## 2 Multi-State Lane-Changing Decision-Making System
### Fuzzy Control Rules and Defuzzification  
The control rules in this system mainly include the following two points: (1) As \(v_{subj}\) and \(E_{ra}\) increase, the lane-changing maneuver should be initiated earlier, i.e., \(E_{steer}\) should increase. Also, as \(\mu\) decreases, the lane changes should be advanced, and \(E_{steer}\) should increase. (2) When the input variable \(v_{subj}\) is large or \(\mu\) is small, the output variable \(E_{steer}\) is more sensitive to changes. Fuzzy control rules are the core component of the multi-state lane-changing decision-making system. They provide a logical basis for the lane-changing decision-making of intelligent semi-trailers based on the relationship between different input variables. Through careful consideration of various influencing factors, these rules can determine whether and when a vehicle should change lanes. The following is a detailed introduction to the fuzzy control rules formulated according to different input variables. These rules are summarized in Tables 1 and 2, respectively. Table 1 shows the fuzzy inference rules of the first-level fuzzy inference system (FIS1). In it, rows represent different fuzzy sets of the vehicle's own speed \(\widetilde{v}_{subj}\), and columns represent different fuzzy sets of the road adhesion coefficient \(\mu\). The element \(E_{r}\) in the table is the fuzzy set of the collision risk factor inferred from \(\mu\) and \(\widetilde{v}_{subj}\). For example, when \(\mu\) is NB (Negative Big) and \(\widetilde{v}_{subj}\) is NB (Negative Big), \(E_{r}\) is ZO (Zero). This indicates that, in this case, the collision risk factor is at a relatively low level. Table 2 shows the fuzzy inference rules of the second-level fuzzy inference system (FIS2). In it, rows represent different fuzzy sets of risk avoidance factor \(E_{ra}\), and columns represent different fuzzy sets of risk factor \(E_{r}\). The element \(E_{steer}\) in the table is the fuzzy set of the lane-changing decision factor inferred from \(E_{ra}\) and \(E_{r}\). For example, when \(E_{ra}\) is PB (Positive Big) and \(E_{r}\) is PS (Positive Small), \(E_{steer}\) is PB (Positive Big). At this time, \(E_{steer}\) is much greater than 0.5, and the vehicle will be more inclined to change lanes to avoid potential risks or obtain more favorable driving conditions. In this way, the fuzzy \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(E_{r}\) & & & & \(\widetilde{v}_{subj}\) & \\ \cline{3-6}  & & NB & **NS** & **ZO** & **PS** & **PB** \\ \hline  & NB & ZO & PS & PS & PB & PB \\  & NS & NS & ZO & PS & PB & PB \\ \(\mu\) & ZO & NS & NS & ZO & PS & PS \\  & PS & NB & NS & NS & ZO & ZO \\  & PB & NB & NB & NS & NS & ZO \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fuzzy inference rules for FIS1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & \(E_{ra}\) & & \\ \cline{3-6}  & & **NB** & **NS** & **ZO** & **PS** & **PB** \\ \hline  & NB & NB & NB & NS & ZO & ZO \\  & NS & NB & NS & ZO & PS & PS \\ \(E_{r}\) & ZO & NS & ZO & ZO & PS & PS \\  & PS & ZO & ZO & PS & PS & PB \\  & PB & ZO & PS & PS & PB & PB \\ \hline \hline \end{tabular} Where ZO represents zero, PS represents positive small, PB represents positive big. NS represents negative small, and NB represents negative big.  
\end{table} 
Table 2: Fuzzy inference rules for FIS2. control rules achieve effective control over the lane-changing decision-making of intelligent semi-trailers by comprehensively processing multiple input variables. On the other hand, compared with other defuzzification methods, the center of gravity method offers distinct advantages. It considers the entire distribution of the fuzzy set, considering both the membership degrees of all elements within the set and their corresponding output values. For example, in our lane-changing decision-making system, when calculating the lane-changing decision coefficient \(E_{ster}\), the center of gravity method does not just focus on individual high-membership elements.