We investigate a negotiation model for the progressive aggregation of interacting multicriteria evaluations. The model is based on a network of interacting criteria and combines the Choquet aggregation framework with the classical DeGroot’s model of consensus linear dynamics. We consider a set $$N = \{ 1,\ldots ,n \}$$ N = { 1 , … , n } of interacting criteria whose single evaluations are expressed in some domain $${\mathbb {D}}\subseteq {\mathbb {R}}$$ D ⊆ R . The pairwise interaction among the criteria is described by a complete graph with edge values in the open unit interval. In the Choquet framework, the interacting network structure is the basis for the construction of a consensus capacity $$\mu $$ μ , whose Shapley indices are proportional to the average degree of interaction between criterion $$i \in N $$ i ∈ N and the remaining criteria $$j \ne i \in N $$ j ≠ i ∈ N . We discuss three types of linear consensus dynamics, each of which represents a progressive aggregation process towards a consensual multicriteria evaluation corresponding to some form of mean of the original multicriteria evaluations. All three models refer significantly to the notion of multicriteria context evaluation. In one model, the progressive aggregation converges simply to the plain mean of the original multicriteria evaluations, while another model converges to the Shapley mean of those original multicriteria evaluations. The third model, instead, converges to an emphasized form of Shapley mean, which we call superShapley mean. The interesting relation between Shapley and superShapley aggregation is investigated.

中文翻译：

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Shapley和superShapley聚合来自多准则Choquet框架中的共识动力学

我们调查一种协商模型，用于逐步进行交互的多标准评估聚合。该模型基于相互作用标准的网络，并将Choquet聚合框架与经典DeGroot的共识线性动力学模型相结合。我们考虑一组交互标准的$$ N = \ {1，\ ldots，n \} $$ N = {1，…，n}，其单个评估值在某些域中表示。$$ {\ mathbb {D}} \子集{\ mathbb {R}} $$ D⊆R。准则之间的成对交互作用由一个完整的图来描述，该图在开放单位间隔中具有边值。在Choquet框架中，相互作用的网络结构是构建共识容量$$ \ mu $$μ的基础，其Shapley指数与标准$$ i \ in N $$ i∈N和其余标准$$ j \ ne i \ in N $$ j≠i∈N之间的平均相互作用程度成正比。我们讨论了三种类型的线性共识动态，每种都代表朝着共识多准则评估的渐进聚合过程，该评估与原始多准则评估的某种形式的均值相对应。所有这三个模型都显着涉及多准则上下文评估的概念。在一个模型中，渐进聚合简单地收敛到原始多标准评估的简单平均值，而另一种模型收敛到那些原始多标准评估的Shapley平均值。相反，第三个模型收敛到Shapley均值的强调形式，我们称其为superShapley均值。