## 3 Risk Perception and Fuzzy Decision-Based Driving Behavior Model
### Risk Quantification  
We successively introduced a risk field model framework that uniformly defines the risks posed by traffic elements, including moving vehicles and signal lights [8; 11]. The model posits that the risk generated by an element varies within a range of 0 to 1.  
For a vehicle, the risk value within its coverage area is equal to 1. At the same speed, as the relative distance from the vehicle increases, the risk in each direction decreases from 1 and gradually approaches 0. Conversely, at the same position, the risk increases with speed but never exceeds 1. Equations (1)-(6) provide the method for quantifying the risk of a moving vehicle in both the lateral and longitudinal directions, characterizing the risk imposed by vehicle \(k\) on \((x,y)\) as follows:  
\[\delta_{\text{vehicle},y,k}(y,t)=\frac{\beta_{\text{vehicle},k,y}\text{max}(|y-y_{k}|-\frac{l_{k}}{2},0)}{ \alpha_{\text{vehicle},k,y}\dot{y}_{k,y}(t)+1}, \tag{1}\]  
\[R_{vehicle,long,k}(y,t)=\frac{1}{\delta_{\text{vehicle},y,k}(y,t)+1}, \tag{2}\]  
\[\delta_{\text{vehicle},x}(x,t)=\frac{\beta_{\text{vehicle},k,x}\text{max}(|x-x_{k}|- \frac{W_{k}}{2},0)}{\alpha_{\text{vehicle},k,x}\dot{x}_{k,x}(t)+1}, \tag{3}\]  
\[R_{vehicle,lateral,k}(x,t)=\frac{1}{\delta_{\text{vehicle},x,k}(x,t)+1}, \tag{4}\]  
\[\delta_{\text{vehicle},k}(x,y,t)=\sqrt{\delta_{\text{vehicle},x,k}^{2}(x,t)+ \delta_{\text{vehicle},y,k}^{2}(y,t)}, \tag{5}\]  
\[R_{vehicle,k}(x,y,t)=\frac{1}{\delta_{\text{vehicle},k}(x,y,t)+1}, \tag{6}\]  
where \(\alpha_{vehicle,k,x}\) and \(\beta_{vehicle,k,x}\) represent the influence of the lateral speed and relative distance of the \(k\)-th vehicle on its lateral risk, respectively; \(\alpha_{vehicle,k,y}\) and \(\beta_{vehicle,k,y}\) represent the influence of the longitudinal speed and longitudinal relative distance, respectively, of the \(k\)-th vehicle on its longitudinal risk; \(\dot{x}_{k,x}(t)\) and \(\dot{y}_{k,y}(t)\) represent the lateral and longitudinal speeds, respectively, of the \(k\)-th vehicle at time \(t\); and \(L_{k}\) and \(W_{k}\) represent the length and width of the \(k\)-th vehicle, respectively.  
Figure 1 illustrates the risk generated by moving vehicles, exhibiting a spatial pattern that radiates outward from the vehicle coverage area and gradually decreases. The higher the speed of vehicles, the greater the risk imposed at a given location.  
Similarly, risks arising from traffic lights are regarded as risks arising from virtual static obstacles at the stop line. Equations (7)-(10) describe the risk field model of traffic lights, which is a form of multiplying time and spatial variation functions.  
\[\delta_{i}(x,y)=\sqrt{\left[\beta_{i,x}\cdot\text{max}(|x|-\frac{1}{2}\cdot d _{i},0)\right]^{2}+\left[\beta_{i,y}\cdot\text{max}(|y|-\frac{1}{2}\cdot l_{i },0)\right]^{2}}, \tag{7}\]\[R_{stopline,j}(x,y)=\frac{1}{\delta_{i}(x,y)+1},\] (8) \[R_{j}(t)=\begin{cases}0,&nT_{j}<t\leq nT_{j}+t_{j,g}\\ \frac{t-(nT_{j}+t_{j,g})}{t_{j,g}}e^{1.719[t-(nT_{j}+t_{j,g})-t_{j,g}]},&nT_{j} +t_{j,g}<t\leq nT_{j}+t_{j,g}+t_{j,g}\\ 1,&nT_{j}+t_{j,g}+t_{j,g}<t\leq nT_{j}+t_{j,g}+t_{j,g}+t_{j,g}\\ &R_{signal,j}(x,y,t)=R_{j}(t)\cdot R_{stopline,j}(x,y),\end{cases}\] (9) where \(l_{i}\) and \(d_{i}\) represent the length and width of the \(i\)-th stop line; \(\beta_{i,x}\) and \(\beta_{i,y}\) represent the influence degree of the relative spacing of the \(i\)-th stop line on the longitudinal and lateral risk; \(t_{j,g}\), \(t_{j,g}\), \(t_{j,r}\), \(T_{j}\) are the durations of green light, yellow light, red light, and signal cycle at the \(j\)-th traffic light; and \(n\) is a natural number.  
Visually, at a certain moment, the risks at signal lights present a spatial pattern with the stop line as the center, radiating outwardly and gradually decreasing, as shown in Figure 2.  
When the risks generated by different objects at the same time and space overlap, we take the largest value among them.