Research Project: Conditioning of belief functions
We are also studying the problem of conditioning a belief function b with respect to an event A by geometrically projecting such belief function onto the simplex associated with A in the belief space. Two different such simplices can be defined, as each belief function can be represented as the vector of its basic probability values or the vector of its belief values. We show here that defining geometric conditional BFs by minimizing Lp distances between b and the conditioning simplex in the mass space produces simple, elegant results with straightforward interpretations in terms of degrees of belief. This opens the way to a systematic exploration of geometric conditioning in the belief space too, and the relationships of these results with classical approaches to the problem.
Relevant papers:
  • Fabio Cuzzolin
    Geometric conditioning of belief functions
    Proceedings of the First International Workshop on the Theory of Belief Functions
    Brest, Belgium, April 2010
    Poster .odp (open office)
  •   Fabio Cuzzolin
    Geometric conditioning in belief calculus,
    submitted to IEEE Transactions on Fuzzy Systems, October 2013
    (I.F. 6.306)
Lab Member(s): Fabio Cuzzolin