# An Assessment Model for Air Passenger Risk Classification
## 2 Assessment Model for Air Passenger Risk Classification
### Improved Fuzzy Comprehensive Evaluation Method
#### 2.3.4 Improved Fuzzy Relation Matrices
Similarly, in the interval of 14-18 years old, the fitting results of \(y_{1}\) and \(y_{2}\) are shown in Figure 2, where \(y_{1}=0.0071x^{2}-0.1786x+1.1943\), \(y_{2}=-0.0071x^{2}+0.2786x-2.3943\). Then \(y_{3}=-0.1x+2.2\) is calculated by Equation (7). In the interval of 19-30 years old, the fitting results of \(y_{1}\) and \(y_{2}\) are shown in Figure 3, where \(y_{1}=0.0018x^{2}-0.0607x+0.7943\), \(y_{2}=0.3\). Then \(y_{3}=-0.0018x^{2}+0.0607x-0.0943\) is calculated by Equation (7). Figure 1: Single factor evaluation for under 14 years old. Figure 2: Single factor evaluation for 14-18 years old. In the interval of 31-50 years old, the fitting results of \(y_{1}\) and \(y_{2}\) are shown in Figure 4, where \(y_{1}=-0.012x+0.98\), \(y_{2}=-0.0009x^{2}+0.0746x-1.2686\). Then \(y_{3}=0.0009x^{2}-0.0626x\) + 1.2886 is calculated by Equation (7). In the interval of 51-60 years old, the fitting results of \(y_{1}\) and \(y_{2}\) are shown in Figure 5, where \(y_{1}=-0.0018x^{2}+0.175x-3.8657\), \(y_{2}=0.3\). Then \(y_{3}=0.0018x^{2}-0.175x+4.5657\) is calculated by Equation (7). Figure 4: Single factor evaluation for 31-50 years old. Figure 3: Single factor evaluation for 19-30 years old. In the interval of over 60 years old, the fitting results of \(y_{1}\) and \(y_{2}\) are shown in Figure 6, where \(y_{1}=0.0003x^{2}-0.0489x+2.1829,y_{2}=-0.0006x^{2}+0.0777x-2.3657\). Then \(y_{3}=0.0003x^{2}-0.0288x+1.182\) is calculated by Equation (7). The single factor evaluation vectors of other second-level indexes can be determined by the same method. Figures of the fitting functions corresponding to the single factor evaluation vectors of the other continuous second-level indexes except age are included in Appendix C. The results are shown in Tables 9-13, in which the amount of aviation insurance is divided according to 200,000 yuan each, the time of buying tickets is in days, and 12 h before departure is counted as 0.5 days. Then, the fuzzy relation matrix \(R_{i}\) of the first-level indexes is established. In the actual calculation, each element in the single factor evaluation vector can be in [0, 1] by rounding, and the sum is 1. Figure 5: Single factor evaluation for 51–60 years old. Figure 6: Single factor evaluation for over 60 years old. \begin{table}
\begin{tabular}{c c c} \hline
**Second-Level Indexes** & **Dimension** & **Single Factor Evaluation Vectors** \\ \hline \multicolumn{3}{c}{Administrative organ or institution} & \([0.2,0.3,0.5]\) \\ Occupation \(u_{21}\) & State-owned enterprise & \([0.2,0.4,0.4]\) \\  & Private enterprise and others & \([0.3,0.5,0.2]\) \\  & Unemployment & \([0.6,0.3,0.1]\) \\ Place of residence \(u_{22}\) & Areas without terrorist attacks in \(x\) years & \([0.0014x^{2}-0.0642x+0.7532,\) \\  & Areas without terrorist attacks in \(x\) years & \(-0.0014x^{2}+0.0146x+0.2933,\) \\  & & \(0.0496x-0.0465\) \\  & Islam & \([0.5,0.4,0.1]\) \\  & Christianity & \([0.4,0.4,0.2]\) \\ Religious belief \(u_{23}\) & Buddhism & \([0.3,0.5,0.2]\) \\  & Others & \([0.3,0.4,0.3]\) \\  & None & \([0.2,0.3,0.5]\) \\  & Married with children & \([0.2,0.3,0.5]\) \\  & Married without children & \([0.3,0.3,0.4]\) \\ Marital status \(u_{24}\) & Unmarried & \([0.3,0.4,0.3]\) \\  & Divorced with children & \([0.3,0.5,0.2]\) \\  & Divorced without children & \([0.5,0.3,0.2]\) \\  & Bad & \([0.2,0.3,0.5]\) \\ State of health \(u_{25}\) & General & \([0.4,0.3,0.3]\) \\  & Good & \([0.5,0.3,0.2]\) \\ \hline \end{tabular}
\end{table} 
Table 10: Single factor evaluation of personal status indexes.