## 3 Methodology
### Ranking Strategies
#### 3.3.2 Fuzzy AHP  
AHP is a broadly applied method for determining the weights of criteria in a structured manner based on pairwise comparison [47]. To handle subjective judgements in comparison, fuzzy sets are combined with AHP. Thus, fuzzy AHP assigns membership degrees to exact numbers in order to describe the extent to which these numbers belong to a linguistic expression. The relative weight of an SSC is assessed by processing the triangular \begin{table}
\begin{tabular}{c c} \hline \hline
**Linguistic Term** & **Membership Function** \\ \hline Very Low (VL) & (0, 0, 1, 2) \\ Low (L) & (1, 2, 2, 3) \\ Fairly Low (FL) & (2, 3, 4, 5) \\ Moderate (M) & (4, 5, 5, 6) \\ Fairly High (FH) & (5, 6, 7, 8) \\ High (H) & (7, 8, 8, 9) \\ Very High (VH) & (8, 9, 10, 10) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Linguistic scale for ranking the improvement strategies. Figure 4: Membership functions of the linguistic variables. Figure 3: Survey questionnaire for weighting SSCs. fuzzy preference numbers elicited from the questionnaire survey in Figure 3 through the fuzzy AHP method, in a manner similar to that presented by [PERSON] and [PERSON] [48]. The triangular fuzzy preference of the \(i\)th SSC over the \(j\)th SSC is shown as \((L_{ij},\ M_{ij},\ U_{ij})\), where the parameters \(L\), \(M\), and \(U\) denote the smallest possible value, the most promising value, and the largest possible value that describe the relative importance of the \(i\)th SSC over the \(j\)th SSC, respectively. The steps of the proposed fuzzy AHP can be described as follows. Step 1: Calculate the fuzzy sum. The fuzzy sum value with respect to the \(i\)th SSC, which is a TFN, is defined as  
\[FS_{i}=\left(L_{FS_{i}},M_{FS_{i}},U_{FS_{i}}\right)=\left(\sum_{j=1}^{4}L_{ij},\sum_{j=1}^{4}M_{ij},\sum_{j=1}^{4}U_{ij}\right) \tag{1}\]  
Step 2: Calculate the fuzzy synthetic extent (\(S\)). The \(S\) value with respect to the \(i\)th SSC, which is a TFN, is defined as  
\[S_{i}=\left(L_{S_{i}},M_{S_{i}},U_{S_{i}}\right)=\left(\frac{L_{FS_{i}}}{\sum_ {j=1}^{4}U_{FS_{j}}},\frac{M_{FS_{i}}}{\sum_{j=1}^{4}M_{FS_{j}}},\frac{U_{FS_{ i}}}{\sum_{j=1}^{4}L_{FS_{j}}}\right) \tag{2}\]  
where \(S_{1}\), \(S_{2}\), \(S_{3}\), and \(S_{4}\) are the fuzzy synthetic extent of IC, IF, WA, and IR, which equal (0.1891, 0.3092, 0.4936), (0.1697, 0.2743, 0.4317), (0.1314, 0.2120, 0.3489), and (0.1291, 0.2046, 0.3408), respectively. Step 3: Calculate the degree of possibility (\(V\)). The \(V\) value with respect to the \(i\)th SSC is defined as  
\[V_{i}=\min_{j\
eq i}\left(v\left(S_{i}>S_{j}\right)\right) \tag{3}\]  
where \(v(S_{i}>S_{j})\) is calculated as follows  
\[v(S_{i}>S_{j})=\left\{ \begin{array}{ll}1,&if\ M_{S_{i}}\geq M_{S_{j}}\\ 0,&if\ L_{S_{j}}\geq U_{S_{i}}\\ \frac{L_{S_{i}}-U_{S_{i}}}{\left(M_{S_{i}}-U_{S_{i}}\right)-\left(M_{S_{j}}- L_{S_{j}}\right)},&otherwise\end{array} \right. \tag{4}\]  
Step 4: Calculate the relative weight of SSCs (\(W\)). The \(W\) value with respect to the \(i\)th SSC is determined by normalizing \(V_{i}\) as follows  
\[W_{i}=V_{i}/\sum_{j=1}^{4}V_{j}\quad\forall i=1\ to\ 4 \tag{5}\]  
where \(W_{1}\), \(W_{2}\), \(W_{3}\), and \(W_{4}\) are the relative weights of IC, IF, WA, and IR, which equal 0.324, 0.283, 0.201, and 0.192, respectively  
Step 5: Assess the consistency ratio (CR). The consistency of the respondents' pairwise comparisons in the questionnaire survey (see Figure 3) is assessed to determine whether any re-examination of the survey pairwise judgments is required. This is performed by computing the CR of the matrix \(\widetilde{A}\), which includes the fuzzy preference numbers of the relative importance of each SSC versus another. Based on the approach used by [PERSON] et al. [3], matrix \(\widetilde{A}\) is defuzzified into two crisp matrices. The first matrix, \(A_{1}\), includes the most promising value of the fuzzy numbers of matrix \(\widetilde{A}\), and the second matrix, \(A_{2}\), includes the geometric mean of the lower and upper bounds of the fuzzy numbers.