Fuzzy mathematical methods for soil survey and land evaluation

SUMMARY The rigid-data model consisting of discrete, sharply bounded internally uniform entities that is used in hierarchical and relational databases of soil profiles, choropleth soil maps and land evaluation classifications ignores important aspects of reality caused by internal inhomogeneity, short-range spatial variation, measurement error, complexity and imprecision. Considerable loss of information can occur when data that have been classified according to this model are retrieved or combined using the methods of simple Boolean algebra available in most soil and geographical information systems. Fuzzy set theory, which is a generalization of Boolean algebra to situations where data are modelled by entities whose attributes have zones of gradual transition, rather than sharp boundaries, offers a useful alternative to existing methodology. The basic principles of fuzzy sets, operations on fuzzy sets and the derivation of membership functions according to the Semantic Import Model are explained and illustrated with data from case studies in Venezuela and Kenya.