Natural Objects with Indeterminate Boundaries

Abstract

The aim of this introduction is to provide a backdrop for subsequent chapters, particularly those in Parts 5 and 6. It reviews the basic concepts of ‘objects’ and ‘fields’ used for modelling geographic objects and their handling using conventional discrete logic and explains how these conventional approaches are insufficient for working with complex, polythetic natural phenomena. The basic principles of geostatistics for dealing with quantitative variation in fields are explained. The main ideas of fuzzy set theory and fuzzy k-means classification are introduced and illustrated by applications that (a) demonstrate the decrisping of idealized polygon boundaries, and (b) the extraction of crisp boundaries as zones of confusion between interpolated, polythetic, overlapping classes.