## 3 Methods
### Grey Relational Analysis (GRA)  
The grey system theory (GST) has been considered as a better method for doing research on an exploratory explanation. GRA is the most important topic in GST, whose main function is the measurement between two discrete sequences. GRA makes use of relatively simple mathematical procedures and a small amount of data and works with a great variability in factors to arrive at salient relationships in a complex system [29]. Hence, GRA is chosen as the mathematical core to analyze the state of ranking the critical risks of picking and material-handling accidents in warehouse facilities.  
A Likert scale involved in research usually uses a 5, 7, or 9-point scale to respond to subjective or objective evaluation. GRA is an important weight analysis method that is weighted on a 5-point scale by this article to respond to relative importance evaluation, as shown in Table 3. The obtained data are usually expressed as the specific range of a grey interval number and are the upper and lower limits of the information separately. GRA-associated equations are described as follows [17; 18].  
Step 1. Identify the response variables  
A normalization of the response variables was performed to prepare raw data for analysis where the original sequence is transferred to a comparable sequence. The process of linear normalization of the original sequence is a larger-the-better characteristic, which is used to normalize the original sequence using the following equation:  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Linguistic Variables** & **Codes** & **Grey Numbers** \\ \hline
1 & Very poor & VG & [1,2] \\
2 & Poor & P & [2,4] \\
3 & Strongly important & M & [4,6] \\
4 & Good & G & [6,8] \\
5 & Very good & VG & [8;9] \\ \hline \hline \end{tabular}
\end{table}
Table 3: The scale for the weighted elements [29].  
\[x_{j}(k)=\frac{x_{j}{{}^{(0)}}(k)-\text{min}x_{j}{{}^{(0)}}(k)}{\text{max}x_{j}{{} ^{(0)}}(k)-\text{min}x_{j}{{}^{(0)}}(k)} \tag{4}\]  
For the smaller-the-better (undercut) quality characteristic of the original reference sequence, the following expressions are used for normalization:  
\[x_{i}{{}^{*}}(k)=\frac{\text{max}x_{i}{{}^{(0)}}(k)-x_{i}{{}^{(0)}}(k)}{\text{ max}x_{i}{{}^{(0)}}(k)-\text{min}x_{i}{{}^{(0)}}(k)} \tag{5}\]  
Step 2. Determination of Deviation Sequences  
The deviation sequence \(\Delta_{0i}(k)\) is the absolute difference between the reference sequence \(x_{0}{{}^{*}}(k)\) and the comparability sequence \(x_{i}{{}^{*}}(k)\) after normalization. The value of \(x_{0}{{}^{*}}(k)\) is considered as 1. It is determined using Equation (6) as given below:  
\[\Delta_{0i}(k)=\left|x_{0}{{}^{*}}(k)-x_{i}{{}^{*}}(k)\right| \tag{6}\]  
Step 3. Calculation of Grey Relational Coefficient (GRC)  
Grey relational coefficients for all the sequences express the relationship between the ideal and actual normalized response variables. The grey relational coefficient \(\gamma(x_{0}(k),x_{i}(k))\) can be expressed by Equation (7):  
\[\gamma(x_{0}(k),x_{i}(k))=\frac{\Delta\text{min}+\xi\ \Delta max}{\Delta_{0i}( k)+\xi\ \Delta max} \tag{7}\]  
where \(\Delta\) min is the smallest value of \(\Delta_{0i}(k)\) = min \(\left|x_{0}{{}^{*}}(k)-x_{i}{{}^{*}}(k)\right|\) and \(\Delta\) max is the largest value of \(\Delta_{0i}(k)\) = max \(\left|x_{0}{{}^{*}}(k)-x_{i}{{}^{*}}(k)\right|\), \(x_{0}{{}^{*}}(k)\) is the ideal normalized values, \(x_{i}{{}^{*}}(k)\) is the normalized comparability sequence, and \(\xi\) is the distinguishing coefficient. The value of (\(\xi\)) is taken as 0.5 for all response variables and is substituted in Equation (7). The gray relational grade for all the experimental runs were calculated.  
Step 4. Determination of Grey Relational Grade (GRG)  
Based on the different weights of BWM calculation, the grey relational grade is a sum of the grey relational coefficient, which is defined as follows:  
\[\gamma(x_{0},x_{i})=\sum_{i=1}^{m}W_{i}*(x_{0}(k),x_{i}(k)) \tag{8}\]  
where \(\gamma(x_{0},x_{i})\) is the grey relational grade for the \(j\)th experiment.