## 7 The Effect of the Conditional Probabilities in this Method  
Suppose the conditional probability values are changed from 0.30 to 0.70 in steps of 0.1, and the decision results based on rules (4)-(6) are listed in Table 11. To present the situation more intuitively where the 3 WD results of each alternative change with the conditional probability, we show the results in Figure 3.  
During the variation of the conditional probability values, some differences in results occur, but the changes seem to be very small. At a conditional probability of 0.3-0.5, alternatives \(A_{1}\)-\(A_{3}\) are classified as accepted, and \(A_{4}\) is in the boundary region for investment, fortunately with no alternative in the rejected region. When the conditional probability is increased, a minor change is observed. At 0.6-0.7, \(A_{1}\) and \(A_{2}\) remain in the positive region for investors, and \(A_{3}\) moves to the boundary region. Alternatives \(A_{3}\) and \(A_{4}\) are in the unclear environment.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Alternatives** & \(A_{1}\) & \(A_{2}\) & \(A_{3}\) & \(A_{4}\) \\ \hline \hline
**Decision** & _Accepted_ & _Accepted_ & _Accepted_ & Boundary \\ \hline \hline \end{tabular}
\end{table}
Table 10: Decision results.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Probability** & **Accepted** & **Boundary** & **Rejected** \\ \hline
**0.3** & \(\{A_{1},A_{2},A_{3}\}\) & \(\{A_{4}\}\) & \(\{\varnothing\}\) \\ \hline
**0.4** & \(\{A_{1},A_{2},A_{3}\}\) & \(\{A_{4}\}\) & \(\{\varnothing\}\) \\ \hline
**0.5** & \(\{A_{1},A_{2},A_{3}\}\) & \(\{A_{4}\}\) & \(\{\varnothing\}\) \\ \hline
**0.6** & \(\{A_{1},A_{2}\}\) & \(\{A_{3},A_{4}\}\) & \(\{\varnothing\}\) \\ \hline
**0.7** & \(\{A_{1},A_{2}\}\) & \(\{A_{3},A_{4}\}\) & \(\{\varnothing\}\) \\ \hline \end{tabular}
\end{table}
Table 11: Effects of the probability values.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Alternatives** & \(\mathbf{a_{\mathcal{P}}}\) & \(\mathbf{a_{\text{B}}}\) & \(\mathbf{a_{N}}\) \\ \hline \(\mathbf{A_{1}}\) & (0.1431,0.5163) & (0.1760,0.4986) & (0.1574,0.4456) \\ \hline \(A_{2}\) & (0.0986, 0.5133) & (0.1339, 0.4485) & (0.1379, 0.5046) \\ \hline \(\mathbf{A_{3}}\) & (0.0940,0.4764) & (0.1537,0.5255) & (0.1546,0.3858) \\ \hline \(A_{4}\) & (0.1343, 0.4794) & (0.1286, 0.4967) & (0.1848, 0.4840) \\ \hline \end{tabular}
\end{table}
Table 8: Aggregation of risk values by operators.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Alternatives** & \(\mathbf{A_{1}}\) & \(\mathbf{A_{2}}\) & \(\mathbf{A_{3}}\) & \(\mathbf{A_{4}}\) \\ \hline \hline
**Decision** & _Accepted_ & _Accepted_ & _Accepted_ & Boundary \\ \hline \hline \end{tabular}
\end{table}
Table 10: Decision results.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Alternatives** & \(\mathbf{A_{1}}\) & \(\mathbf{A_{2}}\) & \(\mathbf{A_{3}}\) & \(\mathbf{A_{4}}\) \\ \hline \hline
**Decision** & _Accepted_ & _Accepted_ & _Accepted_ & Boundary \\ \hline \hline \end{tabular}
\end{table}
Table 11: Effects of the probability values.  
Based on Figure 3, we can conclude that \(A_{1}\) and \(A_{2}\) are classified as accepted, while \(A_{4}\) is in the unclear environment. The classification of \(A_{3}\) depends on the value of the probability. It is a positive outcome that, in this scenario, there is no alternative in the rejected region. However, it is important to note that in other situations, the rejected region may not be empty.