3.2.1. Step 1. Obtaining Rough Direct Relation Matrix *Q*˜

<sup>⇒</sup> *<sup>A</sup>*˜(3) = 3˜ = [2.333, 3.667];

After screening, there are *n*∗ criteria and each expert evaluates the direct impact of the criteria *i* on the criteria *j* according to DEMATEL's evaluation ratings (Table 3). Then, the subjective opinions of all experts will be converted into a set of interval-type interval numbers by the rough number operation in rough theory and a rough direct relation matrix *Q*˜ can be obtained. As shown in Equation (6).

$$\vec{\mathcal{Q}} = [\vec{q}\_{\vec{i}\vec{j}}]\_{n^\* \times n^\*} \, \vec{\imath} = \, \vec{\jmath} = 1, 2, \dots, n^\* \tag{6}$$

where *q*˜*ij* = [*qL ij*, *<sup>q</sup><sup>U</sup> ij* ].


**Table 3.** DEMATEL's evaluation ratings.

3.2.2. Step 2. Establishing the Normalized Rough Influence Relation Matrix *D*˜

The rough direct relation matrix *Q*˜ can obtain a normalized rough influence relation matrix *D*˜ through Equations (7) and (8). The normalized program can convert the evaluation value to between 0 and 1.

$$
\mathcal{D} = \varepsilon \times \tilde{\mathcal{Q}} \tag{7}
$$

$$\varepsilon = \min \left\{ 1/\max\_{i} \sum\_{j=1}^{n^\*} q\_{ij}^{lI}, 1/\max\_{j} \sum\_{i=1}^{n^\*} q\_{ij}^{lI} \right\}, i = j = 1, 2, \dots, n^\* \tag{8}$$

where *D*˜ = [ ˜ *dij*] *<sup>n</sup>*∗×*n*∗, 0 <sup>≤</sup> ˜ *dij* < 1 and ˜ *dij* = *dL ij*, *<sup>d</sup><sup>U</sup> ij* . In *<sup>n</sup>*<sup>∗</sup> *j*=1 *dU ij* and *<sup>n</sup>*<sup>∗</sup> *i*=1 *dU ij* , the sum of any row or column is less than or equal to 1.
