*3.1. Criteria Importance through Inter-Criteria Correlation (CRITIC)*

In MCDM problems, the identification of criteria and the determination of their weights are very important processes, since weights of criteria can significantly affect the final output of the decision-making framework. The CRITIC method [5] is one of the frequently used MCDM methods to obtain the importance of criteria. In this method, the objective importance of the criteria is obtained by applying the contrast intensity of each criterion, which is considered as the standard deviation, while conflicts between criteria are considered as the correlation coefficient between criteria. Steps of the CRITIC method for an MCDM problem with *m* alternatives and *n* criteria are presented below.

**Step 1**. The decision-maker constructs the initial decision matrix.

$$\mathbf{x}\_{lj} = \begin{bmatrix} \mathbf{x}\_{11} & \cdots & \mathbf{x}\_{1n} \\ \vdots & \ddots & \vdots \\ \mathbf{x}\_{m1} & \cdots & \mathbf{x}\_{mn} \end{bmatrix} (i = 1, 2, \dots, m \text{ and } j = 1, 2, \dots, n). \tag{1}$$

The elements (*xij*) of the decision matrix (*X*) represent the performance value of the *i-*th alternative on the *j-*th criterion.

**Step 2**. Equations (2) and (3) normalize the initial decision matrix considering the benefit and cost criteria.

$$r\_{ij} = \frac{\mathbf{x}\_{ij} - \min\_{\bar{i}} \mathbf{x}\_{ij}}{\max\_{\bar{i}} \mathbf{x}\_{ij} - \min\_{\bar{i}} \mathbf{x}\_{ij}} \text{ for benefit criterion.} \tag{2}$$

$$r\_{ij} = \frac{\max\_{\vec{i}} \mathbf{x}\_{i\vec{j}} - \mathbf{x}\_{i\vec{j}}}{\max\_{\vec{i}} \mathbf{x}\_{i\vec{j}} - \min\_{\vec{i}} \mathbf{x}\_{i\vec{j}}} \text{ for cost criterion.} \tag{3}$$

**Step 3**. A symmetric linear correlation matrix (*mij*) is calculated by the decision-maker.

**Step 4**. In order to obtain the objective importance of a criterion, the standard deviation and the correlation of each criterion with other criteria are calculated. With this information, the importance of each criterion can be determined via Equation (4).

$$\mathcal{W}\_{\dot{j}} = \frac{\mathbb{C}\_{j}}{\sum\_{j=1}^{n} \mathbb{C}\_{j}},\tag{4}$$

where *C<sup>j</sup>* is the amount of information contained in the criterion *j* and is calculated using Equation (5).

$$\mathcal{C}\_{j} = \sigma \sum\_{j=1}^{n} 1 - m\_{ij}. \tag{5}$$

In Equation (5), σ is the standard deviation of the *j-*th criterion. In fact, the CRITIC method assigns higher weights to criteria with higher values of σ and lower correlation with the other criteria. A higher value of *C<sup>j</sup>* denotes a higher amount of information included in a specific criterion; therefore, it is assigned a higher weight value.
