Consensus Reaching Processes (CRPs) deal with those group decision-making situations in which conflicts among experts' opinions make difficult the reaching of an agreed solution. This situation, worsens in large-scale group decision situations, in which opinions tend to be more polarized, because in problems with extreme opinions it is harder to reach an agreement. Several studies have shown that experts' preferences may not always follow a linear scale, as it has commonly been assumed in previous CRP. Therefore, the main aim of this paper is to study the effect of modeling this nonlinear behavior of experts' preferences (expressed by fuzzy preference relations) in CRPs. To do that, the experts' preferences will be remapped by using nonlinear deformations which amplify or reduce the distance between the extreme values. We introduce such automorphisms to remap the preferences as Extreme Values Amplifications (EVAs) and Extreme Values Reductions (EVRs), study their main properties and propose several families of these EVA and EVR functions. An analysis about the behavior of EVAs and EVRs when are implemented in a generic consensus model is then developed. Finally, an illustrative experiment to study the performance of different families of EVAs in CRPs is provided.

中文翻译：

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群体决策中的非线性偏好。极值放大和极值减少

达成共识的过程 (CRP) 处理那些专家意见之间的冲突导致难以达成一致解决方案的群体决策情况。这种情况在大规模群体决策情况下会恶化，在这种情况下，意见往往更加两极分化，因为在意见极端的问题中，很难达成一致。几项研究表明，专家的偏好可能并不总是遵循线性标度，因为它通常在以前的 CRP 中被假设。因此，本文的主要目的是研究在 CRP 中对专家偏好（由模糊偏好关系表示）的这种非线性行为进行建模的效果。为此，将通过使用非线性变形来重新映射专家的偏好，从而放大或缩小极值之间的距离。我们引入了这样的自同构来重新映射作为极值放大 (EVA) 和极值减少 (EVR) 的偏好，研究它们的主要属性并提出了这些 EVA 和 EVR 函数的几个系列。然后对在通用共识模型中实施时 EVA 和 EVR 的行为进行分析。最后，提供了一个说明性实验来研究不同系列的 EVA 在 CRP 中的性能。