Factorization of Dempster-Shafer Belief Functions Based on Data

The Dempster-Shafer (DS) Theory (DST) or the Theory of Evidence is considered by many researchers as an appropriate tool to represent various 2 ANDRZEJ MATUSZEWSKI, MIECZYS lAW A. K lOPOTEK aspects of human dealing with uncertain knowledge, especially for representation ofpartial ignorance. However, one particular obstacle in applying DST is its relationship to frequencies [12]. Though, in general a belief function may be derived from frequencies under some particular database representation [5], there exist serious difficulties in finding factorizations of belief functions from data. In probability theory and in classical statistics the factorizations are usually related to notion of (conditional) independence and such possibility istested accordingly. However, in DST conditional belief distributions prove to be non-proper belief functions (that is ones connected with negative "frequencies").This makes statistical testing of potential conditional independencies practically impossible, as no coherent interpretation could be found so far for negative belief function values.