## 5 Case Study and Discussion
### Experiment Results and Discussion  
According to the data in Tables 6 and 9, the empirical data for multi-factor diagnosis with fuzzy comprehensive evaluation are obtained as shown in Table 10, and the corresponding membership degrees as shown in Equation (45) are calculated by the approach in Section 4.2. Here, the fuzzy factor set and fuzzy classification set are expressed as follows:  
\[X=(\text{''sr''},\text{ ''mc1''},\text{ ''c1''},\text{ ''de1''},\text{ ''de2''},\text{ ''de3''},\text{ ''de4''},\text{ ''bh''},\text{ ''imp''},\text{ ''hel''}) \tag{43}\]  
\[Y= (\text{''om11''},\text{ ''om13''},\text{ ''mat''},\text{ ''mt''},\text{ ''pw11''},\text{ ''pw13''},\text{ ''pw53''},\text{ ''cm1''}, \tag{44}\] \[\text{''cm2''},\text{ ''ht1''},\text{ ''ht2''},\text{ ''tem1''},\text{ ''tem2''})\]  
Figure 11: Evolutionary curves of the average value of the best fitnesses. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline Index & 1 & **2** & 5 & 11 & **14** & 15 & **16** & **17** & **19** & **21** \\ \hline _S(PG, KPG)_ & 0.79 & **0.84** & 0.79 & 0.79 & **0.82** & 0.79 & **0.82** & **0.80** & **0.80** & **0.82** \\ \hline Index & **25** & **26** & **27** & **32** & **33** & **35** & **36** & **37** & **38** & \\ \hline _S(PG, KPG)_ & **0.81** & **0.80** & **0.80** & **0.82** & **0.82** & **0.82** & **0.83** & **0.80** & **0.82** & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Synthetic similarities between the target gene and related knowledge genes (data with bold fonts are the indexes and synthetic similarities of available knowledge genes.). \[R=\left[ \begin{array}{cccccccccccccccc}0.11&0.09&0.06&0.14&0.11&0.06&0.03&0.06&0.11 &0.11&0&0.09&0.03\\ 0.03&0.1&0.23&0.1&0.03&0.03&0.1&0.32&0&0&0&0.06&0\\ 0&0.09&0.14&0.14&0.09&0.14&0.14&0.14&0&0.04&0.04&0.04\\ 0&0&0.17&0.32&0&0&0.17&0.17&0&0&0&0.17&0\\ 0&0.25&0&0&0.25&0.5&0&0&0&0&0&0&0\\ 0.14&0.29&0&0&0.14&0&0&0&0&0&0&0.29&0\\ 0.23&0.11&0.11&0.22&0.22&0&0&0.11&0&0&0&0&0\\ 0.09&0.14&0&0&0.09&0.14&0.09&0.04&0.09&0.09&0&0.14&0.09\\ 0.04&0.04&0.13&0.04&0.08&0.04&0&0.13&0.37&0.13&0&0&0\\ 0.03&0.03&0.15&0.09&0&0.03&0.15&0.12&0.06&0.19&0&0.06&0.09\\ \end{array} \right] \tag{45}\]  
According to the information of the target gene and the definition of Equation (32), the defects set is encoded as  
\[DV=(3,1,0,0,0,0,0,0,0) \tag{46}\]  
where each value in \(DV\) represents the frequency of a defect appeared in the target gene. For instance, the first \"3\" indicates that \"sr\" appears three times in the target gene, the first \"1\" indicates that \"mc1\" appears one time in the target gene, and so on. According to Equations (36) and (37), the result set is calculated by  
\[RV=DV\cdot R=(0.09,0.09,0.1,0.13,0.09,0.05,0.05,0.12,0.09,0.09,0,0.08,0.02) \tag{47}\]  
where each value in \(RV\) represents the degree of correlation between a cause and the defects in the target gene. For instance, the first \"0.09\" indicates that the possibility of attributing the defects to \"om11\" is 0.09, the second \"0.09\" indicates that the possibility of attributing the defects to \"om13\" is also 0.09, and so on. Here, b = 1, then 1/b = 0.08. According to the rule defined in the last paragraph of Section 4.2 and the result set as shown in equation (47), it can be easily observed that the values of \(rv_{1}\), \(rv_{2}\), \(rv_{3}\), \(rv_{4}\), \(rv_{5}\), \(rv_{8}\), \(rv_{9}\), \(rv_{10}\), and \(rv_{12}\) meet the rule. Therefore, \"om11\", \"om13\", \"mat\", \"mt\", \"pw11\", \"cm1\", \"cm2\", \"ht1\" and \"tem1\" are the possible causes of defects of the target gene. According to the data of the target gene as shown in Figure 5, the possible causes in the experiment of this study are analyzed as shown in Table 11.