Inspired by the real needs of group decision problems, aggregation of ordered weighted averaging (OWA) operators is studied and discussed. Our results can be applied for data acting on any real interval, such as the standard scales [0, 1] and [0, ∞[ , bipolar scales [-1, 1] and R =] - ∞, ∞[ , etc. A direct aggregation is shown to be rather restrictive, allowing the convex combinations to be considered only, except the case of dimension n = 2. More general is the approach based on the aggregation of related cumulative weighting vectors. The piecewise linearity of OWA operators allows us to consider bilinear forms of aggregation of related weighting vectors. Several interesting examples yielding the link between the aggregation of OWA operators and the related ANDness and ORness measures are also included. Some possible applications and generalizations of our results are also discussed.

中文翻译：

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OWA算子聚合


受群决策问题实际需求的启发，对有序加权平均（OWA）算子的聚合进行了研究和讨论。我们的结果可以应用于作用于任何实区间的数据，例如标准尺度 [0, 1] 和 [0, ∞[ ，双极尺度 [-1, 1] 和 R =] - ∞, ∞[ 等。直接聚合被证明是相当有限制的，只允许考虑凸组合，除了维度 n = 2 的情况。更一般的是基于相关累积权重向量聚合的方法。 OWA 算子的分段线性使我们能够考虑相关权重向量聚合的双线性形式。还包括几个有趣的示例，这些示例产生了 OWA 运算符聚合与相关 ANDness 和 ORness 度量之间的联系。还讨论了我们的结果的一些可能的应用和概括。