Fuzzy description of topological relations I: A unified fuzzy 9-intersection model

First, the impacts of uncertainty of position and attribute on topological relations and the disadvantages of qualitative methods in processing the uncertainty of topological relations are concluded. Second, based on the above point, the fuzzy membership functions for dividing topology space of spatial object and for describing uncertainty of topological relations are proposed. Finally, the fuzzy interior, exterior and boundary are defined according to those fuzzy membership functions, and then a fuzzy 9-intersection model that can describe the uncertainty is constructed. Since fuzzy 9-intersection model is based on fuzzy set, not two-value logic, the fuzzy 9-intersection model can describe the impacts of position and attribute of spatial data on topological relations, and the uncertainty of topological relations between fuzzy objects, relations between crisp objects and fuzzy objects, and relations between crisp objects in a united model.