# Research on a Comfort Evaluation Model for High-Speed Trains Based on Variable Weight Theory
## 3 Establishing the Model of Evaluating
### High-Speed Train Comfort Index Classification  
According to the comfort evaluation index system of high-speed train, the comfort degree is divided into five grades: grade I, grade II, grade III, grade IV, and grade V. Comfort level progresses from Class V to Class I on high-speed trains. Grade V indicates that passengers feel very uncomfortable during the ride due to poor physical, physiological, and psychological stimuli. Grade I indicates that passengers feel very good stimuli regarding physical, physiological, and psychological aspects during the ride, making people feel very comfortable. The specific classification is shown in Table 1. Referring to the relevant evaluation criteria and norms in China, the evaluation criteria of some indicators can be obtained in Table 2.  
We establish a membership function \(S(x)\) based on the comfort levels in Table 1. Grade I membership function \(S_{1}(x)\) is shown as follows in Equation (5). II-IV level membership function \(S_{i}(x)\) general formula is shown as follows in Equation (6).  
\[S_{1}(x)=\left\{\begin{array}{ll}1&x\geq 100\\ \frac{x-90}{100-90}&90\leq x<100\\ 0&x<90\end{array}\right. \tag{5}\]  
\[S_{i}(x)=\left\{\begin{array}{ll}0&x\geq a_{1}\ or\ x<a_{3}\\ \frac{a_{2}-x}{a_{1}-a_{2}}&a_{2}\leq x<a_{1}\\ \frac{x-a_{3}}{a_{2}-a_{3}}&a_{3}\leq x<a_{2}\end{array}\right. \tag{6}\]  
Among them, \(a_{1},\ a_{2},\ a_{3}\) are the endpoint values of the evaluation interval, and different values are taken as the evaluation level changes, as follows:  
\[\left\{\begin{array}{ll}i=2&a_{1}=100,\ a_{2}=90,\ a_{3}=70\\ i=3&a_{1}=90,\ a_{2}=70,\ a_{3}=50\\ i=4&a_{1}=70,\ a_{2}=50,\ a_{3}=30\end{array}\right.\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Comfort Grade** & **I** & **II** & **III** & **IV** & **V** \\ \hline Score Values & [90,100] & [70,90) & [50,70) & [30,50) & [0,30) \\ State Evaluation & Very Comfortable & Comfortable & Nearly Comfortable & Uncomfortable & Very Uncomfortable \\ \hline \end{tabular}
\end{table}
Table 1: Comfort Classification.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Index** & & & & **Evaluation Criterion** & \\ \hline Riding Steadiness & W \(\leq\) 2.5 (Excellent) & & 2.5 \(<\) W \(\leq\) 2.75 (Good) & & 2.75 \(<\) W \(\leq\) 3.0 (Qualified) \\ Riding Comfort & N \(<\) 1 & 1\(\leq\) N \(<\) 2 & 2 \(\leq\) N \(<\) 4 & 4 \(\leq\) N \(<\) 5 & N \(\geq\) 5 \\ Transverse Acceleration & & (Very comfortable) & (Comfortable) & (Nearly comfortable) & (Uncomfortable) & (Very uncomfortable) \\ Vertical Acceleration & & & \(<\)2.5 m/s\({}^{2}\) & & \\ Passenger Room Noise & & & \(\leq\)65 dB(A) & & \\ Driver Room Noise & & & \(\leq\)76 dB(A) & & \\ Passing Platform Noise & & & \(\leq\)78 dB(A) & & \\ \hline \end{tabular}
\end{table}
Table 2: Evaluation Criteria for Some Indicators.  
Grade V membership function \(S_{5}(x)\) is as follows:  
\[S_{1}(x)=\left\{\begin{array}{ll}0&x\geq 50\\ \frac{50-x}{50-30}&30\leq x<50\\ 1&0\leq x<30\end{array}\right. \tag{7}\]  
According to the membership function established above and the calculated value of the index, the membership degree of each index value belonging to grade I, II, III, IV, and V can be calculated in turn. According to the principle of fuzzy comprehensive score and maximum membership degree, the final comfort evaluation result can be determined. At the same time, the corresponding indexes can be analyzed and discussed according to the membership degree of the obtained indexes, which provides theoretical and data support for the comparison of the advantages and disadvantages of the evaluation in the two states of variable weight and constant weight.  
The membership degree of the calculated \(m\) indexes about \(n\) grade intervals is composed of the membership degree matrix \(R\):  
\[R=\left[\begin{array}{cccc}r_{11}&r_{12}&\cdots&r_{1n}\\ r_{12}&r_{22}&\cdots&r_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ r_{m1}&r_{m2}&\cdots&r_{mn}\end{array}\right] \tag{8}\]