.. DEX Method documentation master file

.. _DexMethod:

Method DEX
==========

DEX (Decision EXpert) is a multi-criteria decision modeling
(`MCDM <https://en.wikipedia.org/wiki/Multi-criteria_decision_analysis>`__)
(Greco, et al., 2016) method, aimed at supporting decision makers in complex
:ref:`decision-making tasks and processes <MethDecisionMaking>`. DEX was
conceived in the 1980s as a fusion of multi-criteria decision analysis and artificial
intelligence. From MCDM, it adopted the ideas of modeling decision situations
using multiple criteria, structuring and decomposing complex decision problems in
smaller and less complex sub-problems, and solving problems through evaluation
and analysis of decision alternatives. From artificial intelligence, it primarily adopted
concepts used in `expert systems <https://en.wikipedia.org/wiki/Expert_system>`__:
using qualitative (symbolic) variables, representing decision knowledge in terms of “if–then” rules,
handling imprecision and uncertainty, emphasizing the transparency of decision models,
and facilitating the explanation of results. DEX also includes some elements of
`rule-based machine learning <https://en.wikipedia.org/wiki/Rule-based_machine_learning>`__,
e.g., for constructing :ref:`compact decision rules <DexComplex>` from decision tables.

According to the classification of Ishizaka and Nemery (2013),
DEX belongs to the category of *full aggregation* or “American school” methods.
This approach is characterized by using an explicit multi-criteria model, which is developed first,
more or less independently from individual decision alternatives. These alternatives are
then evaluated by the model, first by scoring them for each criterion and then aggregating these evaluations
into a global score.

The key characteristics of DEX are (Bohanec, 2022):

- DEX is *hierarchical*: a DEX model consists of :ref:`hierarchically structured attributes <DexTree>`
  (in MCDM, also called criteria or performance variables). In this aspect, DEX is similar to other
  hierarchical MCDM methods, such as AHP (Saaty, 2012) and MCHP (Corrente, et al., 2012).

- DEX is *qualitative*: attributes in a DEX model are :ref:`symbolic <DexQualitative>`,
  taking values that are words rather than numbers, such as “bad”, “medium”, “excellent”, “low”, or “high”.
  This relates DEX to verbal decision analysis (Moshkovich and Mechitov, 2013),
  linguistic MCDM (García-Lapresta and del Pozo, 2019), and MCDM methods that use words,
  such as MACBETH (Bana e Costa, et al., 2003).

- DEX is *rule-based*: hierarchical aggregation of values is defined with :ref:`decision rules <DexAggregation>`,
  acquired and represented in the form of decision tables. In this way, DEX is most similar to
  Dominance-Based Rough Set Analysis (DRSA, Greco et al., 2002), which also uses decision tables and
  constructs decision rules from them.

With extensions, implemented in `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__,
DEX also became *probabilistic* and *fuzzy*: it allows using
`probability distributions <https://en.wikipedia.org/wiki/Probability_distribution>`__ and
`fuzzy sets <https://en.wikipedia.org/wiki/Fuzzy_set>`__ in place of attribute values and evaluates alternatives
using probabilistic and fuzzy aggregation.

Another `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__ extension allows
using :ref:`numeric attributes <DexContinuous>` as terminal nodes of a decision model,
bringing DEX a little bit closer to *quantitative* MCDM methods.

The DEX method is defined from two aspects: static and dynamic. The static aspect
gives a description of concepts and components that constitute a :doc:`DEX model <DEX_Model>`.
The :doc:`dynamic aspect <DEX_Dynamic>` addresses algorithms and tools necessary to
develop and modify the model and to use it for decision support.

Brief history
-------------

The development of DEX can be traced back to Efstathiou and Rajkovič (1979), who
proposed using fuzzy sets and fuzzy inference rules to represent and evaluate
decision alternatives. The authors also suggested representing decision knowledge in
terms of a decision table together with fuzzy operators. The following development of
DEX was mainly continued at the `Jožef Stefan Institute, Ljubljana, Slovenia <https://kt.ijs.si/>`__,
where elements of expert systems and machine learning were gradually
added to the basic concepts, leaving the fuzzy aspects somewhat aside. The method,
presented by Rajkovič, et al. (1988) and Bohanec and Rajkovič (1988) under
the name DECMAK, already had all the main ingredients: tree-structured qualitative
attributes, decision tables and decision rules, and algorithms supporting knowledge
acquisition and explanation, including a graphical representation of decision tables
and a machine-learning algorithm for constructing aggregate rules.

The name DEX (Decision EXpert) was first used in Bohanec and Rajkovič (1990),
to denote both the method and the supporting software that was developed at that time.
In 2000, the DEX software was replaced by software called
`DEXi <https://dex.ijs.si/documentation/DEXi/DEXi.html>`__; at that point, the
development team decided to keep the name DEX only for the method and use other
names for its implementations.

DEX Software
------------

DEX has always been closely tied with the supporting software. Due to the combinatorial
nature of DEX’s decision tables, the method is unsuitable for manual construction of
models and becomes practical only when supported by appropriate user interfaces and algorithms
for knowledge elicitation, representation, verification, and explanation.
In many aspects, the definition of the DEX method followed the actual software implementations.

Four generations of DEX-related software have been developed so far:

1. DECMAK (Bohanec and Rajkovič, 1988) was released in 1981 for mini and personal computers under operating systems RT-11, VAX/VMS, and MS-DOS.

2. `DEX <https://kt.ijs.si/MarkoBohanec/dex.html>`__ was released in 1987 as an integrated interactive computer program for VAX/VMS and MS-DOS.

3. `DEXi <https://dex.ijs.si/documentation/DEXi/DEXi.html>`__ was released in 2000 for Microsoft Windows. Originally, DEXi was designed as educational software (the letter “i” in DEXi, pronounced “ee”, actually comes from the Slovenian “izobraževanje”, education). Since 2000, additional features were gradually added to DEXi, which eventually became a complete, stable, and *de-facto* standard implementation of DEX. Until 2021, some additional DEXi software was implemented, forming the `DEXi Classic <https://dex.ijs.si/documentation/DEX_Software/DEXiClassic.html>`__ collection of tools.

4. `DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__ is a collection of software tools, released in 2023, aimed at gradually replacing DEXi Classic. DEXi Suite brings a new software architecture and some methodological extensions, while remaining backward compatible with DEXi.

Examples
--------

In this documentation, method DEX and supporting software
(both `DEXi <https://dex.ijs.si/documentation/DEXi/DEXi.html>`__ and
`DEXi Suite <https://dex.ijs.si/documentation/DEX_Software/DEXiSuite.html>`__)
are illustrated and explained using two examples:

- :ref:`Car Evaluation <ExampleCar>`
- :ref:`Employee Selection <ExampleEmployee>`

Download example models from: `<https://dex.ijs.si/dexisuite/download/DEXiExamples.zip>`__.

References
----------

Bohanec, M., Rajkovič, V. (1988): `Knowledge acquisition and explanation for multi-attribute
decision making <http://kt.ijs.si/MarkoBohanec/pub/Avignon88.pdf>`__.
In: *Proceedings of the 8th International Workshop Expert Systems and Their
Applications AVIGNON 88*, vol. 1, pp. 59–78, Avignon.

Bohanec, M., Rajkovič, V. (1990): DEX: an expert system shell for decision support. *Sistemica* 1(1),
145–157.

Bohanec, M. (2022): DEX (Decision EXpert): A qualitative hierarchical multi-criteria method. Multiple Criteria Decision Making (ed. Kulkarni, A.J.), Studies in Systems, Decision and Control 407, Singapore: Springer, doi: 10.1007/978-981-16-7414-3_3, 39-78.

Bana e Costa, C., De Corte, J.-M., Vansnick, J.-C. (2003): MACBETH (Overview of MACBETH
multicriteria decision analysis approach). *International Journal of Information Technology & Decision Making* 11, 359–387.

Corrente, S., Greco, S., Słowiński, R. (2012): Multiple criteria hierarchy process in robust ordinal
regression. *Decision Support Systems* 53(3), 660–674.

Efstathiou, J., Rajkovič, V. (1979): Multiattribute decisionmaking using a fuzzy heuristic approach.
*IEEE Transactions on Systems, Man, and Cybernetics* SMC-9, 326–333.

García-Lapresta, J.L., del Pozo, R.G. (2019): An ordinal multi-criteria decision-making procedure
under imprecise linguistic assessments. *European Journal of Operational Research* 279(1), 159–167.

Greco, S., Matarazzo, B., Słowiński, R. (2002): Rough sets methodology for sorting problems in
presence of multiple attributes and criteria. *European Journal of Operational Research* 138(2), 247–259.

Greco, S., Ehrgott, M., Figueira, J. (2016): *Multi Criteria Decision Analysis: State of the art Surveys*.
Springer, New York.

Ishizaka, A., Nemery, P. (2013): *Multi-criteria Decision Analysis: Methods and Software*. Wiley,
Chichester.

Moshkovich, H.M., Mechitov, A.I. (2013): Verbal decision analysis: foundations and trends. *Advances in
Decision Sciences* 2013, 697072.

Rajkovič, V., Bohanec, M., Batagelj, V.  (1988): Knowledge engineering techniques for utility
identification. *Acta Physiologica* 683(1–3), 271–286.

Saaty, T.L., Vargas, L.G.: *Models, Methods, Concepts and Applications of the Analytic
Hierarchy Process*. Springer, US, New York.

.. toctree::
   :hidden:

   DEX_DecisionMaking
   DEX_Model
   DEX_Dynamic
   DEX_Car
   DEX_Employee

.. only:: html

..   Indices and tables
..   ==================

..   * :ref:`genindex`
..   * :ref:`modindex`
..   * :ref:`search`