## 5 Discussion  
This study's key insight is the significant advantage of integrating the AHP/ANP with Shapley values in complex decision-making, particularly where the criteria and alternatives are interdependent. The numerical example of urban planning demonstrates this method's practicality, highlighting how different rankings between the AHP/ANP and Shapley value methods emphasize the need to consider cooperative alternatives. The Shapley values enhance decision-making by providing a holistic assessment and acknowledging each alternative's contribution in a cooperative scenario. This method's versatility extends its application to various contexts, offering a comprehensive tool for complex decision-making challenges. In both the AHP and ANP cases, we can observe the rank reversal situation, which occurs when the introduction of a new factor (in this case, the Shapley values) alters the relative preferences among the alternatives. The rank reversal in our example highlights the importance of considering the cooperative nature of the alternatives. While the AHP/ANP focuses on the individual performance of each alternative based on the criteria, our proposed method takes into account the potential synergies and complementarities that may arise when the alternatives form coalitions. The integration of Shapley values reveals that the subway alternative contributed more to the overall performance of the transportation system when considering its cooperative potential. This insight led to a higher ranking for subway compared to the conventional AHP, where it was ranked second. This example demonstrates the value of our proposed method in addressing the limitations of the conventional AHP and providing decision-makers with a more realistic and equitable assessment of the alternatives. The rank reversal problem, in this case, is not a flaw but rather a strength of our method, as it incorporates relevant factors that were previously overlooked, leading to a more informed and socially responsible decision-making process. Compared to traditional MCDM algorithms, such as the AHP, the ANP, TOPSIS, and DEMATEL, our proposed approach offers several distinct advantages:  
1. Consideration of cooperative alternatives: While most MCDM algorithms focus on evaluating alternatives based on their individual merits, our method integrates Shapley values to capture the cooperative dynamics among the alternatives. This allows decision-makers to account for the synergistic or hindering effects that may arise when the alternatives form coalitions, providing a more realistic and comprehensive assessment of their performance. 2. Equitable resource allocation: By incorporating Shapley values, our approach ensures a fair distribution of resources among the alternatives based on their marginal contributions to coalitions. This is particularly important in resource allocation problems, where the goal is to optimize the overall performance of the system while ensuring that each alternative receives its due share of resources. 3. Flexibility in handling interdependence: Our method is capable of addressing both independent and interdependent criteria and alternatives, thanks to the integration of the AHP/ANP with Shapley values. This flexibility allows decision-makers to model complex decision problems more accurately, capturing the intricate relationships among the criteria and alternatives that may be overlooked by other MCDM algorithms. 4. Robustness in decision-making: The combination of the AHP/ANP and Shapley values provides a robust framework for decision-making, as it leverages the strengths of both approaches. The AHP/ANP helps in structuring the problem and eliciting expert judgments, while Shapley values introduce the concept of fairness and cooperation into the evaluation process. This dual perspective enhances the reliability and acceptability of the decision outcomes. 5.