Evaluating the degree of fuzziness of thematic maps with a generalized entropy function: A methodological outlook

Abstract

In the remote sensing literature, a number of fuzziness indices have been proposed for quantifying the uncertainty in categorical labelling of thematic map locations. However, despite its vast potential applicability, none seems to be generally preferred. A more complete summary of fuzziness at the pixel level is possible if, instead of one single index, one uses a parametric index family whose members have varying sensitivities to the presence of rare and abundant thematic map classes. While traditional indices supply point descriptions of fuzziness, according to a parametric fuzziness family H f there is a continuum of possible fuzziness measures that differ in their sensitivity to the presence of dominant and rare thematic map classes within the fuzzy partition as a function of the parameter f . Therefore, changing f allows for vector description of the uncertainty in categorical labelling of thematic map locations. The purpose of this letter is thus to introduce a parametric generalization of Shannon's entropy to quantify the fuzziness of thematic map cells. Comparing thematic map cells by fuzziness profiles may be considered a very useful feature of parametric fuzziness indices, for example, to evaluate how the presence of dominant, subdominant or rare classes within the fuzzy partition influence uncertainty as data are transformed within a geographical information system.