## 5 Analysis of Calculation Examples
### Calculation of Profit Allocation in the Case of E-Commerce Logistics Alliance of Forest Products  
From Tables 3 and 4, it can be concluded that when the three forest product e-commerce logistics enterprises form a grand alliance for transportation, the profit \(\widetilde{v}_{ABC}=\) [4442, 4778, 5023, 5279]  
Figure 5: The changing trends of the total cost and the total profit under different alliance structures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Enterprise** & & & \\
**Alliance** & **Quote (CNY)** & **Cost (CNY)** & **Profit (CNY)** \\ \hline
[A] & 3252 & [2416, 2535, 2650, 2809] & [443, 602, 717, 836] \\
[B] & 3447 & [2444, 2565, 2681, 2842] & [605, 766, 882, 1003] \\
[C] & 3690 & [2465, 2586, 2703, 2865] & [825, 987, 1104, 1225] \\
[AB] & 6699 & [4676, 4895, 5106, 5397] & [1302, 1593, 1804, 2023] \\
[AC] & 6942 & [4697, 4917, 5129, 5421] & [1521, 1813, 2025, 2245] \\
[BC] & 7137 & [4726, 4947, 5161, 5455] & [1682, 1976, 2190, 2411] \\
[ABC] & 10,389 & [5110, 5366, 5611, 5947] & [4442, 4778, 5023, 5279] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Costs and profits of e-commerce logistics enterprises of forest products under different alliance forms. is much larger than the sum of the profits \(\widetilde{v}_{A}+\widetilde{v}_{B}+\widetilde{v}_{C}=\left[1873,2354,2702,3064\right]\) when the three forest product e-commerce logistics enterprises operate independently. Moreover, the profits gained by any sub-alliance plus the profits of the enterprises that are not participating in the alliance when they operate alone are all smaller than the total profit of the grand alliance, which meets the conditions for the establishment of an alliance; thus, we calculate the profit allocated to each e-commerce logistics enterprise of forest products in the common transportation. Next, the marginal contribution of the classical Shapley value is replaced by the calculated least square contribution of the trapezoidal fuzzy numbers \(\alpha\)-cut set, and the profit of each e-commerce logistics of forest products company is calculated, as shown in Table 6.  
It is evident from Table 6 that the improved Shapley value with the trapezoidal fuzzy number proposed in this paper satisfies the individual rationality and overall rationality. Specifically, the profit [1146, 1293, 1392, 1491] of e-commerce logistics Enterprise A after joining the grand alliance is significantly higher than the profit [443; 602; 717; 836] before joining. And for any two e-commerce logistics enterprises of forest products, the sum of the profits obtained after joining the grand alliance exceeds the sum of the profits of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Enterprise** & **Profit (CNY)** \\ \hline A & [1146, 1293, 1392, 1491] \\ B & [1445, 1562, 1646, 1733] \\ C & [1851; 1923, 1985, 2055] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Final profit of each enterprise in the e-commerce logistics alliance of forest products. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Enterprise** & **Profit Before Cooperation** & **Profit After Cooperation** & **Super-** & **Whether to Form** \\
**Alliance** & **(CNY)** & **(CNY)** & **Additivity** & **an Alliance** \\ \hline \{AB\} & [1048; 1368; 1599; 1839] & [1302; 1593; 1804; 2023] & Yes & Yes \\ \{AC\} & [1268; 1589; 1820; 2061] & [1521; 1813; 2025; 2245] & Yes & Yes \\ \{BC\} & [1430; 1752; 1986; 2228] & [1682; 1976; 2190; 2411] & Yes & Yes \\ \{ABC\} & [1873, 2354, 2702, 3064] & [4442; 4778; 5023; 5279] & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Profits of e-commerce logistics enterprises of forest products before and after cooperation under different alliance forms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
eg*\) \(\widetilde{x}_{i}\left(\mathcal{S}\right)\) & **Enterprise** & **Alliance** & \(\
eg*\) \(\widetilde{x}_{i}\left(\mathcal{S}\right)\) \\ \hline A & A & [443; 602, 717; 836] & B & B & [605; 766, 882, 1003] & C & C & [825, 987, 1104, 1225] \\ A & AB & [570;  
sub-alliance formed by them independently.