that can be determined at an almost arbitrary level of precision, dependent only on the data-acquisition technique applied. Fuzzy boundaries contrast with crisp boundaries in that a fuzzy boundary is not a precise line, but is rather, itself an area of transition.

A fuzzy boundary is not a precise line, but is rather, itself an area of transition. Fuzzy boundaries are more common in natural phenomena. In recent years, various research efforts have addressed the issue of explicit treatment of fuzzy boundaries, but there is still only limited support in existing GIS software. Typically, the areas identified in a geological classification, are vaguely bounded in reality, but applications of this geological information probably do not require high positional accuracy of the boundaries involved.

As a rule of thumb, crisp boundaries are more common in man-made phenomena, whereas fuzzy boundaries are more common in natural phenomena. In recent years, various research efforts have addressed the issue of explicit treatment of fuzzy boundaries, but there is still only limited support in existing GIS software. Typically, the areas identified in a geological classification, like that depicted in examples of Discrete field, are vaguely bounded in reality, but applications of this geological information probably do not require high positional accuracy of the boundaries involved. Therefore, an assumption that they are actually crisp boundaries will have little influence on the usefulness of the data.