Abstract
Fuzzy set map comparison offers a novel approach to map comparison.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.