A Design of Topological Predicates for Complex Crisp and Fuzzy Regions

For a long time topological predicates between spatial objects have been a main area of research on spatial data handling, reasoning , and query languages. But these predicates still suuer from two main restrictions: rst, they are only applicable to simpliied abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not suucient to cope with the complexity of geographic reality, their generalization is needed which especially has innuence on the nature and deenition of their topological relationships. This paper gives a formal deenition of complex crisp regions, which may consist of several components and which may have holes, and it especially shows how topolog-ical predicates can be deened on them. Second, topological predicates so far only operate on crisp but not on fuzzy spatial objects which occur frequently in geographical reality. Based on complex crisp regions, this paper gives a deenition of their fuzzy counterparts and shows how topological predicates can be deened on them.