Fuzzy set theory and thematic maps: accuracy assessment and area estimation

Traditionally, the classes in thematic maps have been treated as crisp sets, using classical set theory. In this formulation, map classes are assumed to be mutually exclusive and exhaustive. This approach limits the ability of thematic maps to represent the continuum of variation found in most landscapes. Substitution of fuzzy sets allows more flexibility for treatment of map classes in the areas of accuracy assessment and area estimation. Accuracy assessment methods based on fuzzy sets allow consideration of the magnitude of errors and assessment of the frequency of ambiguity in map classes. An example of an accuracy assessment from a vegetation map of the Plumas National Forest illustrates the implementation of these methods. Area estimation based on fuzzy sets and using accuracy assessment data allows estimation of the area of classes as a function of levels of class membership. The fuzzy area estimation methods are an extension of previous methods presented by Card (1982). One interesting result is that the sum of the areas of the classes in a map need not be unity. This approach allows a wider range of queries within a GIS.