## 2 Multiple-Criteria Decision Aid (MCDA)  
Supporting decision making using formal techniques, methods, and languages is as old as civilisation; important examples can be found in the case of direct democracy in Athens, 508-322 BC, where public policy decisions were made during meetings of the citizens' council, in which those present debated and voted [3]. However, it was established as a discipline with the rise of operational research (OR) and decision analysis (DA) after World War II [4; 5]. At their origins, OR and DA have been essentially oriented in modelling decision problems as optimisation problems; however, when looking for efficient algorithms to solve them, it soon appeared necessary to explicitly consider the existence of multiple values, opinions, and scenarios [6; 7; 8; 9; 10]. The result has been the creation of a specific area within OR, named Multiple-Criteria Decision Analysis (the term \"Analysis\" here has often being substituted with \"Making\" or \"Aiding\"). We are not going to make a survey of all the literature around this topic; interested readers can have a look at [PERSON] and [PERSON] [11], [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14]. There exist different ways and approaches as far as categorising the different methods developed in this area is concerned. We will follow the proposal recently suggested in [PERSON] and [PERSON] [15] and in [PERSON] and [PERSON] [16], based upon the use of the strictly necessary primitives for constructing a model for a decision problem:* The set of alternatives, A;
* The problem statement, \(\Pi\);
* The preferences. The set of alternatives can be either an enumeration (a list) or a combinatorial structure or part of a continuous vector space. There exist four fundamental problem statements for any decision problem:  
* Ranking: partition A in ordered equivalence classes with no reference to external norms. * Rating: partition A in ordered equivalence classes with reference to external norms;
* clustering: partition A in unordered equivalence classes with no reference to external norms. * Assignment: partition A in unordered equivalence classes with reference to external norms. Handling preferences (going from raw preference statements to formal models) can be viewed through three different activities:  
* Preference learning;
* Preference modelling;
* Preference aggregation. As far as learning preferences, there are essentially two approaches: direct ones (see [PERSON] et al. (2012), [PERSON] et al. (2014), [PERSON] and [PERSON] (2017)), proposing protocols addressed directly to the user/decision-maker, and indirect ones (see [PERSON] et al. (2014), [PERSON] and [PERSON] (2018)), where preferences are inferred from empirical observations and examples. In this second case, we can also distinguish two approaches: one in which we impose a model, and we infer the parameters of the model through examples and one in which we try to learn both the nature of the model and the parameters specifying it. Modelling preferences implies using specific preference structures (such as weak orders, interval orders, structures implying thresholds), suitable modelling languages (standard first order logic, fuzzy measures, and valued binary relations, four-valued logics, etc.) and possibly the construction of more quantitative models where the difference of preferences are measurable (value and utility functions). For more recent surveys, the reader is referred to [PERSON] et al. (2019) and [PERSON] and [PERSON] (2020). Preference aggregation is distinguishable in two essential archetypes (2012; 2013):  
* The \"Condorcet\" archetype, where differences in preferences are not taken into account and preferences are aggregated using majority procedures and coalition formation games;
* The \"Borda\" archetype, where differences in preferences are considered, and this requires one to solve the commensurability problem among the different dimensions to aggregate.