## 3 Methodology
### MCDM Methods
Later, the VIKOR method will be applied for selecting the most suitable typology, based on a classification list of alternatives that shall provide us with one or more compromise solutions. \"Viekriterijumsko kompromisno rangirane\" (VIKOR) is a Serbian term meaning multicriteria optimization and compromise solution [23]. It was developed to solve a decision problem with a limited number of alternatives (possible solutions) with conflicting criteria and with different units of measurement [22]. Therefore, the VIKOR method is suitable for solving decision-making problems with conflicted and noncommensurable criteria (which means, with different units) or when there are quantitative and qualitative criteria. The VIKOR method has been applied on many occasions for selection of alternatives in infrastructures, as reflected in the literature [36; 37; 38; 39; 40]. For normalization, converting the criteria into dimensional variables, a linear function is used in the VIKOR method that does not depend on a function of value of criteria as in the case of TOPSIS method [21]. The compromise solution shall be the one closest to the optimal solution [22]. To obtain a compromise solution (or solutions), we shall follow the next steps:  
1. \"Best\" and \"worst\" value of each alternative is calculated for each criterion, as follows: \[ \begin{array}{l}f_{i}^{*}=max_{i}f_{ji};\ \ \ f_{i}^{-}=min_{i}f_{ji}.\ \ \text{If criterion i represents a benefit}\.\\ f_{i}^{*}=min_{i}f_{ji};\ \ f_{i}^{-}=max_{i}f_{ji}.\ \ \text{If criterion i represents a cost}. \end{array} \] where \(i\) is the number of criteria and \(j\) is the number of alternatives, so \(f_{ji}\) is an evaluation of the alternative A\({}_{j}\) with respect to criterion \(C_{i}\). 2. Values \(S_{j}\), \(R_{j}\), and \(Q_{j}\) are calculated for each alternative as follows: \[ \begin{array}{l}S_{j}=\sum\limits_{i=1}^{n}w_{i}\big{(}f_{i}^{*}-f_{ji} \big{)}\big{/}\big{(}f_{i}^{*}-f_{i}^{-}\big{)}\\ R_{j}=\max_{i}\big{|}w_{i}\big{(}f_{i}^{*}-f_{ji}\big{)}\big{/}\big{(}f_{i}^{*} -f_{i}^{-}\big{)}\big{|}\end{array} \] (2) where \(w_{i}\) is the weight of criterion \(i\) relative to the rest, that is, it reflects the relative importance of each criterion. At this point, it is necessary to indicate that in the VIKOR method the normalized values are given by the expression: \(\langle f_{i}^{*}-f_{ji}\rangle\)/\(\langle f_{i}^{*}-f_{i}^{-}\rangle\). Thus, normalized values do not depend on the unity of the different criteria [21]. \[ \begin{array}{l}Q_{j}=\vartheta\big{[}\big{(}S_{j}-S^{*}\big{)}\big{/}\big{(} S^{-}-S^{*}\big{)}\big{]}+(1-\vartheta)\big{[}\big{(}R_{j}-R^{*}\big{)} \big{/}\big{(}R^{-}-R^{*}\big{)}\big{]}\end{array}  \tag{4}\]  
where \(S^{*}=\min_{i}S_{j}\), \(S^{-}=\max_{i}S_{j}\), \(R^{*}=\min_{i}R_{j}\), \(R^{-}=\max_{i}R_{j}\), and \(\vartheta\) represent weight of the strategy of \"the majority of criteria\" (or \"the maximum group utility\"). Consensus is for a value \(\vartheta=0.5\)[21]. Other authors have demonstrated how difficult it is to achieve consensus in situations of uncertainty and with large amounts of information and possible alternatives [41]. 3. Different alternatives are sorted according to values \(S\), \(R\) and \(Q\) and the results are three ranking lists. 4. Best-ranked alternative A(1) is identified as a compromise solution, i.e., the alternative with the lowest value of \(Q\). This is true, if the following two conditions are met: Requirement 1: Acceptable advantage. \(Q(\text{A(2)})-Q(\text{A(1)})\geq\text{DQ}\), where besides A(2) is the second alternative according to the value classification of \(Q\), and DQ = 1/(J-1), where J represents the number of alternatives. Requirement 2: Acceptable stability in the decision-making process. Alternative A(1) will also be the best ranked according to the list of values of S and/or R. This alternative solution is stable within a decision-making process.