Modeling and querying approximate direction relations

Existing models of direction relations are mainly designed to handle crisp regions. To accommodate uncertain spatial data, it is necessary to investigate the formalization, uncertain semantics, and composition operators for uncertain direction relations. In this study, direction relations about uncertain regions, i.e., approximate direction relations, are modeled as the combinations of four crisp direction relations. The approximate relations can be interpreted from two aspects: the lower part (only including crisp relations about uncertain region) and the uncertain part (the uncertain directions about uncertain regions). The uncertain semantics of uncertain directions are formalized, such as possibly north, possibly south, possibly southeast, etc. Both crisp and uncertain parts are used to simplify and handle the composition and the query of uncertain direction relations. Approximate direction relations are helpful to model directions concerned with both crisp and uncertain regions; they therefore can play important roles in handling uncertain data (in our case, querying uncertain data).