## 2 Data and Methods
### Methods
#### 2.3.2 New Site Selection Method for Large Yellow Croaker (SSM-LYC)  
To address the problem of selecting sites for large yellow croaker cage aquaculture along the coast of Zhejiang Province, this study proposes a novel site selection evaluation method. This method is based on a large yellow croaker cage aquaculture area environmental factor template summarized from multi-source data, as well as the grey relational analysis method to assess the interrelationships among different factors within the system. The method encompasses five steps as follows.  
Step 1: Determine the reference sequence \(x0\) and the comparison sequence \(xi\) (\(i=1,2,\ldots,n\)).  
Reference sequence \(x0\): This usually refers to the sequence of indicator values in the ideal or optimal state or the target state desired by the decision maker. The reference sequence was determined by combining the actual influencing factors for the establishment of cage aquaculture areas for large yellow croaker (Figure 3) and the corresponding parameters of existing typical cage aquaculture areas for large yellow croaker.  
Comparison sequence \(xi\): A sequence of specific index values for each potential site.  
Step 2: Dimensionless data processing.  
Since the raw data may have different dimensions, it needs to be dimensionless. The common method is Min \(-\) Max Normalization, which ensures that the data are between 0 and 1.  
\[N(xi)=\frac{xi-min(x)}{max(x)-min(x)} \tag{2}\]  
where \(xi\) is the original data point and \(min(x)\) and \(max(x)\) are the minimum and maximum values in the data set, respectively.  
Step 3: Calculate the absolute difference.  
For each data point, the absolute difference \(dik\) between the normalized reference sequence and the comparison sequence is calculated as follows:  
\[dik=|x0k-xik| \tag{3}\]  
Step 4: Calculate the correlation degree.  
The purpose of calculating the degree of association is to quantify and compare the degree of similarity between sequences (the observed values of factors) and a reference  
Figure 3: Influencing factors of site selection for cage aquaculture area of coastal large yellow croaker.  
sequence (values representing an optimal or target state). Therefore, this section uses the formula used in GRA to calculate the correlation degree [30].  
The correlation degree \(Gi\) is calculated as follows:  
\[\xi(Xi)=\frac{min(dik)+\rho\cdot max(dik)}{dik+\rho\cdot max(dik)} \tag{4}\]  
\[Gi=\frac{\sum_{k=1}^{n}\xi(Xi)}{n} \tag{5}\]  
\(\xi(Xi)\) is the grey correlation coefficient between the comparison sequence and the reference sequence. \(\rho\) is the resolution coefficient, usually ranging from 0 to 1, used to adjust the sensitivity of the model. The correlation degree \(Gi\) ranges from 0 to 1, and the larger the value, the higher the correlation degree between the two sequences. n refers to the number of parameters in the reference sequence.  
Step 5: Sort by correlation degree.  
Each comparison sequence is sorted according to the calculated correlation degree, \(Gi\). The higher the correlation degree, the higher the similarity between the sequence and the reference sequence, and correspondingly, the higher the suitability of the location.