.. _DexAttribute:

Attributes
----------

*Attributes* are variables that occur in :ref:`multi-criteria
models <MethMulticriteriaModel>`. They are organized into a hierarchical
structure called :ref:`tree of attributes <DexTree>`. According to
their position in the tree, the attributes are either:

-  *basic attributes*: terminal nodes ("leaves") of the tree, or
-  *aggregate attributes*: internal nodes in the tree.

Basic attributes represent inputs of the DEX model.
:ref:`Alternatives <DexAlternative>` are
described by the values of basic attributes.

Some basic attributes can be :ref:`"linked" <DexLinked>` in order to structure the model as
a full hierarchy rather than a tree.

Aggregate attributes represent :ref:`evaluations <DexEvaluation>` of alternatives.
They include one or more *roots* of the tree, which represent the overall evaluation of alternatives.

In `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__,
each attribute is defined by its:

-  *Name*: main identification of the attribute, which is typically a
   short string used in printouts, table headings, etc.
-  *Description*: usually a longer string providing further
   documentation about the attribute
-  :ref:`Scale <DexScale>`

Aggregate attributes also have associated an :ref:`aggregation or discretization function <DexFunction>`.

.. _DexLinked:

Linked Attributes
~~~~~~~~~~~~~~~~~

In principle, DEX models have a strict :ref:`tree <DexTree>`
structure: :ref:`attributes <DexAttribute>` are structured so that
there is exactly one path from each attribute to the root of
the tree. This means that each attribute, other than the root,
influences exactly one parent in the tree. Sometimes, this is not enough
and we wish to introduce attributes that influence more than one parent.
In other words, we wish to create attribute *hierarchies* (directed
acyclic graphs) rather than ordinary trees.

For this purpose, `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__
uses the concept of *linked attributes*. The idea is that whenever there are two
attributes in the tree that have equal names and equal
:ref:`scales <DexScale>`, and at least one of them is basic, they
are declared 'linked' and they - in a logical sense - represent a single attribute.
Attribute linking is done automatically by `DEXiWin <https://dex.ijs.si/documentation/DEXiWin/DEXiWin.html>`__,
but only when enabled explicitly in preference settings. By default,
linking is disabled and equally named attributes are considered different.

This concept allows that :ref:`DEX models <DexModel>` still
retain their basic tree structure. In tree displays, linked attributes
appear separately, so the tree structure is preserved. However, when defining
:ref:`alternatives <DexAlternative>`, linked attributes appear only once and require only a single data entry.

Terminological Remarks
~~~~~~~~~~~~~~~~~~~~~~

In `MCDM <https://en.wikipedia.org/wiki/Multi-criteria_decision_analysis>`__,
the definitions of terms *goal*, *objective*, *criterion*, *attribute*, *performance variable*, *indicator*
vary to some extent depending on the context, author and method. These terms all refer to "something" that needs to
be achieved by a proper decision and has to be in some way considered in the corresponding :ref:`decision model <MethDecisionModel>`.
Specifically, the terms *criterion* and *attribute* are sometimes considered equivalent, while some other authors
understand *criterion* only as a preferentially ordered attribute.

In `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__, the term *attribute*
is used as a general term for all variables occurring in a :ref:`DEX model <DexModel>`. This is because the
preference order of an attribute is known only *after* it has been associated with a :ref:`scale <DexScale>`;
this can occur or change much later than defining the attribute itself.
According to some strict definitions, the attribute can be understood as a *criterion* only when assigned an ordered scale.
Thus, in general terms, DEX models consist of attributes, and are thus often referred to as *multi-attribute models*.