## 2 Materials and Methods
### Information Technologies Used in the Proposed Model
#### 2.2.4 Fundamentals of the Verbal Decision Analysis  
The Verbal Decision Analysis (VDA) assumes that most decision-making problems can be expressed in natural language and consist of the decision-making process based on the representation related to the problem [50]. Notably, this methodology addresses  
Figure 2: Bayesian Network.  
unstructured issues, characterized by the absence of logical and well-defined procedures, to be applied in its solution.  
These problems are qualitative, and therefore, it is complex to organize, formalize, and numerically measure them. Furthermore, it is unusual to have all the data required to solve them. Thus, the analysis process is subjective, which requires collecting information from the decision-maker. In this research, the decision-makers were highly qualified health professionals with scientific experience and in clinical practice with HIV/AIDS individuals.  
According to [PERSON] [50], the methods that make up the structure of Verbal Decision Analysis are ZAPROS-III, ZAPROS-LM, PACOM, and ORCLASS and their characteristics and applications. These methods require a large quantity of data to be analyzed by humans as follows:  
1. Comparison of two assessments on a verbal scale by two criteria.
2. Assignment of multicriteria alternatives to decision classes.
3. Comparative verbal evaluation of alternatives according to different criteria.  
These methods constitute models for DSS (Decision Support Systems) that help a decisionmaker classify or rank the alternatives of multiple attributes.  
Figure 3 shows a simplified visualization of the various methods that make up the Verbal Decision Analysis methodology according to the problems.  
This work uses the ZAPROS method, which adapts to the characteristics of the problem and allows the structuring of a decision rule used to compare the alternatives that are not changed, even if the set of alternatives is modified. In addition, this applies to problems with many alternatives [51,52].  
In the Verbal Decision Analysis (VDA) structure, the ZAPROS-III-i method can be considered an evolution of the ZAPROS-III and ZAPROS-LM. Like the ZAPROS-LM and PACOM methods, the ZAPROS-III-i method aims to order a group of alternatives, from the most preferable to the least preferable [52].  
Although ZAPROS-III-i applies a similar procedure to obtain the preferences of its successor, it implements modifications that make it more effective and more accurate for inconsistencies. Furthermore, the number of alternatives is substantially less than in ZAPROS-III and ZAPROS-LM.  
The ZAPROS-III-i method is applied in three steps: Problem Formulation, Obtaining Preferences, and Comparing Alternatives [52].  
**A. Problem Formulation:**  
Given:  
1. \(K\) = 1, 2,..., N, representing a set of N criteria;  
Figure 3: Verbal Decision Analysis methodology. Source: adapted from [8].  
2. \(n_{q}\) represents the number of possible values on the scale of q-th criterion, (\(q\in K\)); for ill-structured problems, as in this case, usually \(n_{q}\leq 4\);
3. \(X_{q}=\{x_{iq}\}\) represents a set of values to the q-th criterion, and this set is the scale of this criterion; \(\mid X_{q}\mid=n_{q}\) (\(q\in K\)), where the values of the scale are ranked from best to worst, and this order does not depend on the values of other scales;
4. Y = \(X_{1}\)\(\times\)\(X_{2}\)\(\times\)\(\ldots\)\(\times\)\(X_{n}\) represents a set of vectors \(y_{i}\) (every possible alternative: hypothetical alternatives + real alternatives) in such a way that: \(y_{i}=\big{(}y_{1:}y_{2};\ldots;y_{iQ}\big{)}\), and \(y_{i}\in Y,y_{i}q\in X_{q}\) and \(Q=\mid Y\mid\), such that \(\mid Y\mid=\prod_{q=1}^{Q}n_{q}\).