Estimating Fuzzy Membership Function Based on RMSE for the Positional Accuracy of Historical Maps

When combining data from a time period spanning 300 years, these data will originate from various sources, and will be created by a diversity of techniques. Different spatial data types have different sources of error and provide information at varying accuracy levels. Some changes, detected by comparison of two misregistered maps, are caused by a difference in positional accuracy and have little to do with actual changes. This paper concentrates on this positional error, expressed as a root-mean-square error (RMSE). Due to this positional error, the actual position of the boundaries of for instance forest polygons, is uncertain. The possibility of actually finding forest increases from zero to one within a band around the forest boundaries. The aim of this paper was to analyze the relation between this possibility and the distance to the forest boundary. Using a simulation approach, distorted maps with different RMSE values were created. The superposition of these distorted maps was used to fit several functions. This was done in order to determine an appropriate form of the forest membership function. A sigmoid or a polynomial function yielded the best results, especially if the distortion was low. followed by an inverse difference weighted function. The linear function resulted in the poorest fit. The parameters of a given function type varied when the forest pattern or the RMSE value varied.