## 6 Comprehensive Analysis Based on the FAEWM
### Determination of Factor Weights Based on the Entropy Method  
The entropy value can be utilized to assess the degree of dispersion of a specific index. A smaller information entropy value indicates a higher degree of dispersion for the index, resulting in a greater weight assigned to the index in the overall evaluation. Employing information entropy to calculate each index's weight provides a foundation for the comprehensive evaluation of multiple indexes. The flowchart of the EWM is shown in Figure 9.  
The detailed calculation steps are as follows.  
Step 1: Construct the evaluation matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Principal Ingredient 1** & **Principal Ingredient 2** & **Principal Ingredient 3** \\ \hline Scheme 1 & 60.305\% & 25.819\% & 13.876\% \\ Scheme 2 & 62.929\% & 23.299\% & 13.772\% \\ Scheme 3 & 62.773\% & 23.457\% & 13.771\% \\ Scheme 4 & 53.998\% & 26.27\% & 19.732\% \\ \hline \end{tabular}
\end{table}
Table 20: Factor weighting results.  
Figure 9: Flowchart of the EWM.  
The results of the eight indexes of the four schemes under 45 traffic conditions were formed into a matrix, as shown in (16).  
\[X_{o}=\left[D_{op},T_{op},E_{op},F_{op},C_{op},TTC_{op},PET_{op},CSI_{op}\right] \tag{16}\]  
where \(o\) denotes the design schemes number; \(p\) denotes the combination of traffic conditions, \(p\) = 1 to 45; \(D\) denotes delay; \(T\) denotes travel time; \(E\) denotes CO emissions; \(F\) denotes fuel consumption; and \(C\) denotes the number of conflicts.  
The simulation results of Scheme 1 are represented as a matrix of 8 columns and 45 rows (refer to (17)).  
\[X_{1}=\left[D_{1p},T_{1p},E_{1p},F_{1p},C_{1p},TTC_{1p},PET_{1p},CSI_{1p}\right] \tag{17}\]  
Among  
\[D_{1p}=\left[D_{1,1},D_{1,2},\cdots,D_{1,45}\right]^{T} \tag{18}\]  
In order to evaluate the results of the evaluation indexes of the four schemes under the same traffic combinations, the matrix of the four schemes was decomposed and reorganized to obtain the matrix \(A_{S}\), shown in (19).  
\[A_{s}=\left[\begin{array}{c}X_{1}(s,\cdot)\\ X_{2}(s,\cdot)\\ X_{3}(s,\cdot)\\ X_{4}(s,\cdot)\\ \end{array}\right] \tag{19}\]  
where \(X_{1}(s,\cdot)\) denotes the sth row of \(X_{1}\), i.e., the results of the eight indexes under the sth traffic combination.  
Denote each element in matrix \(A_{S}\) by \(y_{pq}\) to obtain the new matrix \(Y\) (refer to (20)).  
\[Y=\begin{bmatrix}y_{11}&y_{12}&\cdots&y_{1q}\\ y_{21}&y_{22}&\cdots&y_{2q}\\ \vdots&\vdots&\vdots&\vdots\\ y_{p1}&y_{p2}&\cdots&y_{pq}\\ \end{bmatrix} \tag{20}\]  
where \(p\) denotes the number of schemes, \(p\) = 1 to 4, and \(q\) denotes the number of indexes, \(q\) = 1 to 8.  
Step 2: Calculate the contribution of the \(q\)th evaluation index in the \(p\)th program.  
\[p_{pq}=\frac{y_{pq}}{\frac{\sum\limits_{p}y_{pq}}{p}} \tag{21}\]  
Step 3: Calculate the entropy value of the \(q\)th evaluation index.  
\[e_{q}=-\frac{1}{\ln(n)}{\sum\limits_{p}^{n}p_{pq}\ln(p_{pq})} \tag{22}\]  
Step 4: Calculate the coefficient of variation.  
\[d_{q}=1-e_{q} \tag{23}\]  
Step 5: Calculate the weight of each evaluation index.  
\[w_{q}=\frac{d_{q}}{\frac{n}{q}d_{q}} \tag{24}\]