ABSTRACT Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in . The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.

中文翻译：

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实 m 维区间值 OWA 算子的 Orness 及其在确定良好分区中的应用

摘要 有序加权平均 (OWA) 运算符是一类应用广泛的平均聚合函数，即始终产生输入的最小值和最大值之间的值的运算符。引入了 orness 度量以根据权重向量对 OWA 算子的行为进行分类。当我们处理在更复杂的空间（例如间隔或格子）上定义的 OWA 算子时，定义合适的 orness 度量是一项艰巨的任务。在这项工作中，我们为 orness 度量提出了一个合适的定义，以对定义在 m 维区间集上的 OWA 算子进行分类，其中的实际值取 。Orness 度量用于确定哪个是连续范围的最佳划分，该范围应划分为四个语言标签。这个例子显示了提议的 orness 度量的良好行为。