Abstract Observe that for continuous, strictly increasing binary means defined on a unit interval, autodistributivity and bisymmetry are equivalent. Bisymmetric aggregation operations defined on finite linearly ordered scales have been studied in the past, and their behavior is unlike that of corresponding operations defined on the unit interval [ 0 , 1 ] . This paper investigates two families of autodistributive aggregation operations defined on finite linearly ordered scales: one with a neutral element and the other under some partial smoothness-related conditions. The former is fully described as the family of idempotent uninorms and the latter is completely characterized as the family of idempotent t-operators. Through these results, we can deduce that compared with bisymmetry, autodistributivity is much stronger, and the behavior of autodistributive aggregation operations defined on finite linearly ordered scales is significantly different from that of corresponding operations defined on [ 0 , 1 ] .

中文翻译：

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表征在有限线性有序尺度上定义的自动分布聚合操作

摘要 观察到，对于定义在单位区间上的连续、严格递增的二元均值，自分配性和双对称性是等价的。过去已经研究过定义在有限线性有序尺度上的双对称聚合运算，它们的行为不同于定义在单位区间 [ 0 , 1 ] 上的相应运算。本文研究了在有限线性有序尺度上定义的两类自动分布聚合操作：一种具有中性元素，另一种在某些部分平滑相关的条件下。前者被完全描述为幂等单范式家族，而后者被完全描述为幂等 t 运算符家族。通过这些结果，我们可以推断出，与双对称性相比，自分配性要强得多，