# A Path Recommendation Method Considering Individual Driving Preferences
## 3 A Path Satisfaction Model Considering Individual Preferences
### Path Satisfaction Model Based on Improved AHP Algorithm
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Target Layer A** & **Criterion Layer B1** & **Criterion Layer B2** \\ \hline \multirow{8}{*}{A path satisfaction} & \multirow{8}{*}{\(B11\) stability of travel time (STT)} & \(B21\) path travel time (PTT) \\  & & \(B22\) path length (PL) \\  & & \(B25\) number of path intersections (PI) \\ \cline{2-3}  & \multirow{2}{*}{\(B12\) historical inertia (HI)} & \(B22\) path length (PL) \\  & & \(B28\) historical path similarity (HPS) \\ \cline{2-3}  & & \(B23\) number of path lanes (PLN) \\ \cline{2-3}  & \multirow{2}{*}{\(B13\) path difficulty (PD)} & \(B24\) path turning index (PTI) \\  & & \(B25\) number of path intersections (PI) \\  & & \(B27\) maximum path density (PMK) \\ \hline \multirow{2}{*}{\(B14\) traffic status (TS)} & \multirow{2}{*}{\(B26\) average path density (PAK) \(B27\) maximum path density (PMK)} \\ \cline{2-3}  & & \\ \end{tabular}
\end{table} 
Table 3: Main connection relationships for indicators in each layer. where \(a_{ij}\) is determined according to the relative importance of indicator \(B1i\) when compared to indicator \(B1j\). To determine the value of \(a_{ij}\), we introduced an importance score \(value\):  
\[a_{ij}=\left\{ \begin{array}{l}-1,value_{i}<value_{j}\\ 0,value_{i}=value_{j}\\ 1,value_{i}>value_{j}\end{array} .\right. \tag{21}\]  
The importance rating \(value\) of each indicator is crucial, as it determines the strength of importance and the weight given by drivers to that particular factor, ultimately affecting their overall satisfaction with the chosen path. Therefore, it is essential to accurately calculate the importance rating of each indicator which, in turn, affects the accuracy of the weight values assigned to the lower-layer indicators. The calculation methods for the \(value\) of the lower-layer indicators vary across different layers. The particular calculation methods are detailed below. 1. _value_ of indicators from criterion layer B1 affecting target layer \(A\)  
The indicators that were compared from criterion layer \(B1\) were \(B11\) STT, \(B12\) HI, \(B13\) PD, and \(B14\) TS. Referring to Equations (11)-(15), the importance score for \(B11\) temporal stability is calculated as  
\[value_{B11}=CT_{7}(t_{arrive}^{max}-t_{arrive}<\gamma\text{ }or\text{ }T_{L}^{max}-T_{arrive}<\gamma). \tag{22}\]  
Similarly, the calculation methods for the importance scores \(value_{B12}\), \(value_{B13}\), and \(value_{B14}\) of \(B12\) HI, \(B13\) PD, and \(B14\) TS are calculated as follows:  
\[value_{B12}=CT_{7}(L=L_{his}), \tag{23}\]  
\[value_{B13}=CT_{7}(p(diff)<50), \tag{24}\]  
\[value_{B14}=CT_{7}(0.5(p(K_{L}^{max})+p(K_{L}))<50). \tag{25}\]  
2. _value_ of indicators from criterion layer \(B2\) affecting criterion layer \(B1\)  
To calculate the \(value\) for each indicator in criterion layer B2, the following indicators were considered: \(B21\) PTT, \(B22\) PL, \(B23\) PLN, \(B24\) PTI, \(B25\) PI, \(B26\) PAK, \(B27\) PMK, and \(B28\) HPS. Using \(p(B2i)\) to represent the percentile value of the mean of indicator \(B2i\) in a driver's 7-day travel trajectories within the OD, among all the corresponding indicators of the trajectories within the same OD, the calculation method for the importance score of each indicator in criterion layer \(B2\) is as follows:  
\[value_{B2i}=\left\{ \begin{array}{l}100-p(B2i),i=1,2,4,5,6,7\\ p(B2i),i=3,8\end{array} \right.. \tag{26}\]  
Among the  
importance scores being 10, 20, 0, 0, 0, 50, 0, 0, and 0. By performing further calculations using Equation (21), the comparison matrix for indicator B11 can be obtained, as follows: \[B11= \begin{bmatrix}0&-1&1&1&-1&1&1&1\\ 1&0&1&1&-1&1&1&1\\ -1&-1&0&0&-1&0&0&0\\ -1&-1&0&0&-1&0&0&0\\ 1&1&1&1&0&1&1&1\\ -1&-1&0&0&-1&0&0&0\\ -1&-1&0&0&-1&0&0&0\\ \end{bmatrix} .\] (27)
3. _value_ of indicators from alternative layer \(C\) affecting criterion layer \(B2\)  
The evaluation of indicators from criterion layer \(B2\) entails assessing the indicators associated with each path in alternative layer \(C\).