Utility Function
================

*Utility functions* are the components of :doc:`multi-attribute
models <DEXiGlosMAMod>` that define the aggregation aspect of
:doc:`option evaluation <DEXiGlosEval>`. For each aggregate
:doc:`attribute <DEXiGlosAttr>` Y, whose descendants in the :doc:`tree of
attributes <DEXiGlosTree>` are X\ :sub:`1`, X\ :sub:`2`,...,
X\ :sub:`n`, the corresponding utility function f defines the mapping:

f: X\ :sub:`1` × X\ :sub:`2` × ... × X\ :sub:`n` —> Y

.. image:: images/FunctXnY.png
   :alt: Utility function Y=f(X1,X2,...Xn)

In :doc:`DEXi <DEXi>`, a utility function maps all the *combinations*
of the lower-level attribute values into the values of Y. The mapping is
represented in a table, where each row gives the value of f for one
combination of the lower-level attribute values. Rows are also called
*decision rules*, because each row can be interpreted as an *if-then*
rule of the form:

**if** X\ :sub:`1` = value\ :sub:`1` **and** X\ :sub:`2` =
value\ :sub:`2` **and** ... **and** X\ :sub:`n` = value\ :sub:`n`
**then** Y = value (or value :doc:`interval <DEXiGlosIntervals>`)

In the context of representation, such rules are also called *elementary
rules*. This name is used for contrast with :doc:`complex
rules <DEXiGlosComplex>`.

Example
-------

See :doc:`utility functions <DEXiCarFunct>` as defined in the :doc:`Car
Evaluation <DEXiCar>` model.

See also
--------

Editing functions with :doc:`Function Editor <DEXiIntEditFunct>` and
some recommendations on :doc:`function editing <DEXiIntFunctAppr>`.

Representing utility functions with :doc:`complex
rules <DEXiGlosComplex>` and :doc:`weights <DEXiGlosWei>`.

Avoiding :doc:`combinatorial explosion <DEXiGlosExplos>` and
calculating utility function size.

Calculating :doc:`utility function status <DEXiGlosFunctDef>` measures.

Saving functions on :doc:`files <DEXiIntFunctFile>`.

.. toctree::
  :hidden:

  DEXiGlosIntervals
  DEXiGlosComplex
  DEXiGlosWei
  DEXiGlosExplos
  DEXiGlosNonEnt
  DEXiGlosFunctDef