F-Histograms and Fuzzy Directional Spatial Relations

The quantitative (or fuzzy qualitative) assessment of directional spatial relationships (such as “to the right of”, “above”, “south of”...) between two areal objects often relies on the computation of a histogram of angles, which provides a representation of the relative position of the objects. In a recent paper, the notion of the histogram of forces was introduced. Here, we show that this powerful tool of representation lends itself, with great flexibility, to the definition of directional spatial relations. Indeed, any family of directional relations that relied on the construction of angle histograms can be advantageously redefined using force histograms. Moreover, the notion of the histogram of forces enables radically new families to be conceived: definitions which correspond to a coherent and rational perception of the world, but non-realizable by