Measuring Uncertainty in Class Assignment for Natural Resource Maps under Fuzzy Logic

There are two kinds of uncertainty associated with assigning a geographic entity to a class in the classification process. The first is related to the fuzzy belonging of the entity to the prescribed set of classes and the second is associated with the deviation of the entity from the prototype of the class to which the entity is assigned. This paper argues that these two kinds of uncertainty can be estimated if a similarity model is employed in spatial data representation. Under this similarity model, the uncertainty of fuzzy belonging can be approximated by an entropy measure of membership distribution or by a measure of membership residual. The uncertainty associated with the deviation from the prototype definitions can be estimated using a membership exaggeration measure. A case study using a soil map shows that high entropy values occur in areas where soils seem to be transitional and that areas which are mis-classified have higher entropy values. The membership exaggeration is high for areas where soil experts have low confidence in identifi-ing soil types and predicting their spatial distribution. These measures helped in identifying that the high elevation areas were mapped with high accuracy and that error reduction efforts are needed in mapping the soil resource in the low elevation areas.