Let U a set of elementary events, .
One calls possibility measure denoted
a function
defined on the set of all parts
of
, taking values in
such as:
A possibility degree means that the event
is completely
possible, inversely
means that
is impossible.
A possibility distribution assigns to each element of
a
possibility
. The distribution is normalized:
.
Guaranteed possibility
A guaranteed possibility measure is a function defined on the
set of all parts of
,
taking values in
, such as:
Relation between possibility degree and guaranteed possibility degree:
Thus, if
, all elementary events
are
guaranteed possible at level
.
Guaranteed possibility distributions are denoted .
Interpretation of possibility degree and guaranteed possibility degree