Universitat Polit猫cnica de Catalunya. Secci贸 de Matem脿tiques i Inform脿tica
Abstract
This paper verifies a result of [9] concerning graphoidal
structure of Shenoy's notion of independence for Dempster-Shafer theory of
belief functions.
Shenoy proved that his notion of independence has graphoidal properties
for positive normal valuations.
The requirement of strict positive normal valuations as
prerequisite for application of graphoidal properties excludes a wide class of
DS belief functions. It excludes especially so-called probabilistic belief
functions. It is demonstrated that the requirement of positiveness of
valuation may be weakened in that it may be required that commonality
function is non-zero for singleton sets instead, and the graphoidal
properties for independence of belief function variables are then preserved.
This means especially that probabilistic belief
functions with all singleton sets as focal points possess graphoidal
properties for independenc
