## 2 Methodology
### Probability Calculation for Specific Risk  
To determine the likelihood of unfavorable events, the outputs of the fuzzy logic model were combined with empirical probabilities derived from data from real projects [43; 44; 45]. The fuzzy model outputs provide the probability of occurrence for each risk group, while the empirical data offer conditional probabilities of specific adverse events within those groups. This integration enables a more thorough evaluation of risk. The probability of a specific risk \(Ri\) is calculated as follows:  
\[P(Ri)=P(RG)\cdot P(Ri\mid RG)+\alpha\cdot(1-P(RG)\cdot P(Ri\mid RG)) \tag{1}\]  
where:  
\(P(Ri)\)--probability of the specific risk \(Ri\) (within the risk group),  
\(P(RG)\)--probability of the corresponding risk group \(RG\) (calculated from the fuzzy model),  
\(P(Ri/RG)\)--normalized frequency of occurrence of specific risk \(Ri\) within its risk group \(RG\), calculated from empirical project data that are presented later in this paper (for major and secondary risk),  
\(\alpha\)--calibration factor (\(0\leq\alpha\leq 1\)). This equation was specifically developed for this study to integrate empirical risk occurrence rates with a probabilistic approach, serving as an input for the subsequent fuzzy-logic-based risk assessment. The introduction of the calibration factor \(\alpha\) was necessary to enhance the adaptability of the proposed model. Given the inherent uncertainty in empirical data and probabilistic estimates, \(\alpha\) serves as a weighting parameter that adjusts for discrepancies between model calculations and observed real-world occurrences. This approach ensures that the model remains applicable across varying data conditions, allowing for a more precise quantification of risk. Unlike purely data driven statistical methods, which may struggle with limited datasets, or expert-based approaches, which can be subjective, the inclusion of \(\alpha\) provides a balanced integration of both sources. Table 2 provides recommended \(\alpha\) values, adjusted for varying data confidence and uncertainty levels. The calibration factor \(\alpha\) is not required when there is high confidence in the empirical probabilities and initial probabilistic estimates, with minimal uncertainty and fully representative data for the future project. The probabilities of occurrence for individual risks have been established based on previous research, empirical project data, and the applied formulas. These probabilities, covering both major and secondary risks, are comprehensively presented in Table 3. This table provides a detailed overview of the likelihood of each risk, serving as a crucial reference for further analysis and decision making in the context of risk management. Once the probabilities of individual risks are calculated and validated, the next step involves analyzing and prioritizing these risks for proactive risk management. This step guarantees that resources are distributed effectively to mitigate the most critical risks. All \begin{table}
\begin{tabular}{c c} \hline \hline \(\alpha\) & **Description** \\ \hline
0.00–0.25 & Low uncertainty: high confidence in the fuzzy model and empirical data. \\ \hline
0.25–0.50 & Moderate uncertainty: balances model predictions with potential external factors. \\ \hline
0.50–0.75 & Significant uncertainty: additional correction for external or unknown influences is needed. \\ \hline
0.75–1.00 & High uncertainty: relies more on correction than model results. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Suggested values for calibration factor (\(\alpha\)) based on data confidence and uncertainty levels. calculated risks are ranked in descending order based on their probability of occurrence. This provides a clear understanding of which risks are most likely to affect the project.