Consistent belief functions represent collections of coherent or non-contradictory pieces of evidence. As most operators used to update or elicit evidence do not preserve consistency, the use of consistent transformations cs[.] in a reasoning process to guarantee coherence can be desirable. Such transformations are turn linked to the problem of approximating an arbitrary belief function with a consistent one. We study here the consistent approximation problem in the case in which distances are measured using classical Lp norms. We show that, for each choice of the element we want them to focus on, the partial approximations determined by the L1 and L2 norms coincide, and can be interpreted as classical focused consistent transformations. Global L1 and L2 solutions do not in general coincide, however, nor are they associated with the highest plausibility element.
Keywords. Consistent belief function, simplicial complex, approximation, Lp norms.
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Department of Computing
Oxford Brookes University
OX33 1HX OXFORD