多属性决策的关键问题是确定属性的合理权重，考虑到主观赋权和客观赋权各有优点，本文重点对主客观权重的组合方式及其合理性判别进行研究。首先，提出了一种新的主客观组合赋权方法，根据属性权重所传递的信息，将属性权重信息分解为"序信息"和"强度信息"，并对主客观权重的"序信息"和"强度信息"进行了对比和分析，提出了组合权重在兼顾主客观权重的"序信息"和"强度信息"上的原则，为组合赋权优化模型的建立奠定了基础；二是以组合权重与客观权重的偏离最小为目标函数，以与主观权重排序的偏离最小为约束建立组合赋权优化模型，求解主客观组合权重，保证了属性权重对"序信息"和"强度信息"的兼顾性；三是通过一个算例验证了组合权重的合理性和可解释性，通过银行效率评价的实例验证了组合赋权的可行性。本文建立的兼顾序信息和强度信息的主客观组合赋权模型，是在主客观权重信息分解的基础上，从单一属性层面对主客观权重进行组合，组合方式更为灵活，且保证了组合权重的可解释性，为多属性决策的赋权提供了新的思路和参考。
The key issue of multi-attribute decision making is to determine the reasonable weights of the attributes. Considering the different advantages of the subjective weighting methods and the objective weighting methods, focus is put on studying the combination of Subjective-Objective weighting and its rationality. Firstly, according to the information conveyed by the attribute weights, a method is put forward to decompose the attribute weight information into the "ordered information" and "intensity information",The "ordered information" and "intensity information" of Subjective-Objective weights are then compared and analyzed.Furthermore, the principle of combined weights on balancing "ordered information" and "intensity information" which laid the foundation for an optimization model of the combination weighting is put forward. Secondly, an optimization model of the combined weighting method is established to find the Subjective-Objective weighting. The objective function is to minimize the deviation between the combination weight and the objective weight, the constraint is to minimize the deviation of the sequence between the combined weight and the subjective weight which balance the "ordered information" and "intensity information" of the attribute weight. Finally, the validity and the interpretability of the model is verified by an example and the feasibility of the combined weighting method is verified by an example of efficiency evaluation in a bank. Based on the decomposition of subjective and objective weight information, a combination weighting model, which balances "ordered information" and "intensity information" from a single attribute level is established. The combination is more flexible and ensures the compatibility and interpretability. It provides new ideas and references for the empowerment of multi-attribute decision-making.
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