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of expertise' and is referred to as its
frame of discernment (FoD)
[24]. A hypo-
thesis
θ
i
represents the lowest level of discernible information in this FoD;
it is referred to as a
singleton
. Elements in 2
Θ
, the power set of
Θ
,form
all hypotheses of interest. A hypothesis that is not a singleton is referred
to as a
composite hypothesis
, e.g., (
θ
1
,θ
2
). From now on, we use the term
'proposition' to denote both singleton and composite hypotheses. Cardinality
of
Θ
is denoted by
.
A
mass
function or a
basic probability assignment (BPA)
is a function
m
:2
Θ
|
Θ
|
→
[0
,
1] that satisfies
)=0and
A⊆Θ
m
(
∅
m
(
A
)=1
.
(2)
Thus
m
(
A
) can be interpreted as a measure that one is willing to commit
ex-
plicitly
to proposition
A
and not to any of its subsets. Committing support for
a proposition does not necessarily imply that the remaining support is com-
mitted to its negation, thus relaxing the additivity axiom in the probability
formalism. Propositions for which there is no information are not assigned an
a priori mass. Rather, the mass of a composite proposition is allowed to move
into its constituent singleton propositions only with the reception of further
evidence.
The set of propositions each of which receives a non-zero mass is referred
to as the focal elements; we denote it via
is
referred to as the corresponding
body of evidence (BoE)
.The
vacuous BPA
that enables one to characterize complete ignorance is
m
(
A
)=
1
,
if
A
=
Θ
;
0
,
otherwise
.
F
Θ
. The triple
{
Θ,
F
Θ
,m
(
)
}
(3)
The belief of a proposition takes into account the support one has for all
its proper subsets and is defined as
Bel
(
A
)=
B⊆A
m
(
B
)
.
(4)
It is a measure of the unambiguous support one has for
A
.
The notion of
plausibility
is used as a measure of the extent one finds the
proposition
A
plausible and is defined as
Bel
(
A
)=
B∩A
=
∅
Pl
(
A
)=1
−
m
(
B
)
.
(5)
This indicates how much one's belief could be 'swayed' with further evidence.
A probability distribution
Pr
(
) that satisfies
Bel
(
A
)
≤
Pr
(
A
)
≤
Pl
(
A
),
∀
). An example
of such a probability distribution is the
pignistic probability distribution Bp
defined for each singleton
θ
i
∈
A
⊆
Θ
,issaidtobe
compatible
with the underlying BPA
m
(
Θ
[27] as
