Geospatial Modeling Using Dempster–Shafer Theory

Uncertainty in spatial geometrical issues is represented using Dempster-Shafer (D-S) theory. Interval approaches are used for D-S uncertainty of spatial locations and the associated arithmetic operations on such intervals described. Categories of uncertainty for points and lines are defined using interval formulations. Based on these, approaches for calculation of geometric areas, line length and line slopes are given. Compatibility of imprecise point locations is discussed and potential aggregations for similar points considered. Finally, topological spatial relationships are described for objects with uncertain boundaries. This will provide a formal framework for the use of a D-S interval approach for uncertainty in spatial geometric issues.

I. Introduction

Representation of uncertainty in geospatial data can be viewed in context of the most important use of such spatial data in geographic information systems (GISs). GIS are employed extensively throughout governmental and industrial organizations for planning and decision making [16]. Typically underlying a GIS is a spatial database in which many of the imprecision representation issues arise [27], [30]. Computation of geometric quantities from uncertain spatial data can be applied to many of the applications for which a GIS is appropriate.