Fuzzy set approach to assessing similarity of categorical maps

Abstract

For the evaluation of results from remote sensing and high-resolution spatial models it is often necessary to assess the similarity of sets of maps. This paper describes a method to compare raster maps of categorical data. The method applies fuzzy set theory and involves both fuzziness of location and fuzziness of category. The fuzzy comparison yields a map, which specifies for each cell the degree of similarity on a scale of 0 to 1. Besides this spatial assessment of similarity also an overall value for similarity is derived. This statistic corrects the cell-average similarity value for the expected similarity. It can be considered the fuzzy equivalent of the Kappa statistic and is therefore called K_Fuzzy. A hypothetical case demonstrates how the comparison method distinguishes minor changes and fluctuations within patterns from major changes. Finally, a practical case illustrates how the method can be useful in a validation process.