
EXISTING APPROACHES 35
The DS combination operation can be clearly defined mathematically using random
sets. Let S
k
, k = 1,... ,K be random sets—all taking values in 2
Θ
—encoding the
information in K independent DS models concerning θ . The combination operation
corresponds to considering a new random set
S =
K
\
k=1
S
k
,
with the case where S = ∅, called a conflict case, ruled out in a certain way. That is,
the belief for the combined DS models is
bel(A) =
P
S
(S ⊆ A,S 6= ∅)
P
S
(S 6= ∅)
, A ⊆ Θ.
While the above description of DS combination is quite simple, there is one sub-
tle point that we glossed over. That is, in many cases, the individual DS models may
not