Natural Objects with Indeterminate Boundaries

Abstract

This chapter 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. It explains the basic principles of geostatistics for dealing with quantitative variation in fields. The chapter introduces the main ideas of fuzzy set theory and fuzzy k-means classification and illustrates by applications that demonstrate the decrisping of idealized polygon boundaries, and the extraction of crisp boundaries as zones of confusion between interpolated, polythetic, overlapping classes. The standard approach of reductionist science has been very successful in physics, chemistry and biology. The philosophical basis behind the division of geographical space into smaller and smaller, but exactly defined objects, is that of the reductionist approach, which is a hallmark of Western scientific thought.