def _make_key(self, key):
gamble, event = BelFunc._make_key(self, key)
gamble_event = self.pspace.make_event(gamble)
if not gamble_event.is_singleton():
raise ValueError('not a singleton')
if not event.is_true():
raise ValueError('must be unconditional')
return gamble, event
def _make_key(self, key):
gamble, event = BelFunc._make_key(self, key)
gamble_event = self.pspace.make_event(gamble)
if not gamble_event.is_singleton():
raise ValueError('not a singleton')
if not event.is_true():
raise ValueError('must be unconditional')
return gamble, event
def get_lower(self, gamble, event=True, algorithm='linvac'):
r"""Calculate the lower expectation of a gamble conditional on
an event, by the following formula:
.. math::
\underline{E}(f|A)=
\frac{
(1-\epsilon)\sum_{\omega\in A}p(\omega)f(\omega)
+ \epsilon\min_{\omega\in A}f(\omega)
}{
(1-\epsilon)\sum_{\omega\in A}p(\omega)
+ \epsilon
}
where :math:`\epsilon=1-\sum_{\omega}\underline{P}(\omega)` and
:math:`p(\omega)=\underline{P}(\omega)/(1-\epsilon)`. Here,
:math:`\underline{P}(\omega)` is simply::
self[{omega: 1}, True][0]
This method will *not* raise an exception, even if the
assessments are incoherent (obviously, in such case,
:math:`\underline{E}` will be incoherent as well). It will
raise an exception if not all lower probabilities on
singletons are defined (if needed, extend it first).
"""
# default algorithm
if algorithm is None:
algorithm = 'linvac'
# other algorithms?
if algorithm != 'linvac':
return BelFunc.get_lower(self, gamble, event, algorithm)
gamble = self.make_gamble(gamble)
event = self.pspace.make_event(event)
epsilon = 1 - sum(self[{omega: 1}, True][0] for omega in self.pspace)
return ((sum(self[{
omega: 1
}, True][0] * gamble[omega]
for omega in event) + epsilon * min(gamble[omega]
for omega in event)) /
(sum(self[{
omega: 1
}, True][0] for omega in event) + epsilon))
def get_lower(self, gamble, event=True, algorithm='linvac'):
r"""Calculate the lower expectation of a gamble conditional on
an event, by the following formula:
.. math::
\underline{E}(f|A)=
\frac{
(1-\epsilon)\sum_{\omega\in A}p(\omega)f(\omega)
+ \epsilon\min_{\omega\in A}f(\omega)
}{
(1-\epsilon)\sum_{\omega\in A}p(\omega)
+ \epsilon
}
where :math:`\epsilon=1-\sum_{\omega}\underline{P}(\omega)` and
:math:`p(\omega)=\underline{P}(\omega)/(1-\epsilon)`. Here,
:math:`\underline{P}(\omega)` is simply::
self[{omega: 1}, True][0]
This method will *not* raise an exception, even if the
assessments are incoherent (obviously, in such case,
:math:`\underline{E}` will be incoherent as well). It will
raise an exception if not all lower probabilities on
singletons are defined (if needed, extend it first).
"""
# default algorithm
if algorithm is None:
algorithm = 'linvac'
# other algorithms?
if algorithm != 'linvac':
return BelFunc.get_lower(self, gamble, event, algorithm)
gamble = self.make_gamble(gamble)
event = self.pspace.make_event(event)
epsilon = 1 - sum(self[{omega: 1}, True][0] for omega in self.pspace)
return (
(sum(self[{omega: 1}, True][0] * gamble[omega] for omega in event)
+ epsilon * min(gamble[omega] for omega in event))
/
(sum(self[{omega: 1}, True][0] for omega in event)
+ epsilon)
)
