# Occupational Risk Assessment of Wind Turbines in Bangladesh
## 4 Research Methodology
### [PERSON]'s Fuzzy AHP Method  
The traditional AHP method has some limitations [28]. For instance, the AHP methodology is especially used in nearly crisp rating applications [29]. Some other drawbacks of AHP methodology are that the AHP methodology does not take into consideration the unpredictability of human judgment, the ratings given by the AHP methodology are quite broad, and the ratings are subject to the preference and approach of the administrator. Fuzzy theory and AHP have been integrated by many decision-makers to reduce uncertainty. Various versions of FAHP are used for multi-criteria decision analysis work [16; 29]. [PERSON]'s FAHP method is used in this study. [PERSON]'s FAHP steps are as follows [16; 30]:  
Step 1: Develop a pairwise comparison matrix with all the hazards. Use linguistic terms with the pairwise comparisons by asking which hazard is more important compared to another hazard and construct the decision matrix.  
\[\widetilde{M}=\left[\begin{array}{ccccc}1&\widetilde{a}_{12}&\cdots& \widetilde{a}_{1n}\\ \widetilde{a}_{21}&1&\cdots&\widetilde{a}_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ \widetilde{a}_{n1}&\widetilde{a}_{n2}&\cdots&1\end{array}\right]=\left[ \begin{array}{ccccc}1&\widetilde{a}_{12}&\cdots&\widetilde{a}_{1n}\\ \frac{1}{\widetilde{a}_{12}}&1&\cdots&\widetilde{a}_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ \frac{1}{\widetilde{a}_{1n}}&\frac{1}{\widetilde{a}_{2n}}&\cdots&1\end{array}\right] \tag{1}\]  
\[\text{and}\ \ \widetilde{a}_{ij}=\left\{\begin{array}{ccccc}\widetilde{1},& \widetilde{3},&\widetilde{5},&\widetilde{7},&\widetilde{9}&i\text{ is relatively important than }j\\ 1&i=j\\ \widetilde{1}^{-1},&\widetilde{3}^{-1},&\widetilde{5}^{-1},&\widetilde{7}^{-1},&\widetilde{9}^{-1}&j\text{ is relatively important than }i\end{array}\right.\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Risk Score (R)** & **Risk Classification** \\ \hline Above 400 & Very high risk; immediately stop operations \\ In between 200 and 400 & High risk; take quick large corrective actions \\ In between 70 and 200 & More risk; take simple corrective actions \\ In between 20 and 70 & Low risk: attention required \\ Less than 20 & Very low risk; acceptable \\ \hline \hline \end{tabular}
\end{table}
Table 4: Level of risk [13; 27].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rank** & **Consequence (C)** & **Rank** & **Exposer (E)** & **Rank** & **Probability (P)** \\  & **Description** & **Description** & **Description** \\ \hline
100.0 & Catastrophic (many fatalities) & 10.0 & Continuous (multiple times per day) & 10.0 & To be expected \\
40.0 & Disaster (few fatalities) & 6.0 & Recurring (everyday) & 6.0 & Feasible \\
15.0 & Super serious (fatality) & 3.0 & Occasional (weekly) & 3.0 & Unusual but possible \\
7.0 & Serious (serious injury) & 2.0 & Unusual (every month) & 1.0 & Unlikely, possible in the long term \\
3.0 & Not serious (disability) & 1.0 & Moderately rare (approximately once & 0.5 & Highly unlikely, but conceivable \\  & & per year) & 0.2 & Almost unimaginable \\
1.0 & Noticeable & 0.5 & Very rare (less than once per year) & 0.1 & Almost impossible \\ \hline \hline \end{tabular}
\end{table}
Table 3: Scale of risk parameters [13; 27].  
Step 2: By using geometric mean value, determine the fuzzy geometric mean and fuzzy weights of each criterion, based on Equations (3) and (4).  
\[\widetilde{r}_{i}=(\widetilde{a}_{i1}\ \otimes\ \widetilde{a}_{i2}\ \otimes\ \ldots\ \ \otimes\ \widetilde{a}_{in})^{\frac{1}{n}} \tag{2}\]  
\[\widetilde{W}_{i}=r_{i}\otimes(\widetilde{r}_{1}\ \oplus\ \widetilde{r}_{2}\ \oplus\ \ldots\ \ \oplus\widetilde{a}_{n})^{-1} \tag{3}\]  
Here, \(\widetilde{W}_{i}\) indicates the fuzzy weight of criterion \(i\) and, \(\widetilde{W}_{i}=(lw_{i}\,mw_{i}\,uw_{i})\); \(lw_{i},mw_{i}\), \(uw_{i}\) indicate a lower, middle, and upper value of fuzzy weight, respectively.  
Step 3: Finally, calculate the weight by using the following formula.  
\[w_{i}=\frac{[(uw_{i}\ -lw_{i})+(mw_{i}-lw_{i})]}{3}+lw_{i} \tag{4}\]