## 3 Methods
### Navigation Risk Assessment Model
#### 3.2.3 Weighting the Criteria Using CRITIC  
Weights can reflect the importance of each evaluation criterion, and the method of weighting is an important step in building a spatial, multi-objective decision model. The traditional way to obtain weighting data is from an expert's knowledge or a questionnaire, which inevitably involve some subjective uncertainties. With the aim of eliminating subjectivity as much as possible, we collected accident data from 2015 to 2021 in Bohai Sea and Yellow Sea, and reproduced the values of each evaluation factor during the accident using the CRITIC weighting method to get the criteria weights. The CRITIC method determines weights according to the discretization of each criterion and the relationships between them [42], and is widely used in weight determination problems [43; 44]. In this paper, the CRITIC method is used to get the criteria weights from historical accident data. The specific weight determination steps are as follows. * Step 1. The accident value of each criterion is standardized using Equation (7). * Step 2. The standardized data are organized into an evaluation matrix. The columns represent different criteria, and the rows represent the standardized value of the same criteria, as shown in Equation (8): \[\left[ \begin{array}{cccc}x_{11}^{\prime}&x_{12}^{\prime}&\ldots&x_{1k}^{ \prime}\\ x_{21}^{\prime}&x_{22}^{\prime}&\ldots&x_{2k}^{\prime}\\ \vdots&\vdots&\ddots&\vdots\\ x_{n1}^{\prime}&x_{n2}^{\prime}&\ldots&x_{nk}^{\prime}\end{array} \right],\] (8) where \(k\) represents the total number of criteria, \(n\) represents the total number of accident records, and \(x^{\prime}\) represents the standardized value. * Step 3. Calculate the correlation coefficients, and a correlation coefficient matrix is obtained, expressed as Equation (9). Then, the conflict coefficient of each evaluation factor is calculated by Equation (10): \[\left[ \begin{array}{cccc}r_{11}&r_{12}&\ldots&r_{1k}\\ r_{21}&r_{22}&&\ldots&r_{2k}\\ \vdots&\vdots&\ddots&\vdots\\ r_{k1}&r_{k2}&\cdots&r_{kk}\end{array} \right],\] (9) \[R_{z}=\sum_{m=1}^{k}(1-r_{z,m})z\in[1,\ldots,k],\] (10) where \(R_{z}\) represents the conflict coefficient of criterion \(z\), and \(r_{z,m}\) represents the correlation coefficients between criteria \(z\) and \(m\). Note that a bigger correlation between criterion \(z\) with other criteria produces a smaller \(R_{z}\). * Step 4. Calculate the sample standard deviation of each criterion using Equation (11): \[\mathrm{S}_{z}=\sqrt{\frac{\sum_{l=1}^{n}\left(x_{l}^{\prime}-\overline{x^{ \prime}}\right)^{2}}{n-1}},\] (11) where \(\mathrm{S}_{z}\) represents the sample standard deviation of criterion \(z\), and \(\overline{x^{\prime}}\) is the mean of the standardized values. * Step 5. The amount of information for criterion \(z\) is calculated with the conflict coefficient \(R_{z}\) obtained in Step 3 via Equation (12): \[\mathrm{C}_{z}=\mathrm{S}_{z}\cdot R_{z},\] (12) where \(\mathrm{C}_{z}\) represents the amount of information of criterion \(z\). * Step 6. Normalize the amount of information and get the CRITIC weights for each criterion following Equation (13): \[w_{z}^{c}=\frac{\mathrm{C}_{z}}{\sum_{m=1}^{k}\mathrm{C}_{m}},\] (13) where \(w_{z}^{c}\) represents the CRITIC weight of criterion \(z\). Through the above six steps, the CRITIC method can be used to obtain the different criteria weights. When the correlations between a criterion and other criteria are large and the variances are small, the CRITIC weight of this criterion will be relatively small. Thus, this method can make a tradeoff between the correlations and the standard deviations of the different factors, and hence give more reasonable weight values.