Further developments of a fuzzy set map comparison approach

Fuzzy set map comparison offers a novel approach to map comparison (Hagen 2003). The approach is specifically aimed at categorical raster maps and applies fuzzy set techniques, accounting for fuzziness of location and fuzziness of category, to create a similarity map as well as an overall similarity statistic: the Fuzzy Kappa. To date, the calculation of the Fuzzy Kappa (or K-fuzzy) has not been formally derived and the documented procedure was only valid for cases without fuzziness of category. Furthermore, it required an infinitely large, edgeless map. This paper presents the full derivation of the Fuzzy Kappa; the method is now valid for comparisons considering fuzziness of both location and category and does not require further assumptions. This theoretical completion opens opportunities for use of the technique that surpass the original intentions. In particular, the categorical similarity matrix can be applied to highlight or disregard differences pertaining to selected categories or groups of categories and to distinguish between differences due to omission and commission.