## 3 Materials and Methods
### The AHP-TOPSIS-2N Method  
The decision-making process generally involves a choice between several alternatives. The feasible alternatives of meeting the objective, and selected for evaluation, are compared according to criteria and under the influence of attributes [23]. The MCDM methods are very useful to support the decision-making process in these cases, because they consider value judgments and not only technical issues, to evaluate alternatives to solve real problems, presenting a highly multidisciplinary [24]. The MCDM methods have been employed to support the decision-making process in several recent complex problems, as presented in [25; 26; 27; 28; 29; 30]. The AHP-TOPSIS-2N hybrid method, initially proposed by [11], consists of two MCDM techniques that are usually adopted in complex scenarios, characterized by multiple and conflicting objectives: the AHP and TOPSIS methods. To understand the method, it is necessary a prior understanding of the two techniques that compose it. The AHP method, developed by [31], is a quantitative MCDM technique for problems, being one of the most used worldwide, due to its ease and because it is intuitive. The method is applied to obtain the weights of the criteria, through pairwise comparisons based on the Saaty fundamental scale (Table 3). One of the advantages of the AHP method is the possibility to identify the inconsistencies of decision-makers (DM). A Consistency Ratio (CR) less than 0.10 is considered acceptable, while a CR greater than 0.10 generates the need for the decision-taker to make assessments or judgments again [32]. The TOPSIS method, presented by [33], orders the alternatives according to the proximity of the Positive Ideal Solution (PIS). The best alternative is the one that is closer to the PIS and the farthest from the Negative Ideal Solution (NIS). TOPSIS is a method that, after being applied in solving problems of the multicriteria type, results in an ordering of the existing alternatives. This ordering is based on the idea that the best alternative should be the one that presents minimum distance to the ideal solution \"PIS\" and maximum distance to the solution anti-ideal or \"NIS\". The method aims to generate a decreasing ordering of the coefficients of the calculated distances. This coefficient is known in the literature as relative proximity. Several decision problems can be solved with TOPSIS, being these of the only type decider or decision in group [34]. TOPSIS can be approached individually, based on precise input data previously determined by the DM, as well as with other methods in the literature. In situations where the lack of information is present in the problems, TOPSIS should be integrated with other approaches to its application [34]. For the application of the AHP-TOPSIS-2N method, [PERSON] et al. [11] defined nine steps, described below: \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Degree of Importance** & **Definition** & **Explanation** \\ \hline
1 & Equal importance & The two activities contribute equally to the goal Experience and judgment slightly favor one activity over another Experience and judgment \\
3 & Moderate importance & Neighbor favor one activity over another Experience and judgment strongly favor one activity over another One activity is favored over another is very dominant as shown in practice \\
9 & Extremely important & The evidence is in favor of one activity over another, to the greatest extent possible They are used to express preferences that are between the values of the above scale \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Saaty fundamental scale. 1. Establishment of the Decision Matrix, expressing the score of each alternative in each criterion analyzed;
2. Preparation of the Weighting Matrix, using the Saaty fundamental scale (Table 3), by evaluating alongside each criterion;
3. By applying the AHP method, the weights of each criterion are obtained. The importance of calculating CR should be less than 0.1 to ensure the consistency of the analysis;
4.