## 1 Introduction  
In the contemporary epoch, with the rapid development of e-commerce, the number of e-commerce logistics enterprises of forest products continues to grow, and the market competition is also increasingly fierce. In order to effectively deal with such a competitive situation and effectively avoid market risks, e-commerce logistics enterprises of forest products must pay more attention to improve their competitiveness [1, 2, 3]. The establishment of an e-commerce logistics alliance [4] and the implementation of joint transportation have transmuted into an efficacious strategy. Within an e-commerce logistics alliance of forest products, the profitability of the alliance is affected by a number of factors, including transportation vehicles, freight volume, fuel prices, transportation distance, and customer satisfaction. A fair and reasonable distribution of alliance profits is essential to ensure the long-term stable development of alliances. In academic research, the matters of profit allocation [5; 6] and cost sharing [7; 8] within e-commerce logistics alliances of forest products have been encompassed within the domain of cooperative game theory. Theoretically, numerous renowned solutions of cooperative games, such as the Shapley value [9] and the Banzhaf value [10], can be utilized to redress these problems. However, these classical solutions are mainly applicable to exact contexts and have limited effectiveness in dealing with problems in fuzzy contexts. In addition, the classical Shapley value is mainly based on the marginal contribution of the players and ignores the satisfaction of the players in making profit allocation; thus, it is not comprehensive and effective in making profit allocation. Forest products e-commerce enterprises usually use container transportation in the export process. However, the mismatch between the type of container vehicles and the freight volume and the incompatibility of business models have resulted in a high rate of empty containers and a low utilization rate. This in turn affects the profits of e-commerce logistics enterprises of forest products, leading to a generally low level. Therefore, many e-commerce logistics enterprises of forest products tend to form logistics alliances [11; 12; 13] for common transportation to reduce transportation costs and increase profits. Nevertheless, in order to realize the long-term and stable development of the alliance, it is of vital importance to distribute alliance profit fairly and equitably. In order to realize the long-term stable development of alliances and solve the problem of unfair profit allocation of alliances, this paper proposes a method of improved Shapley value with trapezoidal fuzzy numbers [14]. The method not only satisfies the important properties of classical Shapley value, such as existence, efficiency, additivity, and symmetry, but it also provides a more reasonable profit allocation scheme with full consideration of player satisfaction. This paper makes at least the following three contributions to the field of cooperative game:  
1. This paper takes into account the dissatisfaction of the players in the game when utilizing the Shapley value for profit allocation. The least square contribution is used to replace the marginal contribution of the classical Shapley value, which makes the profit allocation more reasonable;
2. In the calculation of the efficiency of the improved Shapley value, instead of simply distributing the difference between the sum of the initial distribution of profits of the players in the innings and the profits of the grand alliance equally to each player, this paper takes into account the profits made by the individual players when they strike out alone and makes a more reasonable secondary distribution accordingly;
3. In this paper, trapezoidal fuzzy numbers are introduced to further optimize the improved Shapley value so that it has wider applicability in dealing with fuzzy numbers, breaking through the limitation that the classical Shapley value has with fuzzy numbers.