*2.2. Application of the AHP Method*

#### 2.2.1. Prioritization

The AHP requires a preference or priority to each alternative decision, considering the extent to which each criterion contributes. A mathematical procedure called synthesis summarizes the information and provides a hierarchy of criteria for alternatives in terms of global preference [23].

#### 2.2.2. Paired Comparisons and Paired Comparison Matrix

The fundamental bases of the AHP are the paired comparisons [23]. The AHP uses the Saaty table to assess relative preferences when comparing two elements. The matrix of paired comparisons contains alternative comparisons or criteria. Therefore, if one considers a matrix *A* of dimensions *n* × *n*, with the relative judgments about the criteria, and *aij* is the element (*i*, *j*) of *A*, for *i* = 1, 2, . . . , *n*, and *j* = 1, 2, . . . , *n*.

Then, one can state that *A* is a matrix of paired comparisons of *n* criteria if *aij* is the measure of the preference of the criterion in the row *i* when compared to the criterion in the column *j*. When *i* = *j*, the value of *aij* will be equal to 1 since the criterion is being compared with itself.

$$A = \begin{bmatrix} 1 & a\_{12} & \cdots & a\_{1n} \\ a\_{21} & 1 & \cdots & a\_{2n} \\ \vdots & \vdots & \vdots & \vdots \\ a\_{n1} & a\_{n2} & \cdots & 1 \end{bmatrix} \tag{1}$$

In addition, it is fulfilled that: *aij* = *aji* = 1 that is:

$$A = \begin{bmatrix} 1 & a\_{12} & \cdots & a\_{1n} \\ 1/a\_{12} & 1 & \cdots & a\_{2n} \\ \vdots & \vdots & \vdots & \vdots \\ 1/a\_{1n} & 1/a\_{2n} & \cdots & 1 \end{bmatrix} \tag{2}$$

The complexity of these decisions becomes more significant the greater the scope of the problem is. This can be addressed by using methodologies that allow structuring the problem, modeling it, efficiently weighing the criteria relevant to that decision, and then defining the alternative that best suits them.
