## 3 Methodology
### Step1: Generating the Direct-Relation Matrix (A)  
After preparing the list of relevant barriers or criteria, subject to the DEMATEL scale, every expert was asked to make pairwise comparisons between one barrier with another barrier. After that, any individual options and assessments about the causality among one barrier with another barrier were obtained from each expert's initial-relation matrix by using Equation (1). The scale ranging from 0 to 4 was used, which indicates no influence, very low influence, low influence, high influence, and very high influence to illustrate the inter-relationship among the identified barriers as shown in Table 4. The same method \begin{table}
\begin{tabular}{c c c} \hline \hline
**S.no** & **Barriers Name** & **FDM Threshold Value at 0.60** \\ \hline B1 & Consumers’ lack of knowledge and awareness about reused/recycle & 0.64 \\ \hline B2 & High purchasing cost of environmentally friendly materials & 0.62 \\ \hline B3 & Lack of successful business models and frameworks to implement CE & 0.61 \\ \hline B4 & Lack of support supply and demand network & 0.62 \\ \hline B5 & Obstructing laws and regulations & 0.63 \\ \hline B6 & Design challenge to reuse and recovery products & 0.63 \\ \hline B7 & Limited availability and quality of recycling material & 0.64 \\ \hline B8 & Lack of an information exchange system between different stakeholders & 0.61 \\ \hline B9 & Unclear vision in regards of CE & 0.60 \\ \hline B10 & Insufficient internalization of external costs & 0.61 \\ \hline B11 & High short-term costs and low short-term economic benefits & 0.63 \\ \hline B12 & Make the right decision to implement CE in the most efficient way & 0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The selected key barriers based on Fuzzy Delphi Method result. would be following to fill out all of the experts' options as shown in Equation (1). Indeed, there are p experts where p = {1, 2, 3... _n_}. The equation [93] is as follows:  
\[\text{A}_{\text{p}}=\left[ \begin{array}{cccccc}0&a12&a13&\ldots&a1(n-1)&a1n\\ a21&0&a23&\ldots&a2(n-1)&a2n\\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ a(n-1)1&a(n-1)2&a(n-1)3&\ldots&0&a(n-1)n\\ an1&an2&an3&\ldots&an(n-1)&0\end{array} \right] \tag{1}\]  
where, Ap determines each expert interaction option among barriers. **Step2: Normalizing the Direct-Relation Matrix (X)**  
In this step, the normalizing direct-relation matrix (X) is computed in this process. It is possible by using the formula given in the following equation:  
\[\text{X}=\text{k}\.\ \text{A} \tag{2}\]  
\[\text{Here k}\ =\ \frac{1}{ \begin{array}{c}max\\ 1\leq i\leq n\end{array} }\,\ i,\ j=\ 1,2,\ldots,n \tag{3}\]  
where A indicates the initial-relation matrix as per Equation (1), k is the average of \(a_{ij}\) of all experts, and X denotes the normalized direct-relation matrix. It should be observed that for the DEMATEL approach to be feasible, the number of each column in the normalized direct-relation matrix must be less than one [94]. **Step3: Calculate the Total-Relation Matrix (T)**  
In this step, the total-relation matrix (T) is evaluated using the following equation:  
\[\text{T}=\text{X}\ (\text{I}-\text{X})^{-1} \tag{4}\]  
where I denotes the identity matrix, T indicates the total-relation matrix, and X means the normalizing matrix as per the Equation (2). The total-relation matrix T computes the sum of a number of rows (D) and the sum of a number of columns (R). D and R are calculated in the T matrix with the use of the following equations [40]. \[\text{(D)}\ =\ \left[d_{\text{ij}}\right]_{n\ \times\ 1}\ =\ \left[\sum_{j=1}^{n}d_{ij}\right]_{n\ \times\ 1} \tag{5}\]  
\[\text{(R)}\ =\ \left[r_{\text{ij}}\right]_{1\ \times\ n}\ =\ \left[\sum_{i=1}^{n}r_{ij}\right]_{1\ \times\ n} \tag{6}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Linguistic Terms** & **Numerical Value** \\ \hline No influence & 0 \\ \hline Very low influence & 1 \\ \hline Low influence & 2 \\ \hline High influence & 3 \\ \hline Very high influence & 4 \\ \hline \hline \end{tabular}
\end{table}