Geometric conditional belief functions in the belief space

In this paper we study the problem of conditioning a belief function (b.f.) b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the space of all belief functions. Deflning geometric conditional b.f.s by minimizing Lp distances between b and the conditioning simplex in such \belief" space (rather than in the \mass" space) produces complex results with less natural interpretations in terms of degrees of belief. The question of weather classical approaches, such as Dempster’s conditioning, can be themselves reduced to some form of distance minimization remains open: the generation of families of combination rules generated by (geometrical) conditioning appears to be the natural prosecution of this line of research.

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