## 3 Results
### Case Study of Sugeno Fuzzy Logic System
Table 4 presents the data for the probabilities of major risk groups from the real system, as well as the corresponding simulated indicators obtained as outputs from the fuzzy logic system F1, along with the associated deviations. Figure 2: Structure of the developed fuzzy inference systems. Figure 3: Input variables K1, K2, and K3 with 25 membership functions. Note: Different colors designate different membership functions. It is evident that the highest average deviation occurs in the \"External\" risk category, which may indicate greater variability or the model's lower ability to accurately predict this category. On the other hand, the smallest deviation is observed in the \"Design\" risk category, suggesting that the model approximates this group well. Additionally, the \"Contractor\" and \"Engineer\" risk categories exhibit similar, slightly more significant deviations, while the other categories remain more moderate. The overall average deviation across all categories indicates relatively solid model accuracy but with room for improvement, especially in categories with higher deviations. Table 5 presents the data for the probabilities of secondary risk groups from the real system, as well as the corresponding simulated indicators obtained as outputs from the fuzzy logic system F2, along with the associated deviations. In this case, evident improvements in accuracy can be observed across almost all risk categories; however, there is still room for further enhancements, particularly in the assessment of \"Project\" and \"Engineer\" risks. The testing results of the fuzzy logic systems F1 and F2 demonstrate varying levels of accuracy in estimating the probabilities for different risk groups. However, as observed in the heatmap (Figure 4), the deviations for certain risk groups are at a similar or comparable level. The overall average deviation for both fuzzy logic systems is less than 10%. The difference in accuracy between these fuzzy systems is a result of the differing structures of the training datasets. At the planning and development stage, this level of accuracy meets the requirements. The further optimization of membership functions and rules could help reduce deviations, particularly for categories with larger errors, thereby enhancing both systems for specific applications. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Risk Group**} & \multicolumn{3}{c}{**From a Real Project**} & \multicolumn{3}{c}{**From FIS F1**} & \multirow{2}{*}{**Average**} \\ \cline{2-2} \cline{5-8}  & **Project 1** & **Project 2** & **Project 3** & **Project 1** & **Project 2** & **Project 3** & **Deviation [\%]** \\ \hline Design & 0.7468 & 0.7704 & 0.7888 & 0.7493 & 0.8016 & 0.7841 & 1.6601 \\ \hline External & 0.1 & 0.0925 & 0.0677 & 0.1248 & 0.0894 & 0.0794 & 15.1445 \\ \hline Resource & 0.019 & 0.0231 & 0.0264 & 0.0161 & 0.0219 & 0.026 & 7.3244 \\ \hline Employer & 0.0327 & 0.0308 & 0.0338 & 0.0312 & 0.0335 & 0.034 & 4.6484 \\ \hline Contractor & 0.0065 & 0.0094 & 0.0039 & 0.005 & 0.0087 & 0.0039 & 10.1746 \\ \hline Engineer & 0.0023 & 0.0017 & 0.0027 & 0.0027 & 0.0016 & 0.0025 & 10.2270 \\ \hline Project & 0.0926 & 0.052 & 0.0767 & 0.0937 & 0.0435 & 0.0862 & 9.9733 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Testing results for the fuzzy logic system F1 with average deviation.