## 3 Methodology
### Matching Phase:
Equation 1 gives the formula for the calculation of the total worker risk:  
\[H=\sum_{k=1}^{p}h_{k}\sum_{j=1}^{o}f_{jk}I_{jk} \tag{1}\]  
where \(H\) is the total worker risk (expected rate of labor loss due to accidents during decommissioning work), \(f_{jk}\) is the frequency of occurrence of risk j in work k, \(I_{jk}\) is the severity of risk j in work k, and \(h_{k}\) is the level of risk of work k (weight). The level of structural risk is defined as the height at which the accident can occur, and the level of job risk is defined as the rate of labor loss. The frequency of occurrence of the risk is expressed by the fuzzy function (see Tables 8-10). Collapse or fall is generally classified according to the height of the accident [43] and the UK's Health and Safety Executive categorizes fall-related accidents as either slip, trip or fall on the same level, or fall from a height [44]. In this study, the maximum height of the bio-shield, 12 m, was classified into the following five categories [45]: very low impact (ground or same level falls), low impact (height of 2 m), moderate (height of 2-5 m), high impact (height of 5-10 m), and very high impact (height of more than 10 m). Job risk damage is generally classified into the disability evaluation shown in Table 9, where the evaluation method assesses the labor loss rate on a scale from 0% to 100% based on the type of disability, parts and occupations incurred [46]. The rate of labor loss is classified in terms of five levels, ranging from minor injuries (1%), disorders such as lumbar compression fractures (25%), disorders such as shoulder disarticulation (50%), and serious disorders such as cutting arms (75%) up to death (100%). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Category** & **Occurrence** & **Fuzzy Function** \\ \hline \multirow{4}{*}{\(f_{jk}\)} & Very high & 1:1 & (7.5, 10, 10) \\  & High & 1:0.75 & (5, 7.5, 10) \\ \cline{1-1}  & Moderate & 1:0.5 & (2.5, 5, 7.5) \\ \cline{1-1}  & Low & 1:0.25 & (0, 2.5, 5) \\ \cline{1-1}  & Very low & 1:0 & (0, 0, 2.5) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Structural/job risk occurrence frequency fuzzy function. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Category** & **Damage Definition (by Accident Height)** & **Relative Value** \\ \hline \multirow{4}{*}{\(I_{jk}\)} & Very high impact & Height of over 10 m & 10 \\  & High impact & Height of 5–0 m & 7.5 \\ \cline{1-1}  & Moderate & Height of 2–5 m & 5 \\ \cline{1-1}  & Low impact & Height of 2 m & 2.5 \\ \cline{1-1}  & Very low impact & Occurs at the same level & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Structural risk damage definition and relative values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Category** & **Damage Definition (\%)** & **Relative Value** \\ \hline \multirow{4}{*}{\(I_{jk}\)} & Very high impact & Death (100) & 10 \\  & High impact & Serious disorders such as cutting arms (75) & 7.5 \\ \cline{1-1}  & Moderate & Disorders such as shoulder disarticulation (50) & 5 \\ \cline{1-1}  & Low impact & Disorders such as lumbar compression fractures (25) & 2.5 \\ \cline{1-1}  & Very low impact & Minor injury (1) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Job risk damage definition and relative values. To assess possible structural and job risks using the detailed tasks (Level 3) for cutting derived above, we conducted a survey on risk frequency and intensity through in-depth interviews with 12 experts. The frequency decisions and probabilities were then reconverted through fuzzy integration and defuzzification of the assessment results. The risks of the fuzzified decontamination and decommissioning process are quantitatively calculated as a single value for each task through a defuzzification process. Here, we used the centroid method, which is generally regarded as the most effective defuzzification technique and is thus extensively used for these types of calculations [7].