![]() |
![]() |
![]() ![]() ![]() |
Relations between Possibility Measures and Necessity Measures
The properties of possibility measures
and necessity measures suggest that
they are associated.
The value of a necessity measure N can be obtained from
a possibility measure ,
through the complement
of any part A of
:
|
(43) |
The more an event A is assigned a great necessity value,
the less the complement event
is possible, therefore the more we are certain of the occurrence of A.
The occurrence of event A is certain
(N(A) = 1) if and only if the occurrence of its
complement
is impossible (
,
therefore
).
If possibility measure
is defined from possibility distribution
,
necessity measure N, dual of
,
can be defined as:
|
(44) |
The duality of
and N still appears in the following relations, for any part A
of
:
|
(45) | |||
|
(46) |
These relations impose that, if ,
then
,
which means that any event about which we are certain, at least a little,
is completely possible.
In the same way, if ,
then N(A) = 0. This is interpreted by saying that we have
no certainty about an event which is only relatively possible.