Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning

Spatial information may be endowed with a bipolarity component. Typical examples concern possible vs forbidden places for an object in space, or “opposite” spatial relations such as “possibly to the right of an object and certainly not to its left”. However, bipolarity has not been much exploited in the spatial domain yet. Moreover, imprecision has often to be taken into account as well, for instance to model vague statements such as “to the right of an object”. In this paper we propose to handle both features in the framework of bipolar fuzzy sets. We introduce some geometrical measures and mathematical morphology operations on bipolar fuzzy sets and illustrate their potential for spatial reasoning on a simple scenario in brain imaging.