# Path Planning Strategy for Vehicle Navigation Based on User Habits
## 2 Materials and Methods
### Individual Quantitative Evaluation of Road Performance
#### 2.2.2 Synchronous Standard Quantitative Evaluation of Multi-Index Road Performance
\[\mu_{oj}^{i}=\exp\left(-\left(f_{oj}-a_{j}^{i}\right)^{2}/b_{j}^{i}\right) \tag{12}\]  
Then, we calculate the fitness of each rule by using a multiplicative operator in the fuzzy reasoning layer, as shown in Formula (13). \[\alpha_{o\tau}=\mu_{o1}^{i_{1}}\mu_{o2}^{i_{2}}\cdot\mu_{o3}^{i_{3}}\cdots\mu_ {ok}^{i_{k}}\left(\tau=1,2,\cdots,n^{k}\right) \tag{13}\]  
Finally, to avoid model turbulence caused by the order of magnitude of significant road influencing factors, we perform normalization in the anti-fuzzification layer, as shown in Formula (14). \[\overline{\alpha}_{o\tau}=\frac{\alpha_{o\tau}}{\sum\limits_{i=1}^{n^{k}} \alpha_{oi}} \tag{14}\]  
The post-part network consists of three sub-networks of the same structure for outputting fuzzy rules of time, economy, and comfort indexes. The input layer needs to be supplemented with a constant term, that is, input parameter 1 of the 0 th node, which is used to generate the constant term in the road performance level calculation result. The fuzzy inference layer calculates the consequent of each fuzzy rule, as shown in Formula (15). \[y_{o\tau}=p_{o0}^{i_{1}}+p_{o1}^{i_{2}}f_{o1}+p_{o2}^{i_{3}}f_{o2}+\cdots+p_{ ok}^{i_{k}}f_{ok} \tag{15}\]  
The output of the network is the weighted sum of the fuzzy rules, as shown in Formula (16). The weighting coefficient is the applicability of the rules and the result of the road performance level after the output-clarified process. \[\lambda_{o}=\overline{\alpha}_{o}\otimes y_{o}=\sum\limits_{\tau=1}^{n^{k}} \overline{\alpha}_{o\tau}y_{o\tau} \tag{16}\]  
According to the equilibrium characteristics of the weight distribution of a user's driving style, the overall characteristics of different path tendencies based on user choice is divided into three categories, as shown in the first four columns of Table 3, where \(c_{3}^{1},c_{3}^{2},c_{3}^{3}\), respectively, represent the number of effective features in user eigenvectors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Style Type** & \(\mathbf{\omega_{1}}\) & \(\mathbf{\omega_{m}}\) & \(\mathbf{\omega_{c}}\) & **Personal-Value \(\mathbf{\omega}\)** \\ \hline \multirow{3}{*}{\(c_{3}^{1}\)} & valid & — & — & \(\omega_{T}\lambda_{T}\) \\  & — & valid & — & \(\omega_{M}\lambda_{M}\) \\  & — & — & valid & \\ \hline \multirow{3}{*}{\(c_{3}^{2}\)} & valid & valid & — & \(\omega_{T}\lambda_{T}+\omega_{M}\lambda_{M}\) \\  & valid & — & valid & \(\omega_{T}\lambda_{T}+\omega_{M}\lambda_{M}\) \\  & valid & — & valid & \(\omega_{M}\lambda_{M}+\omega_{c}\lambda_{c}\) \\ \hline \multirow{3}{*}{\(c_{3}^{3}\)} & valid & valid & valid & \(\omega_{T}\lambda_{T}+\omega_{M}\lambda_{M}+\omega_{c}\lambda_{c}\) \\  & valid & — & valid & \(\omega_{T}\lambda_{T}+\omega_{M}\lambda_{M}+\omega_{c}\lambda_{c}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Driving style classification. In addition, to avoid excessive neutralization of the decision-making power of the high weight feature, and ensure the good consistency and universality of the quantitative and the actual evaluation results, an effective definition of the features is presented in Theorem 1. **Theorem 1**. : _For any vector element of the driving characteristics, if any of the following arbitrary conditions are satisfied, the element can be called an invalid feature; otherwise, it is an effective feature._  
(a) \(\omega_{0}>0.35\times\max\)_W_  
(b) \(\overline{\omega}_{o}>0.35\max\)_W_ and \(\omega_{o}\geq 0.5^{*}\)\(\overline{\omega}_{o}\), where \(\overline{\omega}_{o}=W-\max\)_W_ - \(\min\)_W_  
The personalized quantitative evaluation of roads is a weighted summation of the effective characteristics and the corresponding road standard quantification values.