Lp consistent approximations of belief functions

Fabio Cuzzolin
Submitted to the IEEE Transactions on Fuzzy Systems, 2008

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 in a reasoning process to guarantee coherence can be desirable. These are in 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 the approximations determined by both L1 and L2 norms are unique and both coincide, for each choice of the element we want them to focus on, with classical focused consistent transformations. The L1 norm determines for each element of the frame an entire polytope of solutions whose barycenter lies on the L1=L2 approximation. Global L1 approximations are always associated with the maximal plausibility element.
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BibTeX entry

  AUTHOR = "Fabio Cuzzolin", 
  TITLE = "Lp consistent approximations of belief functions",
  JOURNAL = "submitted to the IEEE Transactions on Fuzzy Systems", 
  YEAR = "March 2008"