## 5 Case Study
### Comparisons and Discussions  
To verify the effectiveness and advantages of the proposed PUL-DUCG model, a comparative analysis with the fuzzy-Bayesian network (FBN) [48], the DUCG [1], the intuitionistic fuzzy DUCG (IFDUCG) [20], and the cloud model DUCG (CDUCG) [21] is conducted in this section. The reasoning results of the listed methods are presented in Table 6. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{5}{c}{**Results Given by Model**} & \multirow{2}{*}{**Actual Result**} & \multirow{2}{*}{**Consistency**} \\ \cline{2-2} \cline{5-6}  & **FBN** & **DUCG** & **IFDUCG** & **CDUCG** & **PUL-DUCG** & \\ \hline
1 & AH Low & SV Low & AH Low & AH Low & AH Low & AH Low & Y \\  
L High & EL High & EL High & EL High & EL High & EL High & Y \\
20 & EL High & EL High & EL High & EL High & EL High & EL High & Y \\ Accuracy & 91.10\% & 93.30\% & 95.60\% & 95.60\% & 95.60\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The reasoning results according to the listed methods. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Target Child Events**} & \(SP_{i}\) & \(SN_{i}\) & \(\overline{SP_{i}}\) & \(\overline{SN_{i}}\) & \(AS_{i}\) & **Ranking** \\ \hline \(B_{11}\mid X_{43}X_{51}X_{62}X_{71}\) & 0.000 & 0.021 & 0.000 & 0.925 & 0.462 & 6 \\ \(B_{12}\mid X_{43}X_{51}X_{62}X_{71}\) & 0.122 & 0.000 & 0.411 & 1  
First, the accuracy of PUL-DUCG was the same as the CDUCG, which was 95.6%. This confirms that the proposed PUL-DUCG model is effective for root cause analysis. Furthermore, this method has advantages over the compared methods. Since the DUCG model ignores uncertain information, it is likely to obtain inaccurate reasoning results in complex situations. Compared with the IFDUCG, the proposed model integrates the advantages of PULSs and linguistic variables. Thus, the PUL-DUCG has a more powerful representation ability than the IFDUCG model to handle the fuzziness and vulnerability information in practical situations. In addition, the TOPSIS method in [19] is used to find the root event with a maximum posteriori probability, whereas the proposed model determines the probability ranking of events by the EDAS method. The TOPSIS method did not consider the weights of events, which are not in line with the real situations. Moreover, the CDUCG and the IFDUCG have limitations in handling the inconsistent cognition of experts. Therefore, the knowledge parameters acquired by the proposed PUL-DUCG model are more credible because they are based on a preference modifying-based method. From Table 6, it can be seen that the accuracy of the FBN method is lower than the DUCG. This is mainly because the FBN can only depict the quantitative evaluation information. Within the circumstance of a qualitative depiction, the FBN is unable to describe fuzzy information. In contrast, the PUL-DUCG model is proposed based on the PULSs, which can effectively describe both qualitative and quantitative information. Moreover, the FBN requires a lot of statistics and empirical information to express the precise conditional probability between events. In comparison, the PUL-DUCG permits inadequate information representation, which could significantly diminish the workload and trouble of setting up an information base. From the above comparison analysis, it can be found that more accurate and reasonable knowledge acquisition and reasoning results can be determined by the proposed PUL-DUCG model. Compared with the existing DUCG methods, the advantages of the developed PUL-DUCG model are summarized as follows:  
1. The model used the membership degree and non-membership degree of PULSs to express the fuzzy knowledge of experts. The fuzziness of initial information will be retained, which can avoid information loss and distortion in the process of causal analysis. Hence, the proposed model is more capable of representing and reasoning uncertain information. 2.