Fuzzy set approach to assessing similarity of categorical maps

Abstract

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 cellaverage 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.

Using remotely sensed data to construct and assess forest attribute maps and related spatial products

“…Polygon edges do not disappear and should not be ignored if a polygon assessment unit is used. Because location error cannot be completely eliminated, analyses that account for location errors may be used (Hagen, 2003). Alternatively, reporting accuracy separately for the subset of edge locations and the subset of interior locations provides information for gauging the potential impact of location error on the results.…”

Six decades of changes in the riparian corridor of a Mediterranean river: a synthetic analysis based on historical data sources

“…A further benefit of using fuzzy sets theory is that it provides additional tools for analysing map similarity (Muller et al, 1998). The fuzzy kappa gives more relevance to the spatiotemporal distribution of the landscape mosaic than other statistics because it is not based on a cell-by-cell comparison and it can capture qualitative similarities between two maps (Power et al, 2001) because the categories of neighbouring cells are taken into account (Hagen, 2003;Hagen-Zanker et al, 2005).…”

“…The fuzziness of categories was implemented by assigning to each cell a membership vector instead of a single category. Each element in the vector declares, with a value between 0 (crisply distinct) and 1 (completely identical), the degree of membership for one category (Hagen, 2002;Hagen, 2003;van Vliet et al, 2010). All this information is gathered in the category similarity matrix, where similarity between categories decreases when distance from the diagonal increases.…”

“…The consistency of the resultant matrix was tested using the analytic hierarchy process developed by Saaty (1980). The fuzziness of location considers that the fuzzy representation of a cell depends on the cell itself and, to a lesser extent, on the cells within a certain distance in its neighbourhood (Hagen, 2003). The extent to which the neighbouring cells influence the fuzzy calculation is represented by a distance decay function.…”

“…Additionally, the Map Comparison Kit version 3.2.2 (Research Institute for Knowledge Systems, The Netherlands, 2011) was used to confirm the temporal/spatial changes detected (Visser and de Nijs, 2006). Each pair of categorical raster maps was compared chronologically for each site on the basis of fuzzy set theory, where both fuzziness in category definition and fuzziness in location were considered (Hagen, 2003;Hagen-Zanker et al, 2005). The fuzziness of categories was implemented by assigning to each cell a membership vector instead of a single category.…”