## 2 Preliminaries
### Group Decision-Making  
In this section we describe the basic concepts of group decision-making processes. In these processes, two or more experts express their preferences over a set of alternatives in order to rank them according to their suitability for solving a given problem. A classic way for experts to provide preferences to the system is through the use of preference relations. A group decision-making problem using preference relations can be defined as follows: Starting from a set of preferences [7], \(X=\{X_{1},X_{2},\ldots,X_{n}\}\), and a group of experts \(E=\{e_{1},e_{2},\ldots,e_{n}\}\), each expert, \(e_{i}\), provide their preferences over \(X\) using a preference relation, \(P_{e_{i}}\subset X\times X\), where \(\mu_{P_{e_{i}}}\left(x_{j},x_{k}\right)=p_{i}^{jk}\) is the preference degree of alternative \(x_{j}\) over \(x_{k}\) for \(e_{i}\)[8]. A group decision-making problem consists on sorting \(X\) by using the preference values \(P_{k},\forall k\in[1,n]\), that experts have provided to the system. Within group decision-making processes, two processes are of great importance: consensus and selection. The consensus process allows the experts to reach a final solution that is relatively agreed upon by all, i.e., that has an adequate level of agreement among all experts. The use of consensus measures turns the group decision-making process into a dynamic and iterative process, which may be composed of several rounds where experts express themselves, discuss the different alternatives and try to bring positions closer together. The selection process, on the other hand, uses all individual preferences to obtain a final ranking of alternatives. The alternative that comes first is the most appropriate solution to the problem. Generally, to solve the formulated problem, most of the methods in the literature follow these steps [2]:  
* Providing preferences: First, experts discuss the available alternatives. Next, the experts are asked to provide their preferences [9]. * Aggregating the information: All expert preferences are aggregated into a single piece of collective preference information representing the overall expert opinion [10]. There are a multitude of techniques such as, for example, additive weighted aggregation (AWA) [11]. This operator allows us to derive the ranking of the given alternatives in order to find the most desirable one. Another example is the ordered weighted average (OWA) family of operators [12]. * Calculating consensus: Calculating consensus measures can help us to know whether the experts have reached an agreement or, on the contrary, whether they need to discuss the issue further to reach a reasonable level of consensus. It is important, for the sake of improving the reliability of decision-making results, to allow experts to conduct a thorough discussion before reaching a final decision. Therefore, if the consensus is lower than desired, the experts may be asked to conduct a further round of discussion to bring them closer together. Generally, a maximum number of rounds is also established in case the experts do not reach consensus within a reasonable period of time [13]. * Calculating alternatives ranking: Using the collective preference matrix as a basis, the alternatives are ranked according to the level of preference provided by the experts [10]. This step returns a ranking of alternatives ordered according to the experts' preferences. In Figure 1, we can see a graphical representation of the defined process. Group decision-making processes have a strong presence in the current scientific literature. For example, in [14], a consensus process for large-scale group decision-making is demonstrated, relying on limited trust and social networks. In [15], a new model of expressed and private opinions is developed in a scenario where individual private views are updated by reasoning based on the neighbors' private opinions derived from their actions, while the expressed opinions are influenced by social pressure.