Method DEX

DEX (Decision EXpert) is a multi-criteria decision modeling (MCDM) (Greco, et al., 2016) method, aimed at supporting decision makers in complex decision-making tasks and processes. 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: 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, e.g., for constructing compact decision rules 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:

  • DEX is hierarchical: a DEX model consists of hierarchically structured attributes (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 symbolic, 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 decision rules, 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, DEX also became probabilistic and fuzzy: it allows using probability distributions and fuzzy sets in place of attribute values and evaluates alternatives using probabilistic and fuzzy aggregation.

Another DEXi Suite extension allows using numeric attributes 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 DEX model. The dynamic aspect 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, 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; 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 was released in 1987 as an integrated interactive computer program for VAX/VMS and MS-DOS.

  3. DEXi 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 collection of tools.

  4. DEXi Suite 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.


In this documentation, method DEX and supporting software (both DEXi and DEXi Suite) are illustrated and explained using two examples:

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Bohanec, M., Rajkovič, V. (1988): Knowledge acquisition and explanation for multi-attribute decision making. 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.

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., Słowi´nski, 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.