Blurb::
Discrete, epistemic uncertain variable - integers within a set
Description::
Discrete set variables may be used to specify categorical choices which are
epistemic. For example, if we have three possible forms for a physics
model (model 1, 2, or 3) and there is epistemic uncertainty about
which one is correct, a discrete uncertain set
may be used to represent this type of uncertainty.

This variable is defined by a set of integers, in which the discrete value may
take any value within the integer set (for example, the set may be
defined as 1, 2, and 4)

Other epistemic types include:

- :dakkw:`variables-continuous_interval_uncertain`
- :dakkw:`variables-discrete_interval_uncertain`
- discrete_uncertain_set :dakkw:`variables-discrete_uncertain_set-string`
- discrete_uncertain_set :dakkw:`variables-discrete_uncertain_set-real`

Topics::
discrete_variables, epistemic_uncertain_variables
Examples::

Let `di1` be 2 or 13 and `di2` be 4, 5 or 26.
The following specification is for an interval analysis:

.. code-block::

    discrete_uncertain_set
     integer
     num_set_values 2     3
     set_values     2 13  4 5 26
     descriptors    'di1' 'di2'


Theory::
The ``discrete_uncertain_set-integer``
variable is NOT a discrete random variable.
It can be contrasted to a the histogram-defined random variables:
:dakkw:`variables-histogram_bin_uncertain` and :dakkw:`variables-histogram_point_uncertain`.
It is used in epistemic uncertainty analysis, where one is trying to model
uncertainty due to lack of knowledge.

The discrete uncertain set integer variable is used in both interval analysis
and in Dempster-Shafer theory of evidence.


*interval analysis*

- the values are integers, equally weighted
- the true value of the random variable is one of the integers in this set
- output is the minimum and maximum function value conditionalon the specified inputs


*Dempster-Shafer theory of evidence*

- the values are integers, but they can be assigned different weights
- outputs are called "belief" and "plausibility."Belief represents the smallest possible probability that is consistent with the evidence,
  while plausibility represents the largest possible probability that is consistent with the evidence.
  Evidence is the values together with their weights.

Faq::

See_Also::
