## 3 Materials and Methods
### PC-CRITIC Combined Assignment Method  
The key aspect of the comprehensive assignment method lies in determining the appropriate weights for the indicators, which represent their relative importance in the evaluation process. Assigning accurate and objective weights is critical to achieving a reliable multi-indicator evaluation. To integrate the empirical knowledge of experts with the intrinsic relationships within the data, the PC-CRITIC comprehensive weighting method was applied to determine indicator weights. The precedence chart (PC) approach is based on decision-makers' subjective judgments about the relative importance of each factor. By comparing pairs of factors, scores are assigned to reflect their significance, and the weights are subsequently derived from these scores. The core principle of this method is that the consistency of comparative judgments determines the reliability of the calculated weights [33; 34; 35]. When the decision maker's judgments show a high degree of consistency, the resulting weights are considered more reliable. The main steps involved are as follows:  
1. Defining the Decision Problem and Identifying Factors: The decision problem is clearly defined, and the various factors influencing the decision are identified and listed. 2. Constructing a Precedence Chart: A pairwise comparison is conducted between all factors in the set. Scores are assigned based on the relative importance of each factor, typically ranging from 0 to 4. A score of 0 means two factors are equally important, while 1, 2, 3, and 4 indicate increasing levels of importance, from slightly more important to extremely more important. 3. Populating the Precedence Chart: The precedence chart takes the form of a square matrix where both rows and columns represent the factors being compared. Diagonal elements are assigned a value of zero, as no factor is compared with itself. The off-diagonal elements contain the scores representing the comparison results between different factors. 4. Summing the Scores: The sum of the scores for each row in the precedence chart is calculated, yielding a total score for each factor. 5. Calculating the Weights  
Figure 2: Evaluation of the grouting effect system. The total scores for each factor are normalized by dividing them by the total score of all factors, resulting in the final weights assigned to each factor. Consistency Testing  
To ensure the reliability of the judgments, a consistency test is conducted. The consistency index (CI) and consistency ratio (CR) are computed. If the CR value is below a certain threshold (typically 0.1), the judgments are considered consistent, and the weights are deemed reasonable. If the CR exceeds this threshold, the judgments must be reviewed and potentially revised, or the weights adjusted accordingly. CI is calculated by the following formula:  
\[CI=\frac{\lambda_{max}-n}{n-1} \tag{1}\]  
Here, \(\lambda_{max}\) is the maximum eigenvalue of the judgement matrix, and \(n\) is the number of factors. CR is calculated by the following formula:  
\[CR=\frac{CI}{RI} \tag{2}\]  
The random consistency index (RI) is determined by referencing a table that correlates its value with the number of factors under consideration. Following this, the weights of the factors can be calculated using the preferential order diagram method, offering a structured foundation for multi-criteria decision-making. The CRITIC weighting method offers an objective approach to assigning weights by utilizing two key indicators: contrast intensity and conflict [36; 37]. Contrast intensity is measured by the standard deviation of the data--a greater standard deviation signifies higher fluctuation and consequently a larger weight. Conflict is quantified through the correlation coefficient--a higher correlation between indicators suggests lower conflict, leading to a reduced weight. In determining the final weights, contrast intensity is multiplied by the conflict indicator, and the results are normalized.