  Consistent belief functions represent collections of coherent or
non-contradictory pieces of evidence, but most of all they are the counterparts
of consistent knowledge bases in belief calculus. The use of consistent
transformations cs[.] in a reasoning process to guarantee coherence can
therefore be desirable, and generalizes similar techniques in classical logic.
Transformations can be obtained by minimizing an appropriate distance measure
between the original belief function and the collection of consistent ones. We
focus here on the case in which distances are measured using classical Lp
norms, in both the "mass space" and the "belief space" representation of belief
functions. While mass consistent approximations reassign the mass not focussed
on a chosen element of the frame either to the whole frame or to all supersets
of the element on an equal basis, approximations in the belief space do
distinguish these focal elements according to the "focussed consistent
transformation" principle. The different approximations are interpreted and
compared, with the help of examples.
