On the Imprecision of Boundaries

Imprecision of regional boundaries is subjected to a formal analysis within a fuzzy set theoretic framework. Regions are characterized by linguistic propositions which have precise mathematical translations. It is demonstrated that boundaries are generally fuzzy and exist as gradients rather than lines. Similarly, regions overlap to a certain extent. Though regional characterizations are imprecise, the extent of a fuzzy boundary can be exactly demarcated. Concepts of regional cores and edges are also examined. A simple climatic classification problem is employed to illustrate the theoretical arguments. The framework appears to be more natural, informative, and flexible. It comprises the conventional regional concepts as special cases.