基于损失函数的相似性和相异性的鲁棒分级分类方法及改进的卡片组法
A robust hierarchical nominal classification method based on similarity and dissimilarity using loss function and an improved version of the deck of cards method
摘要：
Cat-SD是一种用于处理名词分类问题的多准则决策辅助方法。行动根据多个标准进行评估，并分配到一个或多个类别。一组引用操作用于定义每个类别。将一个动作分配到给定的类别取决于根据相似性阈值将该动作与每个参考集进行比较。可以为每个类别定义不同的标准权重、交互系数和相似性阈值。我们建议将多准则层次过程（MCHP）应用于Cat-SD。一个适应MCHP建议考虑到可能的相互作用的影响，在层次结构的方式构造的标准之间。在已知的卡片组方法的基础上，我们还考虑了允许考虑标准之间的相互作用和对抗效应的参数的不精确的启发。我们提出的启发过程可以应用于任何Electre方法。为了探索由Cat-SD考虑可能的参数集获得的分配，我们建议应用随机多标准可接受性分析（SMAA）。SMAA方法允许得出关于行动分类的统计结论。所提出的方法，SMAA-hCat-SD，帮助决策者检查在不同层次的分类参数的变化的影响。我们还提出了一个程序，损失函数的概念的基础上，获得一个最终的分类满足决策者给出的一些要求，并考虑到层次的标准和概率分配应用SMAA。此程序也可适用于任何分类的Electre方法。
英文摘要：
Cat-SD is a multiple criteria decision aiding method for dealing with nominal classification problems. Actions are assessed according to multiple criteria and assigned to one or more categories. A set of reference actions is used for defining each category. The assignment of an action to a given category depends on the comparison of the action to each reference set according to likeness thresholds. Distinct sets of criteria weights, interaction coefficients, and likeness thresholds can be defined per category. We propose to apply Multiple Criteria Hierarchy Process (MCHP) to Cat-SD. An adapted MCHP is proposed to take into account possible interaction effects between criteria structured in a hierarchical way. On the basis of the known deck of cards method, we also consider an imprecise elicitation of parameters permitting to take into account interactions and antagonistic effects between criteria. The elicitation procedure we are proposing can be applied to any Electre method. With the purpose of exploring the assignments obtained by Cat-SD considering possible sets of parameters, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA). The SMAA methodology allows to draw statistical conclusions on the classification of the actions. The proposed method, SMAA-hCat-SD, helps the decision maker to check the effects of the variation of parameters on the classification at different levels of the hierarchy. We propose also a procedure, based on the concept of loss function, to obtain a final classification fulfilling some requirements given by the decision maker and taking into account the hierarchy of criteria and the probabilistic assignments obtained applying SMAA. Also this procedure can be applied to any classification Electre method.
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