Assigning membership degrees to points of fuzzy boundaries

There has been a growing interest in the field of geographic information systems (GIS) to model vague and uncertain regions for which information about a given property is available (e.g. soil structure). Vague and uncertain mean in general that some knowledge is available about the position and the circumference of such a region, but that the information is mostly imprecise or lacks certainty. Either this lack of precise data is inherent to the property (e.g. the degree of soil pollution), or it is due to physical limitations in making accurate measurements (e.g. temperature). There has been some research in modeling such regions using fuzzy regions. Fuzzy regions are modeled by means of broad boundaries. A broad boundary is defined as the area enclosed between two non-intersecting crisp edges including these edges, one completely located within the other. Inside and on the inner edge lay the points for which the definition of the property is completely met; outside and on the outer edge lay the points for which the definition of the property is not at all met. Points of the broad boundary meet the definition of the property up to a certain extent. Up to now, mainly the applicability of the traditional set operators on fuzzy regions (intersection, inclusion and union) has been addressed in the literature. Furthermore, almost no contributions treat the degree to which the points in the fuzzy region come up to the given definition of a property. We present two methods to solve the latter problem, both from a theoretical as well as from a practical point of view.