Choquet积分偏好模型与规模作图题的随机多目标可接受性分析
Stochastic Multiobjective Acceptability Analysis for the Choquet integral preference model and the scale construction problem
摘要：
Choquet积分是多准则决策辅助（MCDA）中用于处理准则之间相互作用的偏好模型。随机多目标可接受性分析（SMAA）是一种MCDA方法，用于考虑手头问题的不精确性或缺乏数据。例如，SMAA允许计算一个替代方案在整个可接受的偏好参数空间中排名第k的频率，例如，在通过加权和模型聚合对所考虑的标准的评估的情况下，在与决策者（DM）提供的偏好信息兼容的权重空间中。在本文中，我们建议将SMAA方法与Choquet积分偏好模型相结合，以获得强大的建议，同时考虑到整个空间的偏好参数与DM的偏好信息兼容。在一个共同的尺度上的所有标准的替代品进行评估的情况下，偏好参数给出的能力表示的非加性的权重，代表的重要性标准和它们的相互作用。如果这些标准在不同的尺度上进行评估，除了能力之外，偏好参数还包括共同尺度，在该共同尺度上对标准的评估必须被重新编码以进行比较。我们的方法允许探索整个空间的偏好参数的能力和共同的规模与DM的偏好信息兼容。
英文摘要：
The Choquet integral is a preference model used in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria. The Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology used to take into account imprecision or lack of data in the problem at hand. For example, SMAA permits to compute the frequency that an alternative takes the k-th rank in the whole space of the admissible preference parameters, e.g. in case evaluations on the considered criteria are aggregated through the weighted sum model, in the space of weights compatible with the preference information supplied by the Decision Maker (DM). In this paper, we propose to integrate the SMAA methodology with the Choquet integral preference model in order to get robust recommendations taking into account the whole space of preference parameters compatible with the DM's preference information. In case the alternatives are evaluated by all the criteria on a common scale, the preference parameters are given by the capacity expressing the non-additive weights, representing the importance of criteria and their interaction. If the criteria are instead evaluated on different scales, besides the capacity, preference parameters include the common scale on which the evaluations of criteria have to be recoded to be compared. Our approach permits to explore the whole space of preference parameters being capacities and common scales compatible with the DM's preference information.
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