## 2 Materials and Methods
For example, one of the simplest and most widely used MCDM methods is the simple additive weighting (SAW) method [22]. The fundamental idea behind the SAW (simple additive weighting) method involves calculating the total value of the performance ratings, taking into account the weights assigned to each attribute for every alternative. The SAWmethod necessitates a step where the decision matrix (\(X=\left[x_{ij}\right]_{m\times n}\)) is normalized to a scale that allows for a comprehensive comparison with the ratings of all available alternatives. The formula to perform the normalization for the benefit attribute is as follows:  
\[r_{ij}=\frac{x_{ij}}{Max\left(x_{ij}\right)}, \tag{1}\]  
The formula to perform the normalization for the cost attribute is as follows:  
\[r_{ij}=\frac{Min\left(x_{ij}\right)}{x_{ij}}, \tag{2}\]  
Here \(r_{ij}\) is the normalized performance rating of the alternatives \(A_{i}\) on attribute \(C_{j}\); where \(i=1,2,\ldots,m\) and \(j=1,2,\ldots,n\). The formula to perform the preference value for each alternative is as follows:  
\[V_{i}=\sum_{j=1}^{n}w_{j}r_{ij}, \tag{3}\]  
Another example is the technique for order of preference by similarity to ideal solution (TOPSIS) [23]. The TOPSIS method is a well-known method of multi-criteria decision making, which is based on calculating the distances between each alternative and the ideal alternative, as well as between each alternative and the anti-ideal alternative. TOPSIS operates on the principle of positive and negative ideal solutions, viewed geometrically through Euclidean distance. Positive ideal solutions represent the cumulative best achievable values for each attribute, while negative ideal solutions comprise the worst values attained for each attribute. By comparing the relative distances, alternative priority rankings can be established. The method is widely applied for practical decision-making due to its simplicity and its ability to gauge the relative performance of decision alternatives in a straightforward mathematical format. The formula to perform the normalization is as follows:  
\[r_{ij}=\frac{x_{ij}}{\sqrt{\sum_{k=1}^{m}x_{kj}^{2}}}, \tag{4}\]  
One more example is VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) [24]. The VIKOR method (Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje, meaning \"Multi-criteria optimization and compromise solution\") is also a well-known method of multi-criteria decision making. This method takes into account compromise decisions. It can be useful when there is a set of conflicting criteria. The VIKOR method aims to maximize collective benefits while minimizing individual regret. This approach revolves around devising a solution that aligns closely with the ideal solution within the parameters of alternatives and criteria. VIKOR establishes the compromise ranking list, identifies the compromise solution, and delineates weight stability intervals to ensure preference stability for the compromise solution, determined by the assigned weights. Additionally, some modifications of these methods can be considered. Fuzzy TOPSIS [25] and fuzzy VIKOR [26] methods are an extension of the TOPSIS method and work with fuzzy data. The method can be used when the criteria are assessed with some degree of uncertainty, i.e., for example, instead of exact numerical values, values such as \"low\", \"medium\", or \"high\" are indicated. The TOPSIS interval method [27] is also an extension of the TOPSIS method, which works with interval data, i.e., when the criteria assessments are expressed not by exact numerical values, but by the ranges of possible values. The TOPSISinterval and fuzzy method [28] is a more complex extension of the TOPSIS method, which works with both interval and fuzzy data. Several MCDM methods have been developed or refined by various authors in recent decades.