In multicriteria group decision-making problems, we need to determine the relative importances among criteria as well as among experts. When doing so, however, we often face the situations where consensuses within experts over different criteria need to be considered, and where uncertainties arise when experts do evaluations. Therefore, we need some special and reasonable methods to generate weights in such situations. In this study, three elaborately devised methods suggest ways to generate relative importance among experts, criteria, and the combination of them, respectively. The first one elicits the consensus extents within experts over different criteria, by which it can generate suitable weights among different criteria. The second one fully considers the uncertain nature when experts do evaluations, and proposes a fuzzy model which can generate weighting vector among experts according to the certainty degrees of valuations given by all the experts. In the last method, when relative importances among both experts and criteria are predetermined in the form of two capacities with dimension n and m, respectively, we find an interesting mechanism to successfully melt them into one nm-dimensional capacity which is based on given cognitive strength and on the proposed concept of compromised active/passive consensus.

中文翻译：

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在多标准群体决策中生成权重和容量的加权模型


在多标准群体决策问题中，我们需要确定标准之间以及专家之间的相对重要性。然而，在这样做时，我们经常面临这样的情况：需要考虑专家内部对不同标准的共识，以及专家评估时出现不确定性。因此，我们需要一些特殊且合理的方法来生成这种情况下的权重。在这项研究中，三种精心设计的方法分别提出了在专家、标准及其组合之间产生相对重要性的方法。第一个是引起专家对不同标准的共识程度，从​​而可以在不同标准之间产生合适的权重。第二个充分考虑了专家评估时的不确定性，提出了一种模糊模型，根据全体专家给出的评估的确定性程度，生成专家间的权重向量。在最后一种方法中，当专家和标准之间的相对重要性分别以维度为 n 和 m 的两种能力的形式预先确定时，我们发现了一种有趣的机制，可以成功地将它们融合为一个基于给定认知的纳米维能力。强度以及所提出的妥协主动/被动共识的概念。