## 4 Case Study
### Analysing Failure Modes for IVIS
#### 4.2.2 Aggregating Fuzzy Opinions for Risk Parameters Assessments for IVIS  
To aggregate the fuzzy opinions of team members for risk parameters assessments, SAM was used. The weighting scores according to the traits of team members are given in Table 11[60]. The weights assigned to each team member based on their traits (see Table 5) are presented in Table 12. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Mode No.**} & \multicolumn{6}{c}{**Fuzzy Evaluations of Team Members**} & \multicolumn{6}{c}{**Aggregation of**} \\ \cline{2-9}  & **TM1** & **TM2** & **TM3** & **TM4** & **TMS5** & **TM6** & **TM7** & **Fuzzy Opinions** & **Defuzzification Value** \\ \hline
1 & M & L & M & L & L & L & M & (0.998, 3.498, 5.998) & 3.498 \\
2 & L & L & L & L & M & L & L & (0.160, 2.660, 5.160) & 2.660 \\
3 & M & M & M & M & M & M & L & (2.396, 4.896, 7.396) & 4.896 \\
4 & M & M & M & M & M & M & M & (2.500, 5.000, 7.500) & 5.000 \\
5 & M & M & L & M & M & M & M & (2.227, 4.727, 7.227) & 4.727 \\
6 & L & L & L & L & L & L & (0.000, 2.500, 5.000) & 2.500 \\
7 & M & M & M & M & L & L & M & (2.033, 4.533, 7.033) & 4.533 \\
8 & L & L & L & L & L & L & (0.000, 2.500, 5.000) & 2.500 \\  
& H & H & VH & H & H & H & (5.271, 7.771, 10.000) & 7.681 \\
23 & M & L & L & M & M & L & M & (1.460, 3.960, 4.640) & 3.960 \\
24 & H & H & M & H & H & M & (4.072, 6.572, 9.072) & 6.572 \\
25 & M & M & M & M & M & L & M & (2.298, 4.798, 7.298) & 4.798 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Fuzzy evaluations and aggregation of opinions for detection. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Mode No. **} & \multicolumn{6}{c}{**Fuzzy Evaluations of Team Members**} & \multicolumn{2}{c}{**Aggregation of**} \\ \cline{2-9}  & **TM1** & **TM2** & **TM3** & **TM4** & **TM5** & **TM6** & **TM7** & **Fuzzy Opinions** & **Defuzzification Value** \\ \hline
1 & H & H & VH & H & H & M & H & (5.085, 7.885, 9.793) & 7.488 \\
2 & H & H & H & H & H & H & M & (4.896, 7.396, 9.896) & 7.396 \\
3 & VH & VH & VH & VH & VH & H & VH & (7.285, 9.785, 10.000) & 9.023 \\
4 & H & M & H & H & M & H & H & (4.519, 7.019, 9.519) & 7.019 \\
5 & H & M & M & H & H & H & (4.406, 6.906, 9.406) & 6.906 \\
6 & L & L & L & L & L & L & M & (0.104, 2.604, 5.104) & 2.604 \\
7 & H & H & M & H & H & H & (4.741, 7.241, 9.741) & 7.241 \\
8 & H & H & H & VH & H & VH & (5.389, 7.889, 10.000) & 7.759 \\
9 & M & M & M & H & M & M & H & (2.967, 5.467, 7.967) & 5.467 \\
10 & M & M & M & H & H & H & (2.967, 5.467, 7.967) & 5.467 \\
11 & H & H & M & H & H & H & (4.364, 6.864, 9.364) & 6.864 \\
12 & H & H & H & H & M & M & H & (4.533, 7.033, 9.533) & 7.033 \\
13 & M & M & M & M & M & L & M & (2.298, 4.798, 7.298) & 4.798 \\
14 & M & M & M & M & M & M & (2.660, 5.160, 7.660) & 5.160 \\
15 & H & H & H & M & H & H & H & (4.741, 7.241, 9.741) & 7.241 \\
16 & H & H &For the risk parameter of occurrence, according to Equations (5) and (6), as regards failure mode No. 1, the agreement matrix can be obtained as follows:  
\[AM= \begin{bmatrix}1.000&0.200&0.143&0.200&0.143&1.000&1.000\\ 0.200&1.000&0&1.000&0.200&0.200\\ 0.143&0&1.000&0&1.000&0.143&0.143\\ 0.200&1.000&0&1.000&0.200&0.200\\ 0.143&0&1.000&0&1.000&0.143&0.143\\ 1.000&0.200&0.143&0.200&0.143&1.000&1.000\\ 1.000&0.200&0.143&0.200&0.143&1.000&1.000\\ \end{bmatrix} \]  
By using Equation (7), the average agreement degree (AAD) can be calculated, and then the relative agreement degree (RAD) can be derived according to Equation (8). On the basis of RAD and the weights of the team members, the consensus degree coefficient (CDC) can be calculated according to Equation (9). The computed AAD, RAD, and CDC for occurrence are given in Table 13. By using Equation (10), the aggregation result was obtained as follows: \(R=(5.072,\ 7.572,\ 9.382)\). Consequently, by using Equation (4), the defuzzification value for the aggregated fuzzy opinions can be obtained, whose result was 7.342.