On possible measures for evaluating the degree of uncertainty of fuzzy thematic maps

In the remote sensing literature, a number of indices have been proposed for quantifying the uncertainty in categorical labelling of fuzzy thematic map locations. Most of these measures derive their conceptual basis from Shannon's entropy. Nonetheless, the Shannon entropy implies a probabilistic interpretation of class membership values, Such that their application is appropriate only for fuzzy thematic maps obtained by softening the output of a maximum likelihood classification. There is therefore a need to derive measures of classification uncertainty for raster thematic maps obtained from non-probabilistic soft classifiers. The purpose of this paper is to introduce a family of measures that are based on the notion of non-specificity for quantifying the pixel-level categorical uncertainty associated to non-probabilistic fuzzy classifications of remotely sensed images.