## 3 Materials and Methods
### The Process of Decision-Making Using the AHP Methodology  
Today, there are various tools, in the form of new technologies and various methods that greatly assist in the decision-making process, which managers themselves decide on. The AHP method is one of the most commonly used methods in the analytical approach to decision-making for the purpose of solving multi-criteria decision-making problems. The theoretical basis of the analytical hierarchy process, including the main steps, is given below. The AHP method, developed by [PERSON] [52] in the 1980s, is the most common MCDM method used in decision-making problems in the transport sector. This method is one of the most widely used methods that solves a problem by breaking it down into components. The main characteristic of the AHP method is the use of pairwise comparisons, which are used both to compare options with respect to different criteria and to assess the weight of criteria [53]. When applying the aforementioned method, matrices are the basic tool. AHP is based on the following four principles (four main steps, as per Figure 2): decomposition, prioritization, synthesis, and sensitivity analysis [54]. The main advantage of the method is its ease of use. Figure 3 shows the four main AHP principles using the example from this research. In the first step, the goal is set--obtaining the optimal LOS for LCC airlines, then the criteria/sub-criteria, and alternatives; in the second step, mutual pairwise comparisons are made using [PERSON]'s scale of relative importance; in the third step, the weights of the criteria/sub-criteria and alternatives are calculated; and in the fourth step, sensitivity analysis is conducted. When applying the AHP method, the multi-criteria decision-making problem is structured hierarchically. At the top of the hierarchy is the goal, at level one are the criteria, and at level two are the alternatives [55]. Figure 4 shows the basic structure of the analytical hierarchical process, which includes three levels, on the example from this research. Figure 3: Steps for implementing the AHP method [54]. Once the levels in the hierarchical structure have been established, each parameter (criterion or alternative) needs to be compared with each parameter within the same level. Such a comparison is generally made according to [PERSON]'s scale of relative importance, as shown in Table 3. The decision-maker must evaluate the criteria according to his or her own free judgment. The scale of relative importance established by [PERSON] consists of nine levels where the scale of importance is shown by numbers. Odd numbers refer to basic values, while even numbers represent intermediate values. For example, an intensity of importance of one represents an equal contribution of two different alternatives to the final goal. In contrast, nine represents the highest degree of dominance where one activity is absolutely favored over the other. Matrices are the main mathematical tool used in the AHP method. The element \(a_{ij}\) of the matrix A denotes the relative importance of criterion \(i\) in relation to criterion \(j\). Let \(n\) be the number of criteria (or alternatives) whose weights (priorities) \(w_{i}\) should be determined based on the estimation of the values of their ratios, which are denoted by [56]:  
\[a_{ij}=\frac{w_{i}}{w_{j}}. \tag{1}\]  
From the ratio of relative importance \(a_{ij}\), matrix A of relative importance is formed:  
\[\text{A}=\left[ \begin{array}{cccc}\frac{w_{1}}{w_{1}}&\frac{w_{1}}{w_{1}} \dots&\frac{w_{1}}{w_{n}}\\ \frac{w_{2}}{w_{1}}&\frac{w_{2}}{w_{2}}\dots&\frac{w_{2}}{w_{n}}\\ \dots&\dots&\dots&\dots\\ \frac{w_{n}}{w_{1}}&\frac{w_{2}}{w_{2}}\dots&\frac{w_{n}}{w_{n}}\\ \end{array} \right]=\left[ \begin{array}{cccc}a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{2n}\\ \dots&\dots&\dots&\dots\\ a_{n1}&a_{n2}&\dots&a_{nn}\\ \end{array} \right]. \tag{2}\]  
Figure 4: Example of AHP hierarchy of decision problem [55].