## 3 MADM Methodologies
They are most suited for the evaluation of a specific alternative than for a complete ranking. Their disadvantages are many, i.e., the idealistic assumption of linear attribute aggregation, the decision matrix normalization, the acceptance of only positive criteria values, and ranking instability in cases where the input attribute values vary greatly [22; 23]. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Visekriterijumsko Kompromisno Rangiranje (VIKOR), Combinative Distance-based Assessment (CODAS), Multi-Attributive Border Approximation Area Comparison (MABAC), Displaced Ideal Method (D'IDEAL), and Organization, Rangement Et. Syn-these De Donnes Relationnelles (ORESTE) belong to the distance-based MADM family. The distance-based class is regarded to have a moderate complexity, cost, and latency but high stability even at large fluctuations of the input data. This group of MADM methods calculates a pair of ideal geometric points and considers that the optimal alternative is the one that has the smallest distance from the best point and the greatest distance from the worst point; their \begin{table}
\begin{tabular}{c c c} \hline \hline
**Normalization** & **Benefit** & **Expense** \\ \hline \hline Linear: Sum & \(n_{ij}=\frac{a_{ij}}{\sum\limits_{i}a_{ij}}\) & \(n_{ij}=\frac{1/a_{ij}}{\sum\limits_{i}1/a_{ij}}\) \\ Linear: Max & \(n_{ij}=\frac{a_{ij}}{a_{jm}}\) & \(n_{ij}=\frac{a_{jm}}{a_{ij}}\) \\ Linear: Max\(-\)Min & \(n_{ij}=\frac{a_{ij}}{a_{jm}-a_{jm}}\) & \(n_{ij}=\frac{a_{jm}-a_{ij}}{a_{jm}-a_{jm}}\) \\ Vector & \(n_{ij}=\frac{a_{ij}}{\sqrt{\sum\
olimits_{i}1/a_{ij}^{2}}}\) & \(n_{ij}=\frac{1}{1/a_{ij}}\) \\ Data Envelopment Analysis (DEA) & \(n_{ij}=1-\frac{a_{jm}-a_{ij}}{\sum\
olimits_{i}^{2}(a_{jm}-a_{ij})}\) & \(n_{ij}=1-\frac{a_{ij}-a_{jm}}{a_{jm}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Taxonomy of main normalization techniques (\(P\) is the number of alternatives). disadvantages are few, i.e., the decision matrix normalization and Euclidean distance are inefficient for high correlations between the criteria [22; 23]. The Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) belong to the pairwise comparisons MADM family and are regarded as having significant latency, exponential complexity, computational cost, and flexibility. They demand the formulation of a three-level hierarchic structure, and the solution requires good knowledge of eigenvalues and eigenvectors. These methods mix both qualitative and quantitative data types without normalizations. However, they assume largely independent criteria, they are very biased from the subjective opinions of the decision-makers, and modifications are necessary to overcome inconsistency problems [22; 23]. The Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) and Elimination and Choice Expressing Reality (ELECTRE) belong to the outranking MADM family and are regarded as having high flexibility, rationality, and no need for any data transformations or normalizations, but they express a quadratic time complexity and are unfit for more than five criteria. They employ a preference function, e.g., Gaussian, and a number of veto thresholds to perform pairwise comparisons between a set of alternatives and derive preference flows. They can produce partial and complete rankings or select the best action based on outranking relationships [22; 23]. Finally, the Multi Attribution Utility Theory (MAUT) and Multi Attribution Value Theory (MAVT) belong to the utility/valuate MADM family. They are also biased by decision-maker judgment, but they can deal with uncertainties in the data. On the other hand, they demand an immense amount of input data, and the derived results exhibit strong subjectivity [22; 23]. In general, the sensitivity analysis investigates the impact of weighting, the number of alternatives, and the measurement scale on the ranking stability and hence the method's robustness [24; 25].