## 3 Materials and Methods
### Uncertainty Propagation
Consequently, the proposed approach allows decision makers to assess the influence of such factors on the final decision, while also providing quantitative descriptions of their approach to uncertainty. Overall, this paper introduces a comprehensive and robust hybrid DMM that accounts for various sources of uncertainty and provides valuable insights for decision makers grappling with real options under high uncertainty. By incorporating both aleatoric and epistemic uncertainties, the method enables a thorough analysis of investment projects and facilitates the integration of expert knowledge, ultimately bridging the gap between real-world decision making and real option valuation. Because the algorithm treats aleatory and epistemic components separately and only then reunifies them in the pay-off stage, it is immediately applicable to any sector--energy, infrastructure, life-sciences R&D--where data scarcity co-exists with expert insight. Only the cash-flow model needs adaptation; the uncertainty propagation and valuation core remain unchanged. Conceptualization, B.G. and B.R. ; methodology, B.G. and B.R. ; software, B.G. ; validation, B.G. and A.P. ; formal analysis, B.G. and A.P. ; writing--original draft preparation, B.G. ; writing--review and editing, A.P. All authors have read and agreed to the published version of the manuscript. The APC was funded under subvention funds for the Faculty of Management and by-program \"Excellence Initiative--Research University\" for the AGH University of Krakow. Not applicable. The original contributions presented in this study are included in the article: The price and demand datasets analyzed in this study are publicly available from the following open sources: (i) Statistics Poland, Local Data Bank, table \"Price indices of sold production of industry\", monthly series 1996-2016, available online: [[https://stat.gov.pl/en/topics/prices-trade/price-indices/price-indices-of-sold-production-of-industry-in-1996%E2%80%930205,4.1.html](https://stat.gov.pl/en/topics/prices-trade/price-indices/price-indices-of-sold-production-of-industry-in-1996%E2%80%930205,4.1.html)]([https://stat.gov.pl/en/topics/prices-trade/price-indices/price-indices-of-sold-production-of-industry-in-1996%E2%80%930205,4.1.html](https://stat.gov.pl/en/topics/prices-trade/price-indices/price-indices-of-sold-production-of-industry-in-1996%E2%80%930205,4.1.html)) (accessed on: 1 April 2025). (ii) Polish Steel Association (HIPH), Polish Steel Industry--Statistical Yearbooks, annual issues 1997-2022; (iii) World Steel Association, Steel Statistical Yearbook 2022. Available online: [[https://worldsteel.org/publications/yearbook](https://worldsteel.org/publications/yearbook)]([https://worldsteel.org/publications/yearbook](https://worldsteel.org/publications/yearbook)) (accessed on 1 April 2025). Nominal values were deflated with the Polish industrial-price index and expressed in constant-2022 USD using National Bank of Poland average annual exchange rates (NBP Table A). This work was supported by the AGH University of Krakow. The authors declare no conflicts of interest. ## References

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