## 3 Materials and Methods
### Uncertainty Propagation
Utilizing the data from Table 7 allows for conducting valuation analyses using both the Net Present Value (NPV) and real option valuation (ROV) methods. The classical NPV analysis, irrespective of the transformation employed, indicates a negative decision regarding the initiation of the investment Figure 6. Essentially, initiating a project that does not add value to the company would not be rational. Although the standard deviation remains consistent across scenarios, the substantial percentage difference between the optimistic and pessimistic probability bounds highlights the critical importance of considering the option value in investment decisions. Figures 5 and 6 reveal that the project's Net Present Value is not characterized by a single figure but by a band of possible outcomes whose width is driven by epistemic + aleatory uncertainty. Conversely, adopting a real option analysis perspective provides an alternative viewpoint. Real option valuation offers insights into the project's potential upside value. If the potential benefits from the project exceed the cost of obtaining the real option, which enables capturing upside potential in response to changes, then acquiring the option becomes a sensible investment. In this analysis, three distinct outcomes are derived due to the application of three different ROV methodologies. Using pure results from the hybrid simulation (see Figure 6 and the numerical summary in Table 7), the probability of success exhibits a broad range from 8% to 80%, and the corresponding ROV spans from 2 to over 26 thousand USD. The considerable disparity between the optimistic and pessimistic bounds emphasizes the importance of distinguishing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Assumption** & **Smean** & **IQR** \\ \hline Interdependent (a) & 2.51 \(\times\) 10\({}^{-6}\) & 180 \\ Independent (b) & 1.00 \(\times\) 10\({}^{-6}\) & 434 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simple aleatoric-uncertainty metrics for considered assumptions. between data accuracy and expert estimations in the valuation process. Decision makers must evaluate whether to rely on this information for investment decisions. If they find the range excessively broad, they may opt for additional research to reduce subjective uncertainty represented by fuzzy numbers for GBM parameters. However, further analysis may not always be feasible due to various constraints. In such instances, decision makers might opt for one of the available transformations. The pignistic probability transformation can serve as a baseline reference. The unit mass probability represents the subjective probability for each interval \(f_{\infty,j}\). Here, \"subjective\" implies that \(m(f_{\infty,j})\) is proportional to its appearance in simulation outcomes. This interpretation suggests the probability of epistemic states represented by \(f_{\infty,j}\). When each state within intervals is equally probable, the pignistic transformation aligns closely with pure Monte Carlo simulation. In our example, \(\Phi_{bel}(npv)\) closely mirrors \(\underline{\mathcal{Q}}\) (with a success probability of 15%). Thus, the probability of success is influenced by the decision-maker's stance toward uncertainty and expert assessments. The selection of other transformations depends on the perceived nature of epistemic uncertainty. The ambiguity transformation, as illustrated in this study using a weighting of 0.5, is particularly suitable for sensitivity analyses. This measure reflects the decision maker's confidence level in expert opinions, influencing the weighting of optimistic versus pessimistic probability bounds. Finally, the third transformation reflects the decision maker's attitude towards uncertainty, indicating their preference for optimism or pessimism. This approach resembles the possibilistic fuzzy pay-off method for real option valuation described in [56]. It should be emphasized, however, that this transformation does not take into account investors' risk aversion.