英文标题：
《Choquet integral in decision analysis - lessons from the axiomatization》
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作者：
Mikhail Timonin
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最新提交年份：
2016
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英文摘要：
  The Choquet integral is a powerful aggregation operator which lists many well-known models as its special cases. We look at these special cases and provide their axiomatic analysis. In cases where an axiomatization has been previously given in the literature, we connect the existing results with the framework that we have developed. Next we turn to the question of learning, which is especially important for the practical applications of the model. So far, learning of the Choquet integral has been mostly confined to the learning of the capacity. Such an approach requires making a powerful assumption that all dimensions (e.g. criteria) are evaluated on the same scale, which is rarely justified in practice. Too often categorical data is given arbitrary numerical labels (e.g. AHP), and numerical data is considered cardinally and ordinally commensurate, sometimes after a simple normalization. Such approaches clearly lack scientific rigour, and yet they are commonly seen in all kinds of applications. We discuss the pros and cons of making such an assumption and look at the consequences which axiomatization uniqueness results have for the learning problems. Finally, we review some of the applications of the Choquet integral in decision analysis. Apart from MCDA, which is the main area of interest for our results, we also discuss how the model can be interpreted in the social choice context. We look in detail at the state-dependent utility, and show how comonotonicity, central to the previous axiomatizations, actually implies state-independency in the Choquet integral model. We also discuss the conditions required to have a meaningful state-dependent utility representation and show the novelty of our results compared to the previous methods of building state-dependent models.
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中文摘要：
Choquet积分是一种强大的聚合算子，它列出了许多著名的模型作为其特例。我们研究这些特殊情况，并提供它们的公理分析。在文献中已经给出公理化的情况下，我们将现有结果与我们开发的框架联系起来。接下来，我们将讨论学习问题，这对于模型的实际应用尤其重要。迄今为止，Choquet积分的学习主要局限于能力的学习。这种方法需要做出一个强有力的假设，即所有维度（例如标准）都是在同一个尺度上进行评估的，这在实践中很少是合理的。分类数据常常被赋予任意的数字标签（如AHP），数字数据被认为是基本和顺序相称的，有时在简单的标准化之后。这种方法显然缺乏科学严谨性，但在各种应用中都很常见。我们讨论了做出这样一个假设的利弊，并考察了公理化唯一性结果对学习问题的影响。最后，我们回顾了Choquet积分在决策分析中的一些应用。除了MCDA（这是我们研究结果的主要兴趣领域）之外，我们还讨论了如何在社会选择背景下解释该模型。我们详细研究了依赖于状态的效用，并展示了在Choquet积分模型中，作为先前公理化核心的共单调性实际上是如何暗示状态独立的。我们还讨论了具有有意义的状态相关效用表示所需的条件，并显示了我们的结果与以前构建状态相关模型的方法相比的新颖性。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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