Possibilistic uncertainty modeling with hyperellipsoids

The quantification of sparse, imprecise knowledge using possibility theory traditionally forces a compromise between computational efficiency and geometric accuracy. Standard interval arithmetic over axis-aligned hyperrectangles ignores parameter dependencies and yields overly conservative bounds, while sampling-based techniques capture these dependencies but remain computationally intensive and fail to deliver guarantees. By leveraging geometric properties of ellipsoids, we address these challenges by providing a comprehensive operational calculus for possibilistic uncertainty representation using hyperellipsoids. This framework provides methodologies to construct ellipsoidal possibility distributions from data, fuse multiple knowledge sources, propagate distributions analytically through affine functions, and extract both marginal and joint distributions. Furthermore, we demonstrate the practical efficacy of these ellipsoidal possibility distributions by applying them to a filtering application for a mobile robot localization problem.