基于Choquet积分的层次多属性决策方法研究

New Method for Hierarchical Multiple Criteria Decision Making Based on Choquet Integral

为了解决贫信息情形下基于关联的复杂系统决策问题,本文提出一种基于Choquet积分的层次多属性决策方法。该方法首先通过判断矩阵求解决策属性的Shapley值,然后通过Marichal熵理论计算属性和属性集的重要程度,最后通过Choquet积分自下而上计算方案的综合评价值并以此对方案进行排序。最后的算例验证了新方法的合理性和可行性。新方法中属性和属性集权重的确定仅需Shapley值的判断矩阵信息,故大大降低了决策者的工作量。此外,新方法也可用于对属性间相互独立的多属性决策分析问题求解。

The new method of hierarchy multiple criteria decision making is proposed based on Choquet integral. In the new method, Shapley values of decision-making criteria are obtained based on the judgement matrix, fuzzy measures of criteria and their coalitions are calculated by Marichal entropy theory, and synthetical values of alternatives are calculated according to Choquet integral from bottom to top. Finally, an example is given to verify the new method. The method can be applied to practice easily since it can determine the weightes of the criteria and their coalition with the judgement matrix of the Shapley value, thus decreasing the workload of decision maker. Furthermore, the method can also be applied to the problem of multiple criteria decision making and the criteria are independent.