## 2 Materials and Methods
### B. Elicitation of Preferences:  
The scale of preferences for quality variations (Joint Scale of Quality Variations JSQV) is constructed in this stage. The elicitation of preferences follows the order of steps shown in Figure 4[53]. This structure is the same as proposed in [54]; however, substages 2 and 3 (numbered on the left side of the figure) were put together in just one substage.  
Instead of basing the decisionmaker's preferences on the first reference situation and then establishing another scale of preferences using the second reference situation, we propose that the two substages be transformed into one. The questions made considering the first reference situation are the same as those considering the second. Thus, both situations are presented and must be regarded as answering the question not to cause dependence of criteria. The alteration reflects on an optimization of the process: instead of making \(2n\) questions, only \(n\) are made. The questions, about Quality Variations (QV) belonging to just one criterion, are made as follows: supposing a criterion A with X\({}_{A}\) = A\({}_{1}\), A\({}_{2}\), A\({}_{3}\), the decisionmaker is asked about their preferences between the QV, a\({}_{1}\)-a\({}_{2}\), a\({}_{1}\)-a\({}_{3}\) and a\({}_{2}\)-a\({}_{3}\). Thus, there is a maximum of three questions to a criterion with three values (\(n_{q}=3\)).  
The question for two criteria of preferences is formulated differently due to difficulties in understanding and a delay in the decisionmaker's answers when the QV was exposed to different criteria. The question is made by dividing the QV into two items. For example, having the set of criteria \(k\) = A, B, C, where \(n_{q}=3\) and \(X_{q}=\) q\({}_{1}\), q\({}_{2}\), q\({}_{3}\) considering the pair of criteria A, B and the QV a\({}_{1}\) and b\({}_{1}\), the decisionmaker should analyze which imaginary alternative would be preferable: A\({}_{1}\), B\({}_{2}\), C\({}_{1}\) or A\({}_{2}\), B\({}_{1}\), C\({}_{1}\). However, this answer must be the same as the alternatives: A\({}_{1}\), B\({}_{2}\), C\({}_{3}\) and A\({}_{2}\), B\({}_{1}\), C\({}_{3}\). If the decisionmaker answers that  
Figure 4: Elicitation of preferences process.  
the first option is better, then \(\text{b}_{1}\) is preferable to \(\text{a}_{1}\), because it is preferable to have \(\text{B}_{2}\) on the alternative instead of \(\text{A}_{2}\).  
**C. Comparison of Alternatives:**  
In order to reduce the number of cases of incomparability, we applied the same structure as proposed in [54] but modified the comparison of pairs of the alternative substage according to the one proposed in [55]. Figure 5 shows the structure of the comparison of the alternative process.  
According to [31] and [15], the Decision Support Systems (DSS) are computer-based systems that aid the decisionmaker in informing and exploring the implications of their preferences, and this leads to a decision based on the problem comprehension. Figure 6 presents a flowchart with the steps to apply the ZAPROS-III-i/VDA.  
A disadvantage of the method arises when there is exponential growth in the number of alternatives of the problem as well as the amount of information required to obtain the  
Figure 5: Alternative comparison process.  
Figure 6: Procedure for applying the ZAPROS-III-i method. Source: adapted from [8].  
preferences. To control this complexity, the number of criteria and values of the treated criteria are limited.  
The method proposes that the two reference situations generated by the AI Algorithm and the one corresponding to the health professionals' decisions are analyzed simultaneously to optimize the process and avoid criteria dependence [53].  
According to [PERSON] and [PERSON] [52,53], these modifications increased the comparability of the method so that several alternatives defined as incomparable, when applying the ZAPROS method in its pure form, can now be compared directly or indirectly. However, these changes in the method process do not alter its computational complexity [56].