Fuzzy Similarity and Fuzzy Inclusion Measures in Polyline Matching: A Case Study of Potential Streams Identification for Archaeological Modelling in GIS

Abstract When combining spatial data from various sources, it is often important to determine similarity or identity of spatial objects. Besides the differences in geometry, representations of spatial objects are inevitably more or less uncertain. Fuzzy set theory can be used to address both modelling of the spatial objects uncertainty and determining the identity, similarity, and inclusion of two sets as fuzzy identity, fuzzy similarity, and fuzzy inclusion. In this paper, we propose to use fuzzy measures to determine the similarity or identity of two uncertain spatial object representations in geographic information systems. Labelling the spatial objects by the degree of their similarity or inclusion measure makes the process of their identification more efficient. It reduces the need for a manual control. This leads to a more simple process of spatial datasets update from external data sources. We use this approach to get an accurate and correct representation of historical streams, which is derived from contemporary digital elevation model, i.e. we identify the segments that are similar to the streams depicted on historical maps.