\pagestyle{empty}

\section*{Appendices}
In this section, we provide the detailed formulas of membership functions and the extracted fuzzy rules in the paper.

\subsubsection*{Fuzzy Numbers}

The membership functions of the fuzzy numbers with respect to collision time are given as follows.

\begin{equation}\label{E_member}
\nonumber
  E(\Delta T^c)=\left\{
\begin{array}{ccl}
1, & & {0 \leq \Delta T^c \leq t_1}\\
0, & & {\Delta T^c > t_1}
\end{array} \right.
\end{equation}

\begin{equation}\label{D_member}
\nonumber
  D(\Delta T^c)=\left\{
\begin{array}{ccl}
-\frac{\Delta T^c-t_2}{t_2-t_1}, & & {t_1 \leq \Delta T^c \leq t_2}\\
0, & & {\text{others}}
\end{array} \right.
\end{equation}

\begin{equation}\label{A_member}
\nonumber
  S(\Delta T^c)=\left\{
\begin{array}{ccl}
0, & & {\Delta T^c < t_1}\\
\frac{\Delta T^c-t_1}{t_2-t_1}, & & {t_1 \leq\Delta T^c \leq t_2}\\
1, & & {\Delta T^c > t_2}
\end{array} \right.
\end{equation}


The membership functions of the fuzzy numbers with respect to the speed ratio are given as follows.

\begin{equation}\label{MA_member}
\nonumber
  MA(\alpha)=\left\{
\begin{array}{ccl}
0, & & {0\leq \alpha < \alpha_0}\\
\frac{1}{1-\alpha_0} \alpha - \frac{\alpha_0}{1-\alpha_0}, & & {\alpha_0 \leq \alpha \leq 1}
\end{array} \right.
\end{equation}

\begin{equation}\label{DS_member}
\nonumber
  DS(\alpha)=\left\{
\begin{array}{ccl}
\frac{1}{\alpha_0}\alpha, & & {0 \leq \alpha < \alpha_0}\\
\frac{1}{\alpha_0-1}(\alpha-1), & & {\alpha_0 \leq \alpha \leq 1}
\end{array} \right.
\end{equation}

\begin{equation}\label{DL_member}
\nonumber
  DL(\alpha)=\left\{
\begin{array}{ccl}
-\frac{1}{\alpha_0}\alpha+1, & & {0 \leq \alpha \leq  \alpha_0}\\
0, & & {\alpha_0 < \alpha \leq 1}
\end{array} \right.
\end{equation}

\begin{equation}\label{SE_member}
\nonumber
SU(\alpha)=\left\{
\begin{array}{ccl}
1, & & {\alpha =0}\\
0, & & {\text{others}}
\end{array} \right.
\end{equation}

The membership functions of the fuzzy numbers with respect to the orientation change are given as follows.
\begin{equation}\label{VS_member}
\nonumber
  VS(\Delta \theta)=\left\{
\begin{array}{ccl}
-\frac{8}{\pi} \Delta \theta + 1, & & {0 \leq \Delta \theta \leq \frac{\pi}{8}}\\
0, & & {\Delta \theta > \frac{\pi}{8}}
\end{array} \right.
\end{equation}

\begin{equation}\label{S_member}
\nonumber
  S(\Delta \theta)=\left\{
\begin{array}{ccl}
\frac{8}{\pi} \Delta \theta, & & {0 \leq \Delta \theta \leq \frac{\pi}{8}}\\
-\frac{8}{\pi} \Delta \theta + 2, & & { \frac{\pi}{8} < \Delta \theta \leq \frac{\pi}{4}} \\
0, & & {\Delta \theta > \frac{\pi}{4}}
\end{array} \right.
\end{equation}


\begin{equation}\label{M_member}
\nonumber
  M(\Delta \theta)=\left\{
\begin{array}{ccl}
\frac{8}{\pi} \Delta \theta -1, & & {\frac{\pi}{8} \leq \Delta \theta \leq \frac{\pi}{4}}\\
-\frac{8}{\pi} \Delta \theta + 3, & & { \frac{\pi}{4} < \Delta \theta \leq \frac{3\pi}{8}} \\
0, & & {\text{others}}
\end{array} \right.
\end{equation}


\begin{equation}\label{L_member}
\nonumber
  L(\Delta \theta)=\left\{
\begin{array}{ccl}
\frac{8}{\pi} \Delta \theta -2, & & {\frac{\pi}{4} \leq \Delta \theta \leq \frac{3\pi}{8}}\\
-\frac{8}{\pi} \Delta \theta + 4, & & { \frac{3\pi}{8} < \Delta \theta \leq \frac{\pi}{2}} \\
0, & & {\text{others}}
\end{array} \right.
\end{equation}


\begin{equation}\label{VL_member}
\nonumber
  VL(\Delta \theta)=\left\{
\begin{array}{ccl}
\frac{8}{\pi} \Delta \theta -3, & & {\frac{3\pi}{8} \leq \Delta \theta \leq \frac{\pi}{2}}\\
0, & & {\Delta \theta < \frac{3\pi}{8}}
\end{array} \right.
\end{equation}




\subsubsection*{Extracted Fuzzy Rules}

For the scenarios where there is only one intruder, the final fuzzy rules are:

\begin{enumerate}[label=\arabic*.]
  \item \lrule{D}{DL}{VS}
  \item \lrule{S}{DS}{S}
  \item \frule{D}{DL}{S}
  \item \frule{S}{MA}{M}
  \item \rrule{D}{DL}{VS}
  \item \rrule{S}{DL}{L}
\end{enumerate}

For the scenarios where there are two intruders in two of the three regions, the generated 12 fuzzy rules are:
\begin{enumerate}[label=\arabic*.]
\setcounter{enumi}{6}
  \item \lfrule{D}{D}{DL}{S}
  \item \lfrule{D}{S}{DL}{VS}
  \item \lfrule{S}{D}{DS}{S}
  \item \lfrule{S}{S}{MA}{VS}
\end{enumerate}
\begin{enumerate}[label=\arabic*.]
\setcounter{enumi}{10}
  \item \rfrule{D}{D}{DL}{S}
  \item \rfrule{D}{S}{DL}{S}
  \item \rfrule{S}{D}{DS}{VS}
  \item \rfrule{S}{S}{DS}{M}
\end{enumerate}
\begin{enumerate}[label=\arabic*.]
\setcounter{enumi}{14}
  \item \lrrule{D}{D}{DL}{M}
  \item \lrrule{D}{S}{DL}{S}
  \item \lrrule{S}{D}{DL}{VS}
  \item \lrrule{S}{S}{DS}{S}
\end{enumerate}

% given in Table \ref{fuzzy_rule_two_intruders}. The columns under $\textbf{IF}$ describe the premise of each rule and those under $\textbf{THEN}$ denote the consequence of a rule. For example, the 7-$th$ rule in Table \ref{fuzzy_rule_two_intruders} can be described as:
% \begin{enumerate}[label=\arabic*.]
% \setcounter{enumi}{6}
%   \item \lfrule{D}{D}{DL}{S}
% \end{enumerate}


% \begin{table}[!t]
% \caption{Fuzzy Rules for Two Selected Intruders in Two Different Sectors}
% \label{fuzzy_rule_two_intruders}
% \centering
% \begin{tabular}{|c|c|c|c|c|}
% \hline
% \multicolumn{1}{|c|}{\multirow{2}{*}{No.}} & \multicolumn{2}{|c|}{\textbf{IF}} & \multicolumn{2}{c|}{\textbf{THEN}} \\
% \cline{2-5}
%  & $L_{\Delta T^c}$ & $F_{\Delta T^c}$ & $v_c$ & $\Delta \theta$\\
% \hline
% 7 & D&D&DL&S\\
% \hline
% 8 & D&S&DL&VS\\
% \hline
% 9 & S&D&DS&S\\
% \hline
% 10 & S&S&MA&VS\\
% \hline
% \hline
%  & $R_{\Delta T^c}$ & $F_{\Delta T^c}$ & $v_c$ & $\Delta \theta$\\
% \hline
% 11 & D&D&DL&M\\
% \hline
% 12 & D&S&DL&S\\
% \hline
% 13 & S&D&DS&VS\\
% \hline
% 14 & S&S&DS&M\\
% \hline
% \hline
%  & $L_{\Delta T^c}$ & $R_{\Delta T^c}$ & $v_c$ & $\Delta \theta$\\
% \hline
% 15 & D&D&DL&M\\
% \hline
% 16 & D&S&DL&S\\
% \hline
% 17&S&D&DL&VS\\
% \hline
% 18&S&S&DS&S\\
% \hline
% \end{tabular}
% \end{table}

The fuzzy rules obtained in the scenarios where each region contains an intruder are given as follows.
\begin{enumerate}[label=\arabic*.]
\setcounter{enumi}{18}
  \item \allrule{D}{D}{D}{DL}{VL}
  \item \allrule{S}{D}{D}{DL}{L}
  \item \allrule{D}{D}{S}{DL}{L}
  \item \allrule{D}{S}{D}{DL}{M}
  \item \allrule{D}{S}{S}{DL}{M}
  \item \allrule{S}{S}{D}{DL}{M}
  \item \allrule{S}{D}{S}{DL}{VS}
  \item \allrule{S}{S}{S}{DS}{L}
\end{enumerate}

% \begin{table}[!t]
% \caption{Fuzzy Rules for Three Selected Intruders in Three Sectors}
% \label{fuzzy_rule_three_intruders}
% \centering
% \begin{tabular}{|c|c|c|c|c|c|}
% \hline
% \multicolumn{1}{|c|}{\multirow{2}{*}{No.}} & \multicolumn{3}{|c|}{\textbf{IF}} & \multicolumn{2}{c|}{\textbf{THEN}} \\
% \cline{2-6}
% &$L_{\Delta L^c}$ & $F_{\Delta T^c}$& $R_{\Delta T^c}$& $v_c$ & $\Delta \theta$\\
% \hline
% 19&D&D&D&DL&VL\\
% \hline
% 20&S&D&D&DL&L\\
% \hline
% 21& D&D&S&DL&L\\
% \hline
% 22&D&S&D&DL&M\\
% \hline
% 23&D&S&D&DL&M\\
% \hline
% 24&S&S&D&DL&M\\
% \hline
% 25&S&D&S&DL&VS\\
% \hline
% 26&S&S&S&DS&L\\
% \hline
% \end{tabular}
% \end{table}

Finally, we also introduce three fuzzy rules for emergence.
\begin{enumerate}[label=\arabic*.]
\setcounter{enumi}{26}
% \item \lerule{E}{SU}
  \item \lerule{E}{SU}
  \item \ferule{E}{SU}
  \item \rerule{E}{SU}
\end{enumerate}

