We characterize those operators that satisfy the properties of monotonicity, permutation invariance, positive homogeneity, and translation invariance. As these operators do not necessarily satisfy comonotonic additivity, their class is larger than that of ordered weighted averaging (OWA) operators. We give a representation theorem for these operators, which shows, nonetheless, that this more general class can be constructed directly from that of OWA operators. In addition, we characterize the special classes consisting of operators that are either subadditive or superadditive. We suggest applications to the evaluation of complex systems.

中文翻译：

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Mm-OWA：OWA 算子的概括

我们描述了那些满足单调性、置换不变性、正同质性和平移不变性的算子。由于这些算子不一定满足共调可加性，因此它们的类别大于有序加权平均 (OWA) 算子的类别。我们给出了这些算子的表示定理，尽管如此，它表明这个更一般的类可以直接从 OWA 算子的类中构造出来。此外，我们描述了由子可加性或超可加性运算符组成的特殊类。我们建议应用到复杂系统的评估中。