## 3 Methodology
### Ranking Strategies
#### 3.3.3 Fuzzy TOPSIS  
Fuzzy TOPSIS, as another fuzzy MCDM technique, is used for determining the relative importance of each strategy to CLP improvement. TOPSIS is one of the most widely used MCDM methods that works satisfactorily in various application areas [49]. However, it is often difficult for decision makers to assign accurate values to alternatives for the criteria under consideration [48]. Fuzzy TOPSIS allows decision makers to assign linguistic performance ratings to the alternatives instead of precise numbers. This method ranks CLP strategies according to their distance to the fuzzy positive-ideal solution, \(\widetilde{A}^{*}\), and the fuzzy negative-ideal solution, \(\widetilde{A}^{-}\). According to [PERSON] et al. [50], \(\widetilde{A}^{*}\) can be obtained by maximizing the benefit criteria IC, IF, and WA. \(\widetilde{A}^{-}\) can be reached by minimizing the cost criterion, which is IR. Considering a set of \(K\) decision makers as \(\{D_{1};\ D_{2};...;\ D_{K}\}\) and a set of \(m\) CLP improvement strategies as \(\{S_{1};\ S_{2};...;\ S_{m}\}\), the steps of fuzzy TOPSIS for determining the importance of the CLP improvement strategies are given below. Step 1: Construct the fuzzy decision matrix. The linguistic value given by the \(k\)th decision maker to each improvement strategy regarding each SSC is transformed into a trapezoidal fuzzy number as \(\widetilde{R}_{k}=(a_{k};\ b_{k};\ c_{k};\ d_{k})\), using the membership functions in Table 2. The responses of the decision makers are then aggregated as \(\widetilde{R}=(a;\ b;\ c;\ d)\) using the following detailed computations  
\[a=\min_{k}\{a_{k}\}\quad b=\frac{1}{K}\sum_{i=1}^{k}b_{K}\quad c=\frac{1}{K} \sum_{i=1}^{k}c_{K}\quad d=\max_{k}\{d_{k}\} \tag{6}\]  
The fuzzy decision matrix is built with \(m\) rows and \(K\) columns. Each cell of the matrix is shown by \(\widetilde{R}_{ij}=\big{(}r_{ij1};\ r_{ij2};\ r_{ij3};\ r_{ij4}\big{)}\), which is the fuzzy number of the \(i\)th strategy with respect to the \(j\)th criterion. Step 2: Compute the normalized fuzzy decision matrix. For the benefit criteria IC, IF, and WA, normalized \(\widetilde{R}_{ij}\) is computed as  
\[\widetilde{N}_{ij}=\left(\frac{r_{i1}}{r_{j}^{*}};\ \frac{r_{i2}}{r_{j}^{*}};\ \frac{r_{i3}}{r_{j}^{*}};\ \frac{r_{i 1}}{r_{j}^{*}}\right) \tag{7}\]  
where \(r_{j}^{*}\) is calculated as  
\[r_{j}^{*}=\max_{i}\{r_{ij4}\} \tag{8}\]  
For the cost criterion IR, normalized \(\widetilde{R}_{ij}\) is calculated as  
\[\widetilde{N}_{ij}=\left(\frac{r_{j}^{-}}{r_{ij4}};\ \frac{r_{j}^{-}}{r_{ij3}};\ \frac{r_{j}^{-}}{r_{ij2}};\ \frac{r_{j}^{-}}{r_{ij1}}\right) \tag{9}\]  
where \(r_{j}^{-}\) is calculated as  
\[r_{j}^{-}=\min_{i}\{r_{ij1}\} \tag{10}\]  
Step 3: Weight the normalized fuzzy decision matrix. The weighted \(\widetilde{N}_{ij}\) is determined by following formula  
\[\widetilde{V}_{ij}=W_{j}\times\widetilde{N}_{ij} \tag{11}\]  
where \(\widetilde{V}_{ij}\) is the weighted fuzzy number of the \(i\)th strategy with respect to the \(j\)th criterion and is depicted as \(\big{(}v_{ij1};\ v_{ij2};\ v_{ij3};\ v_{ij4}\big{)}\). Step 4: Calculate the distance of each improvement strategy from \(\widetilde{A}^{*}\) and \(\widetilde{A}^{-}\).