## 3 Methodology
### Decision of the Optimal Solution Based on the Coalitional Game Model  
Within the context of this study, the coalitional game model is a multi-objective cooperative game model that is used to analyze design preferences and internal relationships in CV and economic objectives. In this section, the coalitional game model will be used to analyze the coalitional utility of CV and economic objectives in different solutions. The Shapley value will then be adopted to obtain a fair allocation of utilities, to ensure that none of the players (objectives) will try to leave the coalition. Furthermore, the Shapley value of each objective is a fair payoff, which considers the interactions between all objectives in calculating the optimal payoff that maximizes coalitional utility. The Shapley values were obtained via the following procedure:  
Step 1. Construction of the coalition game: Firstly, one must define the players, strategies, and utility of the coalition game model. The model is expressed as \(G=\{P_{c};\,S_{c};\,U_{c}\}\), \(c\in\) P, E, while the CV and economic objectives are projected as players P\({}_{p}\) and P\({}_{E}\), respectively. The strategy of P\({}_{p}\) is \(S_{p}\)(CS\({}_{i}\)) = {P\({}_{1}\)(CS\({}_{j}\)),..., P\({}_{M}\)(CS\({}_{i}\))}, where \(M\) denotes the number of CV criteria, respectively. Similarly, the strategy of P\({}_{E}\) is \(S_{E}\)(CS\({}_{j}\)) = {P\({}_{1}\)(CS\({}_{i}\)),..., P\({}_{N}\)(CS\({}_{i}\))}, where \(N\) denotes the number of economic criteria. Because each conceptual solution corresponds to the strategy sets of a pair of players, \(S=\left(S_{p}\)(CS\({}_{i}\)), \(S_{E}\)(CS\({}_{j}\))), if one selects some strategy set such as CS\({}_{i}\), the player utilities are \(U_{\rm{P}}\)(\(S_{p}\)(CS\({}_{i}\)), \(S_{E}\)(CS\({}_{i}\))), and \(U_{\rm{E}}\)(\(S_{p}\)(CS\({}_{i}\)), \(S_{E}\)(CS\({}_{j}\))). Therefore, once a strategy has been determined for one player, the strategy of the other player is also determined. However, because the solution values of P\({}_{P}\) and P\({}_{E}\) in each evaluation criterion are different, any change in the strategy of P\({}_{p}\) will inevitably affect the designed expectation of P\({}_{E}\), thereby changing the overall designed expectation of the solution. The conflict of interest between P\({}_{p}\) and P\({}_{E}\) must be balanced by selecting the strategy set that best satisfies the design expectations of both players, i.e., the optimal conceptual solution. Step 2. Calculation of player utilities: Given that each strategy set (\(S_{p}\)(CS\({}_{i}\)), \(S_{E}\)(CS\({}_{i}\))) corresponds to a conceptual solution, the player utilities reflect the expected value of each solution for a given strategy. Because each solution represents an attempt by the designer to balance the design requirements of the PSS, the evaluations of the solutions will exhibit conflicts or dependencies with each other, and the utility of one player will inevitably influence that of the other. The objective of the coalitional game is to determine the optimal allocation of utilities to CV and economic objectives, despite their mutual antagonism, to maximize the overall utility of the solution. After the strategy (CS\({}_{i}\)) has been determined, it is necessary to consider the effects of the evaluation criteria (which have different weights) on player utility under the selected strategy set, and then objectively compute the utility of each player. First, the criteria weights (Equation (8)) are adopted to transform the solution's normalized rough values in CV and economic objectives into crisp values \(r^{{}^{\prime}}_{ij}\) (\(\alpha=0.5\)). The weights are then applied to obtain the actual utilities of the players. To ensure that the utilities are expressed in a consistent, comparable and intuitive manner, the actual utilities of each player are averaged by their number of criteria. Finally, the relative average of all criteria relative to the average utility is considered the utility of the CV and economic objectives, as expressed in Equations (14) and (15).